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ECO 501 Advanced Microeconomics IV 2 Units

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UNIVERSITY OF MAIDUGURICENTRE FOR DISTANCE LEARNING

ECO 501: Advanced Microeconomics IV (2 Units)

Course Facilitator: Dr. M. O. Lawan


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STUDY GUIDE

Course Code/ Title: ECO 501: Advanced Microeconomics

IV

Credit Units: 2

Timing: 26hrs

Total hours of Study per each course material should be twenty Six

hours (26hrs) at two hours per week within a given semester.

You should plan your time table for study on the basis of two hours per

course throughout the week. This will apply to all course materials you

have. This implies that each course material will be studied for two

hours in a week.

Similarly, each study session should be timed at one hour including all

the activities under it. Do not rush on your time, utilize them adequately.

All activities should be timed from five minutes (5minutes) to ten

minutes (10minutes). Observe the time you spent for each activity,

whether you may need to add or subtract more minutes for the activity.

You should also take note of your speed of completing an activity for the

purpose of adjustment.


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Meanwhile, you should observe the one hour allocated to a study

session. Find out whether this time is adequate or not. You may need to

add or subtract some minutes depending on your speed.

You may also need to allocate separate time for your self-assessment

questions out of the remaining minutes from the one hour or the one

hour which was not used out of the two hours that can be utilized for

your SAQ. You must be careful in utilizing your time. Your success

depends on good utilization of the time given; because time is money, do

not waste it.

Reading:

When you start reading the study session, you must not read it like a

novel. You should start by having a pen and paper for writing the main

points in the study session. You must also have dictionary for checking

terms and concepts that are not properly explained in the glossary.

Before writing the main points you must use pencil to underline those

main points in the text. Make the underlining neat and clear so that the

book is not spoiled for further usage.

Similarly, you should underline any term that you do not understand its

meaning and check for their meaning in the glossary. If those meanings

in the glossary are not enough for you, you can use your dictionary for

further explanations.


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When you reach the box for activity, read the question(s) twice so that

you are sure of what the question ask you to do then you go back to the

in-text to locate the answers to the question. You must be brief in

answering those activities except when the question requires you to be

detailed.

In the same way you read the in-text question and in-text answer

carefully, making sure you understand them and locate them in the main

text. Furthermore before you attempt answering the (SAQ) be sure of

what the question wants you to do, then locate the answers in your in-

text carefully before you provide the answer.

Generally, the reading required you to be very careful, paying attention

to what you are reading, noting the major points and terms and concepts.

But when you are tired, worried and weak do not go into reading, wait

until you are relaxed and strong enough before you engage in reading

activities.

Bold Terms:

These are terms that are very important towards

comprehending/understanding the in-text read by you. The terms are

bolded or made darker in the sentence for you to identify them. When

you come across such terms check for the meaning at the back of your

book; under the heading glossary. If the meaning is not clear to you, you


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can use your dictionary to get more clarifications about the

term/concept. Do not neglect any of the bold term in your reading

because they are essential tools for your understanding of the in-text.

Practice Exercises

a. Activity: Activity is provided in all the study sessions. Each

activity is to remind you of the immediate facts, points and major

informations you read in the in-text. In every study session there is

one or more activities provided for you to answer them. You must

be very careful in answering these activities because they provide

you with major facts of the text. You can have a separate note book

for the activities which can serve as summary of the texts. Do not

forget to timed yourself for each activity you answered.

b. In-text Questions and Answers: In-text questions and answers

are provided for you to remind you of major points or facts. To

every question, there is answer. So please note all the questions

and their answers, they will help you towards remembering the

major points in your reading.

c. Self Assessment Question: This part is one of the most essential

components of your study. It is meant to test your understanding of

what you studied so you must give adequate attention in answering

them. The remaining time from the two hours allocated for this


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study session can be used in answering the self- assessment

question.

Before you start writing answers to any questions under SAQ, you

are expected to write down the major points related to the

particular question to be answered. Check those points you have

written in the in-text to ascertain that they are correct, after that

you can start explaining each point as your answer to the question.

When you have completed the explanation of each question, you

can now check at the back of your book, compare your answer to

the solutions provided by your course writer. Then try to grade

your effort sincerely and honestly to see your level of performance.

This procedure should be applied to all SAQ activities. Make sure

you are not in a hurry to finish but careful to do the right thing.

e-Tutors: The eTutors are dedicated online teachers that provide

services to students in all their programme of studies. They are expected

to be twenty- four hours online to receive and attend to students

Academic and Administrative questions which are vital to student’s

processes of their studies. For each programme, there will be two or

more e-tutors for effective attention to student’s enquiries.

Therefore, you are expected as a student to always contact your e-tutors

through their email addresses or phone numbers which are there in your


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student hand book. Do not hesitate or waste time in contacting your e-

tutors when in doubt about your learning.

You must learn how to operate email, because e-mailing will give you

opportunity for getting better explanation at no cost.

In addition to your e-tutors, you can also contact your course facilitators

through their phone numbers and e-mails which are also in your

handbook for use. Your course facilitators can also resolve your

academic problems. Please utilize them effectively for your studies.

Continuous assessment

The continuous assessment exercise is limited to 30% of the total marks.

The medium of conducting continuous assessment may be through

online testing, Tutor Marked test or assignment. You may be required to

submit your test or assignment through your email. The continuous

assessment may be conducted more than once. You must make sure you

participate in all C.A processes for without doing your C.A you may not

pass your examination, so take note and be up to date.

Examination

All examinations shall be conducted at the University of Maiduguri

Centre for Distance Learning. Therefore all students must come to the

Centre for a period of one week for their examinations. Your preparation

for examination may require you to look for course mates so that you


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form a group studies. The grouping or Networking studies will facilitate

your better understanding of what you studied.

Group studies can be formed in villages and township as long as you

have partners offering the same programme. Grouping and Social

Networking are better approaches to effective studies. Please find your

group.

You must prepare very well before the examination week. You must

engage in comprehensive studies. Revising your previous studies,

making brief summaries of all materials you read or from your first

summary on activities, in-text questions and answers, as well as on self

assessment questions that you provided solutions at first stage of studies.

When the examination week commences you can also go through your

brief summarizes each day for various the courses to remind you of main

points. When coming to examination hall, there are certain materials that

are prohibited for you to carry (i.e Bags, Cell phone, and any paper etc).

You will be checked before you are allowed to enter the hall. You must

also be well behaved throughout your examination period.


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Study Session I: The Theory of Production Functions (Review)

Introduction

In general, economic output is not a (mathematical) function of input, because any given set of

inputs can be used to produce a range of outputs. To satisfy the mathematical definition of a

function, a production function is customarily assumed to specify the maximum output

obtainable from a given set of inputs. The production function, therefore, describes a boundary

or frontier representing the limit of output obtainable from each feasible combination of input.

Keywords: allocation, efficiency, Leontief production function, constant return to scale.

1.1 Learning Outcomes

At the end of this study session, you should be able to:

1. Define Production Function

2. Identify various forms of Production Functions

3. Discuss stages of Production Functions

4. Differentiate between homogeneous and homothetic production functions.

5. Discuss the criticism of production theory

6. Define production growth and performance


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1.2 Production Function

(Alternatively, a production function can be defined as the specification of the minimum input

requirements needed to produce designated quantities of output.) Assuming that maximum

output is obtained from given inputs allows economists to abstract away from technological and

managerial problems associated with realizing such a technical maximum, and to focus

exclusively on the problem of allocative efficiency, associated with the economic choice of how

much of a factor input to use, or the degree to which one factor may be substituted for another. In

the production function itself, the relationship of output to inputs is non-monetary; that is, a

production function relates physical inputs to physical outputs, and prices and costs are not

reflected in the function.

In the decision frame of a firm making economic choices regarding production—how much of

each factor input to use to produce how much output—and facing market prices for output and

inputs, the production function represents the possibilities afforded by an exogenous technology.

Under certain assumptions, the production function can be used to derive a marginal product

for each factor. The profit-maximizing firm in perfect competition (taking output and input

prices as given) will choose to add input right up to the point where the marginal cost of

additional input matches the marginal product in additional output. This implies an ideal division

of the income generated from output into an income due to each input factor of production, equal

to the marginal product of each input.

The inputs to the production function are commonly termed factors of production and may

represent primary factors, which are stocks. Classically, the primary factors of production were


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Land, Labor and Capital. Primary factors do not become part of the output product, nor are the

primary factors, themselves, transformed in the production process. The production function, a

theoretical construct, may be abstracting away from the secondary factors and intermediate

products, consumed in a production process. The production function is not a full model of the

production process: it deliberately abstracts from inherent aspects of physical production

processes that some would argue are essential, including error, entropy or waste, and the

consumption of energy or the co-production of pollution. Moreover, production functions do not

ordinarily model the business processes, either, ignoring the role of strategic and operational

business management.

The production function is central to the marginalist focus of neoclassical economics, its

definition of efficiency as allocative efficiency, its analysis of how market prices can govern the

achievement of allocative efficiency in a decentralized economy, and an analysis of the

distribution of income, which attributes factor income to the marginal product of factor input.

1.2.1 Specifying the production function

A production function can be expressed in a functional form as follows:

where is the quantity of output and are the quantities of factor inputs

(such as capital, labour, land or raw materials).

If is not a matrix (i.e., a scalar, a vector, or even a diagonal matrix???), then this form does not

encompass joint production, which is a production process that has multiple co-products. On the


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other hand, if maps from , then it is a joint production function expressing the

determination of different types of output based on the joint usage of the specified quantities of

the inputs.

One formulation, unlikely to be relevant in practice, is as a linear function:

where are parameters that are determined empirically. Another is as a Cobb-Douglas

production function:

The Leontief production function applies to situations in which inputs must be used in fixed

proportions; starting from those proportions, if usage of one input is increased without another

being increased, output will not change. This production function is given by

Other forms include the constant elasticity of substitution production function (CES), which is

a generalized form of the Cobb-Douglas function, and the quadratic production function. The

best form of the equation to use and the values of the parameters ( ) vary from

company to company and industry to industry. In a short run production function at least one of

the 's (inputs) is fixed. In the long run all factor inputs are variable at the discretion of

management.


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the inputs.












management.


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the inputs.












management.


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Production Function as a Graph


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Fig 1 Quadratic production function

Any of these equations (where are the equations here???) can be plotted on a graph. A typical

(quadratic) production function is shown in the following diagram (Reference???) under the

assumption of a single variable input (or fixed ratios of inputs so they can be treated as a single

variable). All points above the production function are unobtainable with current technology,

while all points below are technically feasible. All points on the function show the maximum

quantity of output obtainable at the specified level of usage of the input. From the origin, through

points A, B, and C, the production function is rising beyond point X. From point A to point C,


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the firm is experiencing positive but decreasing marginal returns to the variable input. As

additional units of the input are employed, output increases but at a decreasing rate. Point B is

the point beyond which there are diminishing average returns, as shown by the declining slope of

the average physical product curve (APP) beyond point Y. Point B is just tangent to the steepest

ray from the origin hence the average physical product is at a maximum. Beyond point B,

mathematical necessity requires that the marginal curve must be below the average curve.

1.3 Stages of production

To simplify the interpretation of a production function, it is common to divide its range into 3

stages. In Stage 1 (from the origin to point B) the variable input is being used with increasing

output per unit, the latter reaching a maximum at point B (since the average physical product is

at its maximum at that point). Because the output per unit of the variable input is improving

throughout stage 1, a price-taking firm will always operate beyond this stage.

In Stage 2, output increases at a decreasing rate, and the average and marginal physical

product are declining. However, the average product of fixed inputs (not shown) is still rising,

because output is rising while fixed input usage is constant. In this stage, the employment of

additional variable inputs increases the output per unit of fixed input but decreases the output per

unit of the variable input. The optimum input/output combination for the price-taking firm will

be in stage 2, although a firm facing a downward-sloped demand curve might find it most

profitable to operate in Stage 1. In Stage 3, too much variable input is being used relative to the

available fixed inputs: variable inputs are over-utilized in the sense that their presence on the

margin obstructs the production process rather than enhancing it. The output per unit of both the


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fixed and the variable input declines throughout this stage. At the boundary between stage 2 and

stage 3, the highest possible output is being obtained from the fixed input.

1.3.1 Shifting a production function

By definition, in the long run the firm can change its scale of operations by adjusting the level of

inputs that are fixed in the short run, thereby shifting the production function upward as plotted

against the variable input. If fixed inputs are lumpy, adjustments to the scale of operations may

be more significant than what is required to merely balance production capacity with demand.

For example, you may only need to increase production by million units per year to keep up with

demand, but the production equipment upgrades that are available may involve increasing

productive capacity by 2 million units per year.

Fig 2 Shifting a production function


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If a firm is operating at a profit-maximizing level in stage one, it might, in the long run, choose

to reduce its scale of operations (by selling capital equipment). By reducing the amount of fixed

capital inputs, the production function will shift down. The beginning of stage 2 shifts from B1

to B2. The (unchanged) profit-maximizing output level will now be in stage 2.

1.4 Homogeneous and Homothetic Production Functions

There are two special classes of production functions that are often analysed. The production

function is said to be homogeneous of degree , if given any positive

constant , . If , the function exhibits increasing

returns to scale, and on the otherhand,it exhibits decreasing returns to scale if . If it is

homogeneous of degree , it exhibits constant returns to scale. The presence of increasing

returns means that a one percent increase in the usage levels of all inputs would result in a

greater than one percent increase in output; the presence of decreasing returns means that it

would result in a less than one percent increase in output. Constant returns to scale, is the in-

between case. In the Cobb-Douglas production function, referred to above, returns to scale are

increasing if , decreasing if , and constant if

.

If a production function is homogeneous of degree one, it is sometimes called "linearly

homogeneous". A linearly homogeneous production function with inputs, capital and labour, has

the properties that the marginal and average physical products of both capital and labour can be

expressed as functions of the capital-labour ratio alone. Moreover, in this case if each input is


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.






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.






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paid at a rate equal to its marginal product, the firm's revenues will be exactly exhausted and

there will be no excess economic profit.

Homothetic functions are functions whose marginal technical rate of substitution (the slope of

the isoquant, a curve drawn through the set of points in say labour-capital space, at which the

same quantity of output is produced for varying combinations of the inputs) is homogeneous of

degree zero. Due to this, along rays coming from the origin, the slopes of the isoquants, will be

the same. Homothetic functions are of the form where is a monotonically

increasing function (the derivative of is positive ( )), and the function

is a homogeneous function of any degree.

1.4.1 Aggregate production functions

In macroeconomics, aggregate production functions for whole nations are sometimes

constructed. In theory they are the summation of all the production functions of individual

producers. However, there are methodological problems associated with aggregate production

functions, and economists have debated extensively on whether the concept is valid.

1.5 Criticisms of the Production Function Theory

There are two major criticisms of the standard form of the production function.


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On the concept of capital

During the 1950s, '60s, and '70s there was a lively debate about the theoretical soundness of

production functions. Although the criticism was directed primarily at aggregate production

functions, microeconomic production functions were also put under scrutiny. The debate began

in 1953 when Joan Robinson criticized the way the factor input capital was measured and how

the notion of factor proportions had distracted economists. She wrote:

"The production function has been a powerful instrument of miseducation. The student of

economic theory is taught to write Q = f (L, K ) where L is a quantity of labor, K a quantity of

capital and Q a rate of output of commodities. He is instructed to assume all workers alike, and

to measure L in man-hours of labor; he is told something about the index-number problem in

choosing a unit of output; and then he is hurried on to the next question, in the hope that he will

forget to ask in what units K is measured. Before he ever does ask, he has become a professor,

and so sloppy habits of thought are handed on from one generation to the next".

According to the argument, it is impossible to conceive of capital in such a way that its quantity

is independent of the rates of interest and wages. The problem is that this independence is a

precondition of constructing an isoquant. Further, the slope of the isoquant helps determine

relative factor prices, but the curve cannot be constructed (and its slope measured) unless the

prices are known beforehand.

On the empirical relevance


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As a result of the criticism on their weak theoretical grounds, it has been claimed that empirical

results firmly support the use of neoclassical well behaved aggregate production functions.

Nevertheless, Shaikhhas demonstrated that they also have no empirical relevance, as long as

alleged good fit outcomes from an accounting identity, not from any underlying laws of

production/distribution.

Natural resources

Often natural resources are omitted from production functions. When Solow and Stiglitz sought

to make the production function more realistic by adding in natural resources, they did it in a

manner that economist Georgescu-Roegen criticized as a "conjuring trick" that failed to address

the laws of thermodynamics, since their variance allows capital and labour to be infinitely

substituted for natural resources. Neither Solow nor Stiglitz addressed his criticism, despite an

invitation to do so in the September 1997 issue of the journal of Ecological Economics.

1.6 The Practice of Production Functions

The theory of production function depicts the relation between physical outputs of a production

process and physical inputs, i.e. factors of production. The practical application of production

function is obtained by valuing the physical outputs and inputs by their prices. The economic

value of physical outputs minus the economic value of physical inputs is the income generated

by the production process. By keeping the prices fixed between two periods under review we get


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the income change generated by the change of the production function. This is the principle upon

which the production function is made a practical concept, i.e. measureable and understandable

in practical situations.

1.6.1 Production

Economic well-being is created in a production process, meaning all economic activities that aim

directly or indirectly to satisfy human needs. The degree to which the needs are satisfied is often

accepted as a measure of economic well-being. In production there are two features which

explain increasing economic well-being. They are improving quality-price-ratio of commodities

and increasing incomes from growing and more efficient market production. The most important

forms of production are:

i) Market production

ii) Public production

iii) Household production

In order to understand the origin of the economic well-being we must understand these three

production processes. All of them produce commodities which have value and contribute to well-

being of individuals. The satisfaction of needs originates from the use of the commodities which

are produced. The need satisfaction increases when the quality-price-ratio of the commodities

improves and more satisfaction is achieved at less cost. Improving the quality-price-ratio of

commodities is to a producer an essential way to enhance the production performance but this

kind of gains distributed to customers cannot be measured with production data. Economic well-

being also increases due to the growth of incomes that are gained from the growing and more


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efficient market production. Market production is the only one production form which creates

and distributes incomes to stakeholders. Public production and household production are

financed by the incomes generated in market production. Thus market production has a double

role in creating well-being, i.e. the role of producing/developing commodities, and the role of

creating income. Because of this double role, market production is the “primus motor” of

economic well-being and therefore here under review.

1.6.2 Main processes of a producing company

A producing company can be divided into sub-processes in different ways; yet, the following

five are identified as main processes, each with a logic, objectives, and theory and key figures of

its own. It is important to examine each of them individually, and as part of the whole, in order

to be able to measure and understand them. The main processes of a company are as follows:

Fig 3 Main processes of a producing company (Saari 2006,3)

i) Real process

ii) Income distribution process


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i) Real process



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i) Real process



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iii) Production process.

iv) Monetary process.

v) Market value process.

Production output is created in the real process, gains of production are distributed in income

distribution process, and these two processes constitute the production process. The production

process and its sub-processes; the real process and income distribution process occur

simultaneously. Only the production process is identifiable and measurable by the traditional

accounting practices. The real process and income distribution process can be identified and

measured by extra calculation, and this is why they need to be analysed separately in order to

understand the logic of production and its performance.

Real process generates the production output from input, and it can be described by means of the

production function. It refers to a series of events in production in which production inputs of

different quality and quantity are combined into products of different quality and quantity.

Products can be physical goods, immaterial services and most often combinations of both. The

characteristics created into the product by the producer imply surplus valueto the consumer, and

on the basis of the market price this value is shared by the consumer and the producer in the

marketplace. This is the mechanism through which surplus value originates to the consumer and

the producer likewise. It is worth noting that surplus values to customers cannot be measured

from any production data. Instead the surplus value to a producer can be measured. It can be

expressed both in terms of nominal and real values. The real surplus value to the producer is an

outcome of the real process, real income, and measured proportionally it means productivity.


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The concept “real process”, meaning quantitative structure of production process, was introduced

in Finnish management accounting in 1960´s. Since then, it has been a cornerstone in the Finnish

management accounting theory (Riistama et al. 1971).

Income distribution process of the production refers to a series of events in which the unit prices

of constant-quality products and inputs alter causing a change in income distribution among

those participating in the exchange. The magnitude of the change in income distribution is

directly proportionate to the change in prices of the output and inputs and to their quantities.

Productivity gains are distributed, for example, to customers as lower product sales prices or to

staff as higher income pay.

The production process consists of the real process and the income distribution process. A result

and a criterion of success of the owner is profitability. The profitability of production is the share

of the real process result the owner has been able to keep to himself in the income distribution

process. Factors describing the production process are the components of profitability, i.e.,

returns and costs. They differ from the factors of the real process, in that, the components of

profitability are given at nominal prices, whereas in the real process the factors are at

periodically fixed prices.

Monetary process refers to events related to financing the business. Market value process refers

to a series of events in which investors determine the market value of the company in the

investment markets.


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1.6.3 Production growth and performance

Production growth is often defined as a production increase of an output. It is usually expressed

as a growth percentage, depicting growth of the real production output. The real output is the real

value of products, produced in a production process, and when we subtract the real input from

the real output we get the real income. The real output and the real income are generated by the

real process of production from the real inputs.

The real process can be described by means of the production function. The production function

is a graphical or mathematical expression showing the relationship between the inputs used in

production and the output achieved. Both graphical and mathematical expressions are presented

and demonstrated. The production function is a simple description of the mechanism of income

generation in the production process. It consists of two components. These components are a

change in production input and a change in productivity.

Fig. 4. Components of Production Growth


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Figure 4, illustrates an income generation process (exaggerated for clarity). The Value T2 (value

at time 2) represents the growth in output from Value T1 (value at time 1). Each time of

measurement has its own graph of the production function for that time (the straight lines). The

output measured at time 2 is greater than the output measured at time one for both of the

components of growth: an increase of inputs and an increase of productivity. The portion of

growth caused by the increase in inputs is shown on line 1 and does not change the relation

between inputs and outputs. The portion of growth caused by an increase in productivity is

shown on line 2 with a steeper slope, so increased productivity represents greater output per unit

of input.

The growth of production output does not reveal anything about the performance of the

production process. The performance of production measures production’s ability to generate

income. Because the income from production is generated in the real process, we call it the real

income. Similarly, as the production function is an expression of the real process, it could also be

called, “income generated by the production function”.

The real income generation follows the logic of the production function. Two components can

also be distinguished in the income change: the income growth caused by an increase in

production input (production volume) and the income growth caused by an increase in

productivity. The income growth caused by increased production volume is determined by

moving along the production function graph. The income growth corresponding to a shift of the

production function is generated by the increase in productivity. The change of real income also

signifies a move from the point 1 to the point 2 on the production function (above). When we

want to maximize the production performance, we have to maximize the income generated by


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the production function. The sources of productivity growth and production volume growth are

explained as follows:

Productivity growth is seen as the key economic indicator of innovation. The successful

introduction of new products and new or altered processes, organization structures, systems, and

business models generates growth of output that exceeds the growth of inputs. This results in

growth in productivity or output per unit of input. Income growth can also take place without

innovation through replication of established technologies. With only replication and without

innovation, output will increase in proportion to inputs (Jorgenson et al, 2014). This is the case

of income growth through growth in production volume.

Jorgenson et al. (2014) give an empirical example. They showed that the great preponderance of

economic growth in the US since 1947 involves the replication of existing technologies through

investment in equipment, structures, and software and expansion of the labour force. Further,

they showed that, innovation accounts for only about twenty percent of US economic growth.

In the case of a single production process (described above) the output is defined as an economic

value of products and services produced in the process. When we want to examine an entity of

many production processes we have to sum up the value-added created in the single processes.

This is done in order to avoid the double accounting of intermediate inputs. Value-added is

obtained by subtracting the intermediate inputs from the outputs. The most well-known and used

measure of value-added is the GDP (Gross Domestic Product). It is widely used as a measure of

the economic growth of nations and industries.

1.6.4 Absolute (total) and average income


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The production performance can be measured as an average or an absolute income. Expressing

performance both in average (avg.) and absolute (abs.) quantities is helpful for understanding the

welfare effects of production. For measurement of the average production performance, we use

the known productivity ratio

Fig 5 Average and marginal productivity (Saari 2011)

i) Real output / Real input.

The absolute income of performance is obtained by subtracting the real input from the real

output as follows:

ii) Real income (abs.) = Real output – Real input

The growth of the real income is the increase of the economic value which can be distributed

between the production stakeholders. With the aid of the production model we can perform the

average and absolute accounting in one calculation. Maximizing production performance


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output as follows:






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output as follows:






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requires using the absolute measure, i.e. the real income and its derivatives as a criterion of

production performance.

The differences between the absolute and average performance measures can be illustrated by

the following graph (Where is it???) showing marginal and average productivity. The figure is a

traditional expression of average productivity and marginal productivity. The maximum for

production performance is achieved at the volume where marginal productivity is zero. The

maximum for production performance is the maximum of the real incomes. In this illustrative

example the maximum real income is achieved, when the production volume is 7.5 units. The

maximum average productivity is reached when the production volume is 3.0 units. It is worth

noting that the maximum average productivity is not the same as the maximum of real income.

Figure above is a somewhat exaggerated depiction because the whole production function is

shown. In practice, decisions are made in a limited range of the production functions, but the

principle is still the same; maximum real income is the aim. An important conclusion can be

drawn. When we try to maximize the welfare effects of production we have to maximize real

income formation. Maximizing productivity leads to a suboptimum, i.e. to losses of incomes.

A practical example illustrates the case. When a jobless person obtains a job in market

production we may assume it is a low productivity job. As a result average productivity

decreases but the real income per capita increases. Furthermore the well-being of the society also

grows. This example reveals the difficulty to interpret the total productivity change correctly.

The combination of volume increase and total productivity decrease leads in this case to the

improved performance because we are on the “diminishing returns” area of the production


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function. If we are on the part of “increasing returns” on the production function, the

combination of production volume increase and total productivity increase leads to improved

production performance. Unfortunately we do not know in practice on which part of the

production function we are. Therefore a correct interpretation of a performance change is

obtained only by measuring the real income change.

1.6.5 Production models

A production model is a numerical description of the production process and is based on the

prices and the quantities of inputs and outputs. There are two main approaches to operationalize

the concept of production function. We can use mathematical formulae, which are typically used

in macroeconomics (in growth accounting) or arithmetical models, which are typically used in

microeconomics and management accounting.

We use here arithmetical models because they are like the models of management accounting,

illustrative and easily understood and applied in practice. Furthermore they are integrated to

management accounting, which is a practical advantage. A major advantage of the arithmetical

model is its capability to depict production function as a part of production process.

Consequently production function can be understood, measured, and examined as a part of

production process.

There are different production models according to different interests. Here we use a production

income model and a production analysis model in order to demonstrate production function as a

phenomenon and a measureable quantity. Malakooti (2013) provides an overview and problems


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of production models such as Aggregate planning, Push-and-Pull Systems, Inventory Planning

and Control, and so on.

Production income model

Table 1 Profitability of Production Measured by Surplus Value

Source: (Saari 2006,3)

The scale of success run by a going concern is manifold, and there are no criteria that might be

universally applicable to success. Nevertheless, there is one criterion by which we can generalise

the rate of success in production. This criterion is the ability to produce surplus value. As a

criterion of profitability, surplus value refers to the difference between returns and costs, taking


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into consideration the costs of equity in addition to the costs included in the profit and loss

statement as usual. Surplus value indicates that the output has more value than the sacrifice made

for it, in other words, the output value is higher than the value (production costs) of the used

inputs. If the surplus value is positive, the owner’s profit expectation has been surpassed.

The table presents a surplus value calculation. We call this set of production data a basic

example and we use the data through the article in illustrative production models. The basic

example is a simplified profitability calculation used for illustration and modelling. Even as

reduced, it comprises all phenomena of a real measuring situation and most importantly the

change in the output-input mix between two periods. Hence, the basic example works as an

illustrative “scale model” of production without any features of a real measuring situation being

lost. In practice, there may be hundreds of products and inputs but the logic of measuring does

not differ from that presented in the basic example.

In this context, we define the quality requirements for the production data used in productivity

accounting. The most important criterion of good measurement is the homogenous quality of the

measurement object. If the object is not homogenous, then the measurement result may include

changes in both quantity and quality but their respective shares will remain unclear. In

productivity accounting this criterion requires that every item of output and input must appear in

accounting as being homogenous. In other words the inputs and the outputs are not allowed to be

aggregated in measuring and accounting. If they are aggregated, they are no longer homogenous

and hence the measurement results may be biased.


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Both the absolute and relative surplus value have been calculated in the example. Absolute value

is the difference of the output and input values and the relative value is their relation,

respectively. The surplus value calculation in the example is at a nominal price, calculated at the

market price of each period.

Production analysis model

Table 2 Production Model


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Source: (Saari 2006)

A model used here is a typical production analysis model by help of which it is possible to

calculate the outcome of the real process, income distribution process and production process.

The starting point is a profitability calculation using surplus value as a criterion of profitability.

The surplus value calculation is the only valid measure for understanding the connection

between profitability and productivity or understanding the connection between real process and

production process. A valid analysis of production necessitates considering all production inputs,

and the surplus value calculation is the only calculation to conform to the requirement. If we


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omit an input in productivity or income accounting, this means that the omitted input can be used

unlimitedly in production without any cost impact on accounting results.

Accounting and interpreting

The process of calculating is best understood by applying the term ceteris paribus, i.e. "all other

things being the same," stating that at a time, only the impact of one changing factor will be

introduced to the phenomenon being examined. Therefore, the calculation can be presented as a

process advancing step by step. First, the impacts of the income distribution process are

calculated, and then, the impacts of the real process on the profitability of the production.

The first step of the calculation is to separate the impacts of the real process and the income

distribution process, respectively, from the change in profitability (285.12 – 266.00 = 19.12).

This takes place by simply creating one auxiliary column (4) in which a surplus value calculation

is compiled using the quantities of Period 1 and the prices of Period 2. In the resulting

profitability calculation, Columns 3 and 4 depict the impact of a change in income distribution

process on the profitability and in Columns 4 and 7 the impact of a change in real process on the

profitability.

The accounting results are easily interpreted and understood. We see that the real income has

increased by 58.12 units from which 41.12 units come from the increase of productivity growth

and the rest 17.00 units come from the production volume growth. The total increase of real

income (58.12) is distributed to the stakeholders of production, in this case 39.00 units to the

customers and to the suppliers of inputs and the rest 19.12 units to the owners.


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Here we can make an important conclusion. Income formation of production is always a balance

between income generation and income distribution. The income change created in a real process

(i.e. by production function) is always distributed to the stakeholders as economic values within

the review period. Accordingly the changes in real income and income distribution are always

equal in terms of economic value.

Based on the accounted changes of productivity and production volume, we can explicitly

conclude on which part of the production function the production is. The rules of interpretation

are as followings:

The production is on the part of “increasing returns” on the production function, when

i) productivity and production volume increase or

ii) productivity and production volume decrease ???

The production is on the part of “diminishing returns” on the production function, when

iii) productivity decreases and volume increases or

iv) productivity increases and volume decreases.

In the basic example the combination of volume growth (+17.00) and productivity growth

(+41.12) reports explicitly that the production is on the part of “increasing returns” on the

production function (Saari 2006)

Another productivity model also gives details of the income distribution. Because the accounting

techniques of the two models are different, they give differing, although complementary,


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analytical information. The accounting results are, however, identical. We do not present the

model here in detail but we only use its detailed data on income distribution, when the objective

functions are formulated in the next section.

Objective functions

An efficient way to improve the understanding of production performance is to formulate

different objective functions according to the objectives of the different interest groups.

Formulating the objective function necessitates defining the variable to be maximized (or

minimized). After that other variables are considered as constraints. The most familiar objective

function is profit maximization which is also included in this case. Profit maximization is an

objective function that stems from the owner’s interest and all other variables are constraints in

relation to maximizing of profits.

Table 4 Summary of Objective Function Formulations


The procedure for formulating objective functions


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Objective functions












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Objective functions












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The procedure for formulating different objective functions, in terms of the production model, is

introduced next. In the income formation from production the following objective functions can

be identified:

i) Maximizing the real income

ii) Maximizing the producer income

iii) Maximizing the owner income.

These cases are illustrated using the numbers from the basic example. The following symbols are

used in the presentation: The equal sign (=) signifies the starting point of the computation or the

result of computing and the plus or minus sign (+ / −) signifies a variable that is to be added or

subtracted from the function. A producer means here the producer community, i.e. labour force,

society and owners.

Objective function formulations can be expressed in a single calculation which concisely

illustrates the logic of the income generation, the income distribution and the variables to be

maximized.

The calculation resembles an income statement starting with the income generation and ending

with the income distribution. The income generation and the distribution are always in balance

so that their amounts are equal. In this case it is 58.12 units. The income which has been

generated in the real process is distributed to the stakeholders during the same period. There are

three variables which can be maximized. They are the real income, the producer income and the

owner income. Producer income and owner income are practical quantities because they are


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addable quantities and they can be computed quite easily. Real income is normally not an

addable quantity and in many cases it is difficult to calculate.

The Dual Approach for the Formulation

Here we have to add that the change of real income can also be computed from the changes in

income distribution. We have to identify the unit price changes of outputs and inputs and

calculate their profit impacts (i.e. unit price change x quantity). The change of real income is the

sum of these profit impacts and the change of owner income. This approach is called the dual

approach because the framework is seen in terms of prices instead of quantities (ONS 3, 23).

The dual approach has been recognized in growth accounting for long but its interpretation has

remained unclear. The following question has remained unanswered: “Quantity based estimates

of the residual are interpreted as a shift in the production function, but what is the interpretation

of the price-based growth estimates?” We have demonstrated above that the real income change

is achieved by quantitative changes in production and the income distribution change to the

stakeholders is its dual. In this case the duality means that the same accounting result is obtained

by accounting the change of the total income generation (real income) and by accounting the

change of the total income distribution.

A true duopoly (from Greekduoδύο (two) + polein πωλεῖν (to sell)) is a specific type of

oligopoly where only two producers exist in one market. In reality, this definition is generally

used where only two firms have dominant control over a market. In the field of industrial

organization, it is the most commonly studied form of oligopoly due to its simplicity.


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Duopoly models in economics

There are two principal duopoly models, Cournot duopoly and Bertrand duopoly:

1. The Cournot model, which shows that two firms assume each other's output and treat this

as a fixed amount, and produce in their own firm according to this.

2. The Bertrand model, in which, in a game of two firms, each one of them will assume that

the other will not change prices in response to its price cuts. When both firms use this

logic, they will reach a Nash equilibrium

Examples in business

The most commonly cited duopoly is that between Visacard and Mastercard. But, who controls a

large proportion of the electronic payment process market?

Examples where two companies control a large proportion of a market are:

i) Airbus and Boeing in the market for large commercial airplanes.

ii) Televisa and Azteca in the Mexican Television market.

iii) Woolworths and Coles in the Australian supermarket market (share 79% of the

supermarket market).

iv) Mitre 10 MEGAand Bunnings Warehouse in the Australian and New Zealand retail/trade

timber and hardware market (Share 85% of the timber and hardware market).

Monopsony denotes a market condition where there is solitary consumer of a product or service.

It is relevant to any condition in which there is a monopoly constituent in purchasing. For


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example when clients of a certain good are structured, or when a communalist regime legalize

importation or when a definite person comes about to have a liking for some products which no

one else necessitate or when a single big factory in an inaccessible vicinity is the solitary

consumer of some marks of effort there is monopsony. Monopsony is defined as “the case of a

single buyer who is not in competition with any other buyers for the output which he seeks to

purchase and as a situation in which entry into the market by other buyers is impossible.”

Bilateral Monopoly

Bilateral monopoly denotes a market condition in which a solitary manufacturer of

merchandise faces a solitary purchaser of that commodity.

Postulations

1. There is a solitary commodity with no close surrogates

2. The monopolist is its sole manufacturer or seller

3. The monopsonist is its only consumer

4. The monopolist and the monopsonist are equally liberated to optimise their own person

profits

Price output Determination

Given these postulations, price and output ascertainment under bilateral monopoly is presented

in the sketch where D is the demand curve of the monopolist’s product and MR is its

corresponding marginal revenue curve of the monopolist. The MC curve of the monopolist is the


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supply curve S factoring the monopsonist. The upward incline indicates that if monopsonist

wants to buy more he will have to pay a higher price.

So when he buys more units of the product his marginal outlay or marginal expenditure

increases. This is shown by the upward inclination ME curve which is the marginal expenditure

curve to the total supply curve MC/S. The curve D is the marginal utility MU curve of the

monopsonist.

Let us first consider the equilibrium position of the monopolist. The monopolist is in equilibrium

at point E where his MC curve cuts the MR curve from below. His profit maximising price is

OP1 (=MS) at which he will sell OM quantity of the product. The monopsonist is in equilibrium

at point B where his marginal expenditure curve ME intersects the demand curve D / MU.

He buys OQ units of the product at OP2 (=QA) price, as determined by point A on the supply

curve MC / S. So there is disagreement over price between the monopolist who want to charge a

higher price OP1 and the monopolist who wants to pay a lower price OP2. From a theoretical

viewpoint there is indeterminacy in the market. In actuality the actual quantity of the product

sold and its price depends upon the relative bargaining strength of the two.


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The greater the relative bargaining strength of the monopolist the closer will price be to OP1 and

the greater the relative bargaining strength of the monopsonist the closer it will be to OP2. Thus

the price will settle somewhere between OP1 and OP2.

If the monopoly and monopsony firms merge into a single firm, with the monopsonist taking

over the monopoly firm, the MC / S curve of the monopsonist becomes his marginal cost curve.

The merged firm would thus maximise its profits at point F where its MC/S curve cuts the

D/MU. It ill supply and use OT output at OP3 price. In this situation the merged firms get much

larger output (OT) than the monopoly output (OM) at a lower price (OP2) than the monopoly

price (OP1).

However it may not be possible to merge the monopoly firm which the monopsony firm.

Economists have suggested another solution to problem of bilateral monopoly, that of joint profit

maximisation. In this case, the monopolist and monopsonist a free on the quantity to be sold and

bought to each other but disagree on the price to be charged. On this basis they want to maximise

joint profits because they feel that they have got information about each other’s wants and

aspirations.


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This case is illustrated in the below diagrammatic representation where the monopolist is in

equilibrium at X when his MC/S curve = MR curve. He wants to sell OQ quantity at OP1 (=QY)

price. Conversely, the monopsonist is in equilibrium at point Y when his demand curves D / MU

= ME curve.

He wants to buy OQ quantity at OP2 price. Based on the relative bargaining strength of each

other, the price can be anywhere between P2 and P1 and is thus indeterminate. But their joint

profits are P1P2 x OQ that can be divided between the monopolist and the monopsonist in ratio.

ITQ

Discuss the main processes of a producing company

ITA

Main processes of a producing company according to Saari, (2006) are:

i) Real process


iii) Production process

iv) Monetary process and

v) Market value process.

Production output is created in the real process, gains of production are distributed in the income

distribution process and these two processes constitute the production process. The production

process and its sub-processes, the real process and income distribution process occur


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simultaneously, and only the production process is identifiable and measurable by the traditional

accounting practices. The real process and income distribution process can be identified and

measured by extra calculation, and this is why they need to be analysed separately in order to

understand the logic of production and its performance.

1. 7 Activity Advanced Microeconomics IV

Activity Timing

Allow: 10 minutes

Activity Text:

Meet a colleague and discuss price and output determination under monopsony.

1.8 Summary of Study Session 1

In this study session, you have learnt:

1. to define Production Function

2.how to identify various forms of Production Functions

3. Discuss the stages of production functions.

4. How to differentiate between homogeneous and homothetic production functions.

5. about the criticism of production theory

6. how to define production growth and performance

1.9 SAQ

SAQ (LO 1): Define production function

SAQ (LO 2): Discuss 3 stages of production


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SAQ (LO 3): What are the procedures for formulating an objective function?

SAQ (LO 4): Discuss two major principles of duopoly models (give examples).

1.10 References

Jorgenson, D.W.; Ho, M.S.; Samuels, J.D. (2014).Long-term Estimates of U.S. Productivity and

Growth(PDF).Tokyo: Third World KLEMS Conference.

Saari, S. (2006).Productivity. Theory and Measurement in Business(PDF).Espoo, Finland:

European Productivity Conference.

Saari, S. (2011).Production and Productivity as Sources of Well-being. MIDO OY.

1.11 Suggested Reading

Saari, S. (2006).Productivity. Theory and Measurement in Business(PDF).Espoo, Finland:

European Productivity Conference.

Study Session II General Equilibrium Analysis

Introduction

Most microeconomic models analyse equilibrium at stages of individual- partial markets. Such

markets are considered as an independent system, isolated and independent of the whole

economy. This partial analysis enables perception of optimization in firm behaviour and creating

partial equilibria. A partial analysis, however, has necessarily its limits. It does not give

satisfying answers to numerous fundamental questions. The basic shortage of partial analysis


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models is the same; it does not explain functions of the connected system of partial markets, i.e.

the whole economy. Therefore, connecting models of analysing partial markets and models of

general economic equilibrium represent completing and connecting contemporary

microeconomic analyses into a unit system.



1. Discuss critical analysis of microeconomic aspects of general equilibrium.

2. Define general exchange equilibrium

3. Discuss general production equilibrium

4. Identify conditions for general production and exchange

2.2 Fundamental Questions of General Equilibrium

The theory of general economic analysis, except its complexity and difficulties in practical

implementation, gives invaluable benefits in the domain of analysing efficiency and welfare in

microeconomic researches and offering great support in macroeconomic modelling. The subject

of this work is just the comparative and critical analysis of microeconomic aspects of

fundamental questions of the general competitive equilibrium. Introducing problems of general

equilibrium into the economy is connected with the Physiocrats. The role of market mechanisms

in creating equilibrium by means of competition, i.e. the “invisible hand” of market we find in A.

Smith’s teachings. K. Marx brilliantly explained the effects of mechanisms of the law of value.

In his works, we find the laws of stable rate of reproduction and expanded social reproduction,


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which, in principle, explain the possibilities of dynamic and balanced economic growth.

Nevertheless, there are two principal duopoly models; Cournot duopoly andBertrand duopoly.

1. The Cournot’s model, which shows that two firms assume each other's output and treats

this as a fixed amount, and produce in their own firm according to this.

2. The Bertrand model, which, in a game of two firms, where each one of them will assume

that the other will not change prices in response to its price cuts. To his opinion, partial

equilibrium is the equilibrium of economic spheres. Aggregate equilibrium is the

equilibrium between selected aggregate quantities (selected in relation to the analysis,

which should be done), while general equilibrium represents the equilibrium of national

economy. On the other side, with A. Pigou, we find differentiated stable, neutral and

unstable equilibrium.

We should get down to the analysis of general equilibrium as any other analysis in economic

theory, from the row of simplified suppositions. We take the supposition of competitive market,

pure exchange model, production equilibrium, and then simultaneous equilibrium is considered.

2.3 General Exchange Equilibrium

In the analysis of general equilibrium, theoreticians such as Pareto, Edgeworth, Walras and

others started from researching into the so-called general exchange equilibrium, i.e. in their this

analysis, they firstly abstract money, i.e. commodity prices. Equilibrium conditions are explained

starting from the so-called “Edgeworth box” or Edgeworth diagram. At the beginning, they

usually take two individuals who consume two goods. Take for example,individuals A and B,

and goods to be consumed, to be X and Y.


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. X OBt3 Y

Ht2

t1 A3E

G B1A2

A1 B2

B3OA Y

Figure 1,

In Figure 1, in relation to the ordinate OA several curves of indifference (line of equal utility) of

participants in exchange are taken. All the points of the curve of indifference represents such

alternative combinations of goods X and Y for an individual A giving him the same level of

utility. The slope of determined indifference curve expresses the so-called MRS (Marginal Rate

of Substitution), i.e. marginal rate of goods exchange in a determined point of indifference curve,

where the utility level of actor A remains unchanged. If some curve of indifference is further

from the origin, the utility level representing mutual indifferent combinations, presented on it, is

bigger. For that, the relation can express utility values represented by indifference curves of the

individual A: A3 > A2 > A1.

The origin B is in the opposite northeast angle of the Edgeworth closed diagram, and in relation

to it, the indifference curve of Participant B in exchange, i. e. the curves B3 > B2 > B1. Each of

them represents numerous mutually equivalent or indifferent combinations of goods X and Y for

the individual B. The slope of indifference curve is now MRS but for the trader B.

The exchange of goods for individuals is useful, until they are not on indifference curves, which

have not points of contact. The marginal rates of goods substitution X and Y for exchangers


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become equal in points of contact of their indifference curves. As MRS of consumption goods

are appropriate to the relations of their indifference curves, it results that exchange is done until

marginal utilities of these goods X and Y become equal for A and B. The row of these points

represents the general equilibrium of exchange for A and B in the observed model. The

geometric set of equilibrium points gives the so-called Edgeworth contract curve, which

connects OA with OB. When participants of exchange are in this curve, they reach the so-called

Pareto-optimality in exchange. It is said that the “distribution is optimal in the Pareto sense if it is

such that every improvement of the situation causes the aggravation of other situations.” In other

words, some distribution is Pareto optimal only if there is no possibility of such change, which

could improve the situation of one not damaging others. Therefore, every point in the contract

curve represents the Pareto optimality, and this curve is the geometric place in Pareto optimality.

The Pareto optimality was dome in 1896 in the work Coursd’economiepolitique. When the

ordinary understanding of utility was defined (i.e. not the absolute but the relative value or the

level of utility providing comparative combinations of properties) his work

Manualed’economica, the policy in 1906, reached its real importance. In this work, namely, for

the first time, the attitude was defined that maximization of aggregate social utility can be

reached with the relations of exchange, when no individual utility can be increased without

decreasing of somebody else’s utility.

In Figure 1, along the Edgeworth contract curve, there are numerous alternative equilibrium

combinations of exchange. To make the choice between them, it is necessary to define the Social

Welfare Function (SWF). Defining this function is a very complex task. We should start from

the evaluation of values of some situations, evaluation of preferences of social subjects,

especially those who create economic policies, and so on.


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However, this task can be solved with some exactness. Knowing social welfare functions, the

Pareto criterion enables eliminating non-optimal combination in exchange. Now, look at Figure

2. Suppose that the initial distribution X and Y between A and B is at point N, where

the curves of utility and indifference A2 and B cut, it is easy to understand that all points for

participants in exchange in the shaded surface represent better combinations than the ratio of

exchange expressed by point N. The shaded area in Diagram is called the “region of mutual

advantages”, and the interval of Edgworth contract curve between points G and H is called the

“core or path of theeconomy” [Stojanovic, 1944]. X OB

B3 N

B2 B4

B1 H

E A4G

A3

Y A1 A2

OAXFigure 2

Correct definition of the position of SWF enables the choice between optimal exchange

combinations in the line between points G and H. Completing general equilibrium in exchange

requires the introduction of relative prices of properties and incomes of consumers. Namely, it is

generally accepted that consumers or households as traders try to optimize their economic

position, or, in other words, to maximize their consumption utility, starting from the following

factors:

1. Preference consumers’ system expressed by indifference functions;


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2. Amount of money income of consumers;

3. Prices of individual goods and services, P (price), as the indicator of the level of social utility

of goods and services.

In the two-dimensional model of consumers’ choice limits or the so-called budget consumption

limitation are expressed by the so-called line or consumption limit. In case that the variables of

money income of traders A and B are equal in exchange, i.e. IA = IB, and prices of properties X

and Y which come in exchange between them Px and Py, the budget limitation of consumption

for both exchangers can be expressed by the relation:

IA,B= XPX . + YPY = whence (1)

Under the above supposition, the identical budget line can present the limits of consumers’

choice for traders A and B. With unchanged prices of goods and amount of money income, the

position of budget line remains unchanged, and its slope expresses the relation of property prices,

i.e. Px and Py. Look now at Figure 3, the possibilities of general equilibrium in exchange, taking

into consideration the amount of money income and prices of exchanged goods


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Figure 3

In Figure 3, general exchange equilibrium between A and B is at point E on the Egdeworth

contract curve. At this point, namely, we have matching up the slopes of indifference curves of

trader A, on the curve AE and the slope of indifference curve B, the other trader in exchange. In

this point (as in all other points of the contract curve), we have matching up of marginal

substitution rates of X and Y for traders A and B. However, contrary to other points on the

contract curve, in E, the slope of their marginal substitution slope, i. e. MRS (it is in fact the

slope of tangent in some point) is matching up with the slope of their budget line. The slope of

budget line expresses relative prices, in other words, the relation of prices of goods in exchange,

i.e. X and Y. At the equilibrium point E, the following equalities are valid:

MRSA(X,Y) = MRSB(X,Y) = = (4)

(MU – Marginal Utility) At point E, equilibrium goods/ prices have the same mutual relations in

marginal rate of goods substitution, i.e. MRS is equal for both traders in exchange, and at the

same time, it is appropriate to relations of marginal utility of exchanged goods. It means that the

y

x

p

p

y

x

MU

MU


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equilibrium point E is suitable for relation of the proportion where supply and demand of

exchanged goods become equal.

Figure 4

X I/PX OBY

Eb1A1

I/PY A2Eb2 B1 I/PY1A3

Ea3Eb3 B2

Ea3Ea3 PCCA I/PY2

B3PCCB I/PY3

Y (Fig. Not very clear)OA I/PX1 I/PX1/2 I/PX3 X

By the combination of indifference curves and budget lines we obtain the PCC (Price

Consumption Curve), which shows the structure of optimal consumer baskets in case of price

changes of some goods (presupposing that prices of other goods, the level of money incomes of

consumers and their preference system are steady). In Figure 4, we presented the curves of

relations of prices and consumption for individuals A and B, supposing that the product price X

changes for trader A; for trader B, the product price Y is changeable. All other relations and

conditions remain unchangeable.

The curve of relations of price and consumption of trader A, i.e. curve PCCA shows that, starting

from the combination of goods in point Ea1, which is located along with the starting position of

budget line, the trader A is ready to offer increasing quantity of product X for increasing less

quantity of product Y. It is done by gradually price reduction of product X presented by budget

lines I/Px2 and I/Px3. This trader tries to optimize his consumer utility in the conditions of


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changed prices. Contrary to trader A, in northeast angle of Diagram, considering PCCB, i.e. the

curve of relations of price and consumptions of trader B, we see that the latter trader is ready to

exchange more product Y whose price reduces for increasingly less quantity of product X, in

view of maximization of his consumer utility.

In fact, the curve of relations of prices and consumption of the trader A, i. e. PCCA, represents

the curve of offer A, i.e. its readiness to change goods X for Y in exchange. On the other side

PCCB, i.e. the curve of relations of prices and consumption of trader B, presents the curve of

offer B, i.e. acceptable relation of goods exchange X and Y for Individual B, depending on price

change of product Y. Traders of exchange A and B along their offer curves, starting from points

Ea1 and Eb1 to points Ea3 and Eb3 get to indifference curves which become more distant from

the origos, i.e. which express an increasing level of utility for them.

Present, finally, in Figure 5, the curve of relations of prices and consumption of both traders, i.e.

PCCA and PCCB, inside of the so-called “region of mutual advantages”, limited by their starting

indifference curves Ae and Be.

X OBFigure 5

YN

PCCBH

PCCAG E Ae

BeY

OA X


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We can see the point of section of supply curves of observed traders in exchange on the

Edgeworth contract curve and inside of the core of exchange in the interval of points G and H in

point E. It expresses the relations of exchange where the product offer of the individual A (i.e.

his demand for product Y) and product offer by trader B (i.e. his demand for product X). The

general exchange equilibrium is established in point E – of course, in the simplified model with

two traders and two products. However, this model enables to define the general law on

equilibrium of exchange in the following sense: general exchange equilibrium is established with

equality of marginal substitution rates of traders along with equality of supply and demand that

they present.

The analysis of general equilibrium mechanism is needed to continue by researching the

mechanism of general production equilibrium.

2.4 General Production Equilibrium

In analysing the general production equilibrium, we can take the simplified production model

analogous to the model used in the analysis of general exchange equilibrium. In the model, we

suppose that a producer makes two products X and Y, with combination of only two inputs,

labour and capital, i.e. by means of L (Labour) and C (Capital). The general production

equilibrium is established when marginal technical rate of factor substitution equalize, i.e. MRTS

(Marginal Rate of Technical Substitution) for both products. Equilibrium can be established on

the so-called Edgeworth closed production box [Kopanyi, 2003], i.e. in Figure 6. The curves

IX1, IX2, IX3 and IX4 represent isoquants or the so-called curves of equal quantities of the

product X. Therefore, isoquants IY1, IY2, IY3 and IY4 show the curves of equal products for

product Y. If the starting point is point N on isoquants IX1 and IY3, it is visible that production


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maximization X and Y is not realized here, therefore, nor general production equilibrium. The

producer can increase both production X and production Y, i.e. reaches isoquants at the higher

position (i.e. further than the origo) reducing capital consumption for production X on behalf of

production Y and conversely, increasing labor consumption in production X, on behalf of

consumed labor in production Y.

Figure 6 L OYIX1 IX4 K

N IX2 IX3

F IY1

G E

IY4

K IY3 IY2

OX L

With these relations and limitations, production maximization of both products is reached in the

tangential point of production isoquants X and Y, i.e. at point E. In point E, the curve slopes of

equal products X and Y, i.e. Ix2 and Iy3 are equal, i.e. the marginal technical rates of substitution

in their production are equalized. Thence, these relations are valid:

MRTS L,K(Y)= MRTSL,K(X) Then (5)

MRTSL,K = ( MP =Marginal Product) (6)

It means that production equilibrium criterion is realized with the condition

= (7)

k

L

MP

MP

XK

L

MP

MP

YK

L

MP

MP


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The point of equilibrium is on the so-called Edgeworth contract production curve, which

connects origin Ox and origin Oy. When production of goods is on this curve, it is not possible

any more to increase production of one material product without decreasing production of the

other product. On the contract production curve, there are such combinations of production of

goods, which realize the so-called Pareto production equilibrium [Pareto, 1971]. In the above

analysis of production equilibrium, two marginal rates of technical substitution and marginal

products of observed are taken into consideration, but not using the price factor.

In further analysis, suppose that the sum of engaged resources (or TC – total costs) is the

constant for production of goods X and Y. Then, suppose that, with ceteris paribus, labor price,

i.e. PL1 < PL2 < PL3 in production of product X decreases gradually. So, we obtain the isocost

lines (lines of equal costs) in different positions for production of product X. Connecting

tangential points of appropriate isoquant and isocost lines with different labor

I prices, we obtain the production curve of product X, which expresses the optimal combination

of input under cited conditions, i.e. the curve Tx. ??? Fig. not clear also???

Fig 7 L TC/PL OYK

IX1IX1 IX2

TC/PK IX2CY3 TC/PK3IX3 IX3

CY2TX TC/PK2

CY3CX1 TY TC/PK1

CX3 CX2K

OX TP/PL1 TP/PL2 TP/PL3 X


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Figure 8 L OY

K

IY F

TX

E

G IX

K TY

OX L

In production of product Y, we gradually reduce the price of capital used (PK1 < PK2 < PK3)

and analog to logic in production optimization X, we obtain the curve of production T whose

points show the optimal combination of input with different capital prices, i.e. the function Ty

production function Tx and Ty are presented in Figure 7. Curves Tx and Ty cut inside the so-

called “region of mutual production advantages” limited by isoquants Ix and Iy. the curve Tx , on

the one side, represents the factor demand curve (L, K) used for production of product X, and at

the same time, it is the product supply curve X, on the other side. Therefore, the curve Ty

represents the factor demand curve for production of goods Y, but also the supply curve Y.

The slopes of isoquants, i.e. the curve of equal product MRTS, express the technical substitution

possibilities of input factors in the given isoquant point (in fact, the slope of tangent along with

this point) and with the condition that the volume of production remains the same. The slopes of

isocost lines (line of equal costs) express the relations of prices used and combined factors in

production, i.e. the relation Pk/Pl. That means that isoquants and isocost lines of marginal

substitution rates of production factors in the points of tangents are appropriate to the relations of


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current prices of these factors. It is, together, the criterion of optimal factor combination. Thus,

this relation is valid:

MRTSL,K = = (8)

Hence, it gives the following equality on the contract production curve:

= =+

(9)

These equalities “must exist even when more goods are

made and more production factors are used – more than two” [Stojanovic, 1994]. After all these

considerations, we can start to define general production equilibrium in the sense of the Pareto

optimum. In Figure 9, we again draw the amounts of products X and Y.

Figure 9 Y TP

Y3F

Y2

EY1

G

X

X1 X2 X3

The contract curves of production transferred from previous diagrams (Figure 6 and 8), change

into the function of production possibilities or the curve of production transformation. The slope

of transformation curve expresses the marginal rates of product transformation X and Y, i.e.

MRT (Marginal Rate of Transformation). Marginal transformation curves with coordinate axes

express extreme cases, i.e. when only one or only other kind of product is produced. Individual

k

L

MP

MP

K

L

P

P

XK

L

MP

MP

YK

L

MP

MP

K

L

P

P


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points of production transformation curves express different alternatives combinations of final

products X and Y, which can be maximally produced by full employment of available inputs R

and K with available technology. It means that all the combinations along the transformation

production curve satisfy the criteria of Pareto optimum, i.e. general production equilibrium. In

the area under the curve of alternative production possibilities there are differently realizable

possibilities X and Y with suboptimal use of resource use, and combinations in the area of

alternative production possibilities out or above the curve of production transformation are

unrealizable based on available possibilities.

After the differentiated analysis of conditions and suppositions of general equilibrium of

production and exchange, we can analyze the general economic equilibrium in the economy, i.e.

the equilibrium of production and exchange.

2.5 General Equilibrium of Production and Exchange

The cited conditions of general exchange equilibrium and general production equilibrium must

unite in order to make the simultaneous equilibrium of production and exchange, as in reality,

economies where only production or exchange of goods do not exist [Stojanovic, 1994].

In Figure 10, the curve of transformation TP(X,Y) represents the combinations of goods X and

Y. The curve OAOB represents the so-called contract consumption curve – exchange. The

simultaneous or general equilibrium of production and exchange, or the so-called Pareto optimal

equilibrium is realized with the condition:

MRTx/y = (MRSX,Y)A = (MRSX,Y)B (10)

where exchangers of goods X and Y are participants A and B. The general production

equilibrium is realized at point M (or OB) which provides production per 10 units X and Y. The

curve tangent of production possibilities Tp(x,y) at point M expresses the marginal


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transformation rate X in Y, i.e. MRTX,Y. The tangent along the curve Tr(X,Y) expresses the

marginal rate of substitution of cited goods in production, i.e. MRSX,Y. At points M and E there

is pararellism of the cited tangents. They provide genera production equilibrium at point M and

general exchange production at point E. Point E shows also the distribution of made equilibrium

amount of goods X and Y between A and B in the sense: A gets six pieces of X and five units of

Y, while B will obtain four pieces X and five pieces Y.

Figure 10 Y TP

Y3F

Y2

EY1

XX1 X2 X3

The criterion of simultaneous equilibrium of production and exchange in the sense of equalizing

marginal transformation rates and marginal substitution rates can be generalized , of course, in

case of the existence of more kinds of goods, i.e. more producers and consumers. It makes the

economic analysis more complete and near its reality.

MRT, i.e. marginal rate of transformation of goods in equilibrium reflect the relations of their

marginal production costs, and MRS, i.e. the marginal rate of substitution of goods at the

equilibrium level equalize marginal utility goods (and these reflect the relations of their

equilibrium prices). Thus, the criterion of simultaneous general equilibrium in production and

exchange can be expressed in the following way:


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= =

The above relation is valid, of course, also in the model with a large number of goods and

services in case of many producers and consumers.

The presented ( simplified) analysis of general equilibrium of exchange and production, besides

completing the knowledge of functioning connected and complex system of market mechanisms

has a broader importance. The conditions and criteria of general competitive equilibrium are

applied in the analysis of a very important and current subject matter of economic theory to the

so-called welfare economics and the theory of optimum (efficiency) of contemporary market

economy. However, this will be the subject of researching in the next work.

ITQExplain Cournot ‘s and Bertrand’s duopoly models

ITA

Cournot’s duopoly and Bertrand’s duopoly models:

1. The Cournot’s model, which shows that two firms assume each other's output and treat


2. The Bertrand’s model, in which, in a game of two firms, each one of them will assume

that the other will not change prices in response to its price cuts. To his opinion, partial

equilibrium is the equilibrium of economic spheres. Aggregate equilibrium is the

equilibrium between selected aggregate quantities (selected in relation to the analysis,

which should be done), while general equilibrium represents the equilibrium of national

economy. On the other side, with A. Pigou, we find differentiated stable, neutral and

unstable equilibriums.

Y

X

MC

MCA

Y

X

MU

MU

BY

X

MU

MU


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2.6. Activity: Microeconomics 111

Activity Timing

Allow: 10 minutes

Activity Text:

Meet a colleague and discuss briefly the history of general equilibrium model.

2.7 Summary of Study Session II


1. To analyse of microeconomic aspects of fundamental questions of general

equilibrium.

2. how to the define general exchange equilibrium

3. to discuss general production equilibrium

4. how to identify conditions for general production and exchange

2.8 References

Schuman J., “Grundzuge der mikrookonomischenTherie”,JATE Press Szeged 1988

Suvakov T. &Sagi A. (2011), “Mikroekonomija”, Subotica Ekonomskifakultet.

Trivic N.,&Sagi A.(2008), “Savremenimikroekonomskimodeli”,Subotica Ekonomskifakultet.

AndrasSagi, & Eva Pataki, Theory of General Competitive Equilibrium andOptimization

Models of the Consumption andProduction, [email protected] assessed on 25/11/26


Samuelson P., N.(2006) “Economics”, New York, Mc-Graw Hill.


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Study Session III Analysis of Social Cost

Introduction

The goal of a benefit-cost analysis is to determine the net change in social welfare brought about

by a new environmental policy, as measured by changes in the producer and consumer surpluses.

In general, the economic effects of a new environmental policy result in many different people

and firms being affected, both positively and negatively.



1. define Social Cost

2. illustrate examples of social cost and externalities

3. discuss general approach to social cost analysis

4. Understand model tools

5. Estimate social costs of alternative policy approach

3.2 The Theory of Social Cost Analysis

The total social cost is the sum of the opportunity costs incurred by society because of a new

regulatory policy; the opportunity costs are the value of the goods and services lost by society

resulting from the use of resources to comply with and implement the regulation. These costs,

however, do not take into account any of the health, environmental, safety, or other benefits

which offset the social welfare costs.


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The five basic components of total social costs are listed here in the general order of relative ease

of estimation, and hence inclusion, in most social cost analyses of environmental policies. They

include:

3.2.1Real-resource compliance costs:

These direct costs are the principal component of total social costs and are associated with:

(i) purchasing, installing, and operating new pollution control equipment,

i) changing the production process by using different inputs or different mixtures of

inputs,

ii) capturing the waste products and selling or reusing them. (The last two options

can actually result in negative compliance costs.)

These real-resource costs should also include unpriced resources that have opportunity costs

associated with them, such as unpaid labor diverted from other productive uses, and extra

administrative costs associated with compliance. However, the pre-tax compliance costs do not

include any transfers, such as emissions taxes, licensing fees, or subsidies (which are included in

the firm's private costs).

3.2.2 Government regulatory costs:

These include the monitoring, administrative, and enforcement costs associated with new

regulations. This also includes the cost of setting up a new market when incentive based

regulations are established, such as tradable permits.


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3.2.3 Social welfare losses

These are the losses in consumer and producer surpluses associated with the rise in the price (or

decreases in the output) of goods and services that occurs as a result of an environmental policy.

3.2.4 Transitional costs:

These include the value of resources that are displaced because of regulation induced reductions

in production, and the private real-resource costs of reallocating those resources. Offsetting these

costs, in theory, are regulation induced increases in resource use in both primary and related

markets (e.g., more workers and equipment are needed for pollution control).

3.2.5 Indirect costs:

These other costs include the adverse effects policies may have on product quality, productivity,

innovation, and changes in markets indirectly affected by the environmental policy, all of which

may have impacts on net levels of measured consumer and producer surplus.

3.3 An Illustration of Social Costs and Externalities

Exhibit 8-1 illustrates an externality (pollution) associated with the production of a good or

service (Q). In this figure:

i) MR is marginal revenue from selling the good;

ii) MPC is the marginal private real-resource cost of production;


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iii) MSD is the marginal social damage from pollution associated with production; and

iv) MSC is the total marginal social cost of supplying the goods.

The producer operates where marginal revenue (MR) equals marginal private real-resource costs

(MPC), so it produces Q1 items at a price of P1 per item. In this example, the producer also is

assumed to impose a social cost on society due to pollution associated with its production of Q.

Here the actual pre-policy total social cost of supplying the good is measured by the marginal

private real resource cost (MPC) plus the marginal social damage (MSD, also known as an

externality) caused by pollution. Together the MPC plus the MSD gives the true marginal social

cost (MSC) of supplying the good.

Fig. 1 Producer and Consumer Surplus with an External Cost

The producer surplus is indicated by the area of triangle P1GP3 and the consumer surplus is

measured as the area of triangle P1GP4, but the total social damage is indicated by the area of


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P3GF P2. Therefore, the deadweight loss to society (DWL) is equal to the area of triangle EFG.

If producers have to pay for the damage caused by the pollution, their producer surplus is

reduced to area of triangle P2HP1 minus the area of triangle HGF. In this case the firm would be

making negative profits since the area of triangle HGF is larger than their producer surplus. Net

social welfare in this case would be the area of triangle P2EP4 less the area of triangle EFG (the

deadweight loss).

If, however, the optimal amount of the product is produced (i.e., where MR equals MSC), then

the firm's output is Q* at a price of P*. In this case, consumer surplus is equal to the area of

triangle P4EP* and producer surplus is the area of triangle P2EP*. Since there is no deadweight

loss to society, net social welfare has increased and is equal to the area of triangle P2EP4.

Suppose that producers can do nothing to reduce the pollution damages other than decrease the

amount of output supplied. If the government places a tax equal to the MSD on each unit of

pollution, this would increase private production costs (but not private real-resource costs) by the

amount of the MSD, which would cause a rise in consumer (taxpayer) welfare. This occurs

because of the reduction in adverse health effects. Depending on the revenue policy of the

government, it could lead to a possible reduction in consumer taxes, since producers are now

paying an additional tax. Although there is a decrease in the producer surplus (and the obvious

consumer surplus), the overall social welfare has increased because of the reduction in the

externality costs.2 Adding all of these surplus changes together, and subtracting the transfers to

the government (i.e., taxes), yields the net social cost of the policy.

If instead of an emissions tax, a firm is required to install pollution control devices, the private

compliance costs will raise the firm's supply curve (or MPC) up by the amount spent on the new


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equipment. Under a permit system, where a set number of permits are issued for each unit of

pollution, and firms are allowed to buy and sell these permits, then each firm will consider

buying permits if the private cost of a permit is less than the unit cost of reducing pollution.

Conversely, a firm that can reduce its pollution by less than the cost of a permit will consider

selling its "extra" permits. In both cases, the firms' MPC curves will shift up by the price of the

permits, just as it did in the case of an emissions tax.

3.4 General Approach to Social Cost Analysis

The challenge in developing an estimate of the social cost of an environmental policy is to

consider the market(s) being affected by the policy, assess the available data and analytic

methods, and adopt an analytic approach that will yield an estimate suitable for use in the

benefit-cost analysis. An important requirement in measuring social costs is to characterize the

supply and demand equations of the regulated market or behavior. This section briefly reviews

the estimation of supply and demand equations and their relevance to social cost, but

concentrates on the variety of social costs that may be encountered from different types of

environmental policies:

i) direct social costs,

ii) transitional costs, and

iii) Indirect costs.


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Finally, some other issues that arise in characterizing and presenting social costs are examined,

including discounting, difficulties in monetizing costs, consideration of sensitivity analyses, and

simplifying market effects.

3.3.1Estimating the Supply and Demand Equations of All the Affected Markets

Empirical estimates of the supply and demand curves for each market are usually needed to

calculate the social costs of proposed regulations and policies. In addition to private sources,

government reports and academic studies can provide useful information needed to estimate the

equations that govern market supply and demand may be time and resource intensive, in addition

to the formidable tasks of developing the means to structure and compute the considered models.

While many types of markets have been researched in detail by the academic community, others

may be too new to have much information available. It may be difficult to obtain data from the

affected firms or industries because of confidentiality provisions or the proprietary nature of

some data and models. Achieving sufficiently reliable results will often depend on the quality of

the data, and overcoming problems with data will be a primary hurdle in many social cost

analyses.

3.3.2 Definition of Elasticity

In general, economists use the term "elasticity" to refer to the sensitivity of one variable to

changes in another variable. The price elasticity of demand (or supply) refers to changes in the

quantity demanded (or supplied) that would result from a change in the price of a good or

service. Changes are measured assuming all other things, such as incomes and tastes, remain

constant. Demand and supply elasticities are rarely constant and often change depending on the


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quantity of the good. Therefore, when calculating elasticities, it is important to state the price and

quantity of the good.

"Elastic" demand (or supply) indicates that a small percentage increase in price results in a larger

percentage decrease in quantity demanded (or supplied). How much of the price increase that

will be passed on to consumers is determined by the elasticity of demand relative to supply (as

well as the degree of competition within the industry and existing price controls). All other

things equal, an industry facing a relatively elastic demand is less likely to pass on costs to the

consumer because increasing prices will result in reduced revenues.

3.3.3 Determinants of Supply Elasticities

The elasticity of supply depends, in part, on how quickly costs per unit rise as firms increase

their output. Among the many variables that influence this rise in cost are:

i) the availability of close input substitutes;

ii) the amount of time available to adjust production to changing conditions;

iii) the degree of market concentration among producers;

iv) the expected future price of the product;

v) the price of related inputs and related outputs; and

vi) the speed of technological advances in production that can lower costs.

Supply elasticity will tend to increase over time as firms have more opportunities to renegotiate

contracts and change production technologies.

Characteristics of supply in the industries affected by a regulation can be as important as demand

characteristics in determining the economic impacts of a rule. For highly elastic supply curves, it


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is likely that costs will be passed through to consumers. The main determinants of industry

supply curves are the structure of costs and the time period of the analysis. Industry supply

curves are defined as the aggregation of the supply curves of individual firms within an industry.

If detailed financial profiles of individual establishments or categories of establishments and

production data are available, they can be used to define an industry supply curve. Explicit

information on the cost structure of an industry is very useful in predicting impacts more

precisely than is possible using industry average data. A given firm may experience significant

impacts if it is already a relatively high cost producer. Such firms would be more vulnerable to

closure if subjected to high compliance costs.

3.3.4 Obtaining Supply and Demand Elasticities

Elasticity estimates may be obtained from existing literature or from original research. The use

of published estimates avoids the time and expense of gathering the necessary data. Sources for

published estimates include previous agency rule makings or relevant studies found in the

economics literature. The analyst will have to employ careful judgement in deciding whether and

how to use elasticity estimates from previous studies. Estimates should be drawn from studies

based on:

i) values of independent variables are non-stochastic or fixed;

ii) expected mean value of the error term is zero;

iii) expected value of the variance of the error term is constant;

iv) no correlation exists between error terms; and

v) no correlation exists between error terms and independent variables.


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If any of these conditions are violated, the analyst will have to make a corrective adjustment to

the OLS or consider an alternative econometric technique. For example, if one of the

independent variables is endogenous, the first and last condition will be violated, resulting in a

biased and inefficient coefficient estimate. In the context of estimating a demand function, the

price variable is likely to be endogenous, which would render the coefficient estimate and

derived elasticity incorrect. A method known as two-stage least squares (TSLS) represents one

means of accounting for endogeneity. The number of potential econometric approaches,

mathematical requirements, and corrective measures is beyond the scope of this guidance

document. Analysts should consult relevant texts for a more thorough discussion of all of these

issues.

3.3.5 Uses and Substitutes Analysis

A "Uses and Substitutes Analysis" may provide useful information on the characteristics of

demand as a supplement to or substitute for elasticity estimates. This is "...an in depth

examination of each significant use of the substance in question, and an assessment of the costs,

performance, and useful life of substitutes, on a product-by-product basis."7 A "Uses and

Substitutes Analysis" includes four steps:

1) define markets and segments of markets that are relatively homogeneous;

2) assess the cost and performance characteristics of the products in question;

3) identify the most appropriate substitutes; and

4) estimate the incremental costs and performance characteristics of the substitutes in each


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specific application.

The results of the analysis can then be used to generate demand functions, based on the price at

which substitute products become economical for different uses. This analysis can be time and

information intensive and may produce relatively crude results. It is nonetheless a useful

alternative to estimating demand functions when elasticities are not available.

3.3.6 Determinants of Demand Elasticity

Among the many variables that affect the elasticity of demand are:

i) the availability of close substitutes,

ii) the percentage of income a consumer spends on the good,

iii) how necessary the good is for the consumer,

iv) the amount of time available to the consumer to locate substitutes,

v) the level of aggregation used in the study, and

vi) the expected future price of the good.

In this section, only the first four will be discussed.

i) The availability of close substitutes is one of the most important factors that

determine demand elasticities. A product with close substitutes tends to have an

elastic demand, because consumers can readily switch to substitutes rather than

paying a higher price. Therefore, a company is less likely to be able to pass through

costs if there are many close substitutes for its product.

ii) Whether the affected product represents a substantial or necessary portion of

customers' costs or budgets is another factor that affects demand elasticities. When


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price increases occur for products that represent a substantial portion of downstream

producers' costs or consumers' budgets, these producers or consumers may be more

likely to seek alternatives. Where the product subject to the price increase is less

important in customers' budgets, customers may be less motivated to use substitutes

(even if they are available) or to forego consumption entirely. A similar issue

concerns the type of final good involved. Reductions in demand may be more likely

to occur when prices increase for "luxuries" or optional purchases than for basic

requirements.

iii) The time frame considered is another important factor in determining elasticity.

Elasticities tend to increase over time, as firms and customers have more time to respond to changes

in prices. A company facing an inelastic demand curve in the short run may experience greater

losses in demand in the long run, as customers have time to make adjustments that allow use of

substitutes or as new substitutes are developed. It is important to keep in mind that elasticities differ

at the firm versus the industry level. For example, if twenty companies are producing pesticide

formulations that are equally effective, each firm may face an elastic demand curve because of

competition within the industry, although the industry as a whole may face an inelastic demand

curve for its products as a group. In this example, it would not be appropriate to use an industry-level

elasticity to estimate the ability of only one firm to pass on compliance costs when its competitors

are not subject to the same costs.

3.3.7Determinants of Supply Elasticity

The elasticity of supply depends, in part, on how quickly costs per unit rise as firms increase

their output. Among the many variables that influence this rise in cost are:


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i) the availability of close input substitutes;

ii) the amount of time available to adjust production to changing conditions;

iii) the degree of market concentration among producers;

iv) the expected future price of the product;

v) the price of related inputs and related outputs; and

vi) the speed of technological advances in production that can lower costs.

Supply elasticities will tend to increase over time as firms have more opportunities to

renegotiate contracts and change production technologies.

Characteristics of supply in the industries affected by a regulation can be as important as

demand characteristics in determining the economic impacts of a rule. For highly elastic supply

curves, it is likely that costs will be passed through to consumers. The main determinants of

industry supply curves are the structure of costs and the time period of the analysis. Industry

supply curves are defined as the aggregation of the supply curves of individual firms within an

industry.

If detailed financial profiles of individual establishmentsorcategories of establishments and

production data are available, they can be used to define an industry supply curve. Explicit

information on the cost structure of an industry is the speed of technological advances in

production that can lower costs.

3.3.8 Obtaining Supply and Demand Elasticities

Elasticity estimates may be obtained from existing literature or from original research. The use

of published estimates avoids the time and expense of gathering the necessary data. Sources for

published estimates include previous agency rule makings or relevant studies found in the


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economics literature. The analyst will have to employ careful judgement in deciding whether

and how to use elasticity estimates from previous studies. Estimates should be drawn from

studies based on:

i) similar market structure and level of aggregation;

ii) sensitivity to potential differences in regional elasticity estimates;

iii) current economic conditions; and

iv) appropriate time horizon (i.e., short or long run).

This is not an exhaustive list of issues which must be considered in applying existing estimates to

new analyses. There are a number of statistical and technical issues that may influence the

quality of elasticity estimates. Relevant texts cited below should be consulted and technical

assistance sought when necessary.

New or original estimates of elasticities are derived from demand and supply functions for goods

or services that have been estimated using econometric methods.

Econometrics is the use of statistical analysis in applied economic research. For example, the

demand for a good or service is often estimated as a function of its price, the price of related

goods (substitutes and complements), consumer demographic characteristics, as well as variables

that may represent institutional or technological characteristics of a market. Supply and demand

elasticities may be derived from a variety of functional forms that embody various assumptions

about the relationships between the data. Methods of calculating elasticity estimates differ

according to the specification of the function. The analyst should consult relevant texts and seek

technical assistance.


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The availability of sufficient data, both in terms of quantity and quality, is the first threshold that

determines whether econometric tools can be used. Only with sufficient data can elasticity

estimates be considered reliable. The analyst should carefully document data sources. Once the

decision to employ econometrics is made, there are a number of issues which the analyst must

address, including the choice of an appropriate modeling technique, proper functional form, and

ensuring that the mathematical properties required for the chosen technique to yield proper

results are achieved. For example, ordinary least squares (OLS) requires that:

i) values of independent variables are non-stochastic or fixed;

ii) expected mean value of the error term is zero;

iii) expected value of the variance of the error term is constant;

iv) no correlation exists between error terms; and

v) no correlation exists between error terms and independent variables.

If any of these conditions are violated, the analyst will have to make a corrective adjustment to

the OLS or consider an alternative econometric technique. For example, if one of the

independent variables is endogenous, the first and last condition will be violated, resulting in a

biased and inefficient coefficient estimate. In the context of estimating a demand function, the

price variable is likely to be endogenous, which would render the coefficient estimate and

derived elasticity incorrect. A method known as two-stage least squares (TSLS) represents one

means of accounting for endogeneity. The number of potential econometric approaches,

mathematical requirements, and corrective measures is beyond the scope of this guidance

document. Analysts should consult relevant texts for a more thorough discussion of all of these

issues.


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3.3.9 Uses and Substitutes Analysis

A "Uses and Substitutes Analysis" may provide useful information on the characteristics of

demand as a supplement to or substitute for elasticity estimates. This is "...an indepth

examination of each significant use of the substance in question, and an assessment of the costs,

performance, and useful life of substitutes, on a product-by-product basis."7 A "Uses and

Substitutes Analysis" includes four steps:

1) define markets and segments of markets that are relatively homogeneous;

2) assess the cost and performance characteristics of the products in question;

3) identify the most appropriate substitutes; and

4) estimate the incremental costs and performance characteristics of the substitutes in each

specific application.

The results of the analysis can then be used to generate demand functions, based on the price at

which substitute products become economical for different uses. This analysis can be time and

information intensive and may produce relatively crude results. It is nonetheless a useful

alternative to estimating demand functions when elasticities are not available.

3.4 Determining the Different Types of Social Costs

Having established measures of supply and demand, the analysis then considers how equilibrium

price and quantities will change from measured baseline conditions.


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Social cost changes in each of the affected markets are assessed by examining the direct,

indirect, and transitional effects that occur as a result of the new policy. The types of social costs

that need to be examined to determine how the supply and demand equations change are

summarized, with examples in Table 2.1. A short description of direct costs, which include

private and public compliance costs, government regulatory costs, and other types of

social costs, is presented. Other social costs less routinely included in empirical analyses of

social costs, including indirect costs and the transitional costs, are then reviewed.

3.4.1 Direct Social Costs

The direct social costs of a new environmental policy arise from:

i) changes in the private real-resource compliance costs,

ii) additional government regulatory costs,

iii) social welfare losses, and

iv) transitional social costs. The largest fraction of direct social costs arises from the

real resource compliance costs due to the new regulation.

These new compliance costs arise from the installation, operation, and maintenance of new

capital equipment, or are a result of changes in the production process that raise the price of

producing the good.

The additional compliance costs can be used to estimate the new equilibrium price and quantity

in the affected markets which will change social welfare. However, these changes will affect

other markets, resulting in further price and quantity changes in other goods, giving rise to

additional changes in social welfare. The significance of the changes in other markets will


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influence the type of model necessary for the economic analysis. Changes in social welfare also

result from increased government regulatory costs and transitional costs from plant closures and

unemployment.

Private real-resource compliance costs can arise from:

i) the capital costs associated with the purchase, installation, operation, and

maintenance of new pollution control equipment,

ii) changes in the inputs or mixtures used in the production process, or

iii) the capture of waste products that can either be disposed of, sold, or reused.

Real-resource costs are theoretically straightforward to calculate if they arise from the purchase

of new pollution control equipment. For example, having information on the number of factories

and the price of purchasing and operating new equipment required to meet a policy would

provide a means of estimating the compliance costs for the industry. However, since all factories

are not identical, costs may be estimated based on cost studies of representative factories chosen

by random sampling procedures, which can be extrapolated to the universe of affected factories.

Additional costs involve the operating expenses, maintenance, and training associated with the

new equipment. Further costs may occur from maintenance changes in other equipment. Also,

additional administrative costs may be associated with obtaining permits and preparing required

monitoring reports. In the two other methods of compliance, the private costs may actually be

negative and thus need to be included for an accurate estimate of social costs.

When waste products are captured and then disposed of, sold, or reused, the cost calculation is

also straightforward. Disposal charges are easily determined and the selling price of the waste


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product (if it is used as an input for other goods) can also be obtained. However, if the

production process is changed so that different inputs are used or the mixture of the inputs is

altered, the costs involved will be difficult to determine before the change takes place. In

addition, the changes may be considered proprietary information. Government regulatory costs

are incurred by federal, state, or local governments to administer and enforce new policies.

Government regulatory costs include: administration, training, monitoring/reporting

(if they are not included in compliance costs), enforcement, litigation, and the cost of developing

and distributing permits. These incremental costs must be financed through additional taxation or

other governmental financing mechanisms. Because they are hard to translate into producer and

consumer surplus terms, governmental administration and enforcement costs are typically

examined in terms of their dollar costs and staffing requirements (expressed as full-time

equivalent employment (FTEs)). Ultimately, these costs are borne by taxpayers unless other

administrative costs are reduced to accommodate a new policy. Since government costs are

usually small compared to the explicit compliance costs, they are not usually included in partial


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Social Cost Category Examples

Real-resource Compliance Costs • Capital costs of new equipment

• Operation and maintenance of new equipment

• Waste capture and disposal, selling, or reuse

• Change in production processes or inputs

• Maintenance changes in other equipment

Government Sector Regulatory Costs • Training/administration

• Monitoring/reporting

• Enforcement/litigation

• Permitting

Social Welfare Losses• Higher consumer and producer prices

• Legal/administrative costs

Transitional Social Costs • Unemployment

• Firm closings

• Resource shifts to other markets

• Transaction costs

• Disrupted production

Source: Adapted from Harrington et al. (1999).

equilibrium models. However, if they are significant, they should be estimated separately and

added to the surplus-based social cost estimates. Monitoring and enforcement costs, incurred by

the government, can be either (1) the opportunity costs of other activities that are discontinued


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because of fixed government budgets, or (2) the private costs imposed on taxpayers to support

the increased government expenditure necessary for the program. The costs of government

monitoring and enforcement efforts are normally based on the cost of necessary administrative

activities.

Social welfare losses occur when real-resource compliance costs result in higher prices for the

good or service and when additional government regulatory costs result in higher taxes passed on

to the consumer. New regulations may lead to increased legal and administrative costs for the

government, as well as for the regulated entities. The change in social welfare resulting from an

increase in taxes or fees assessed in order to pay for government regulatory

costs will typically be small relative to social welfare losses attributable to the real-resource

compliance costs.

If the imposition of real-resource compliance costs leads to an increase in the price of the good,

this will lead consumers to either buy less or switch to substitutes, thereby leading to a fall in the

consumer surplus. The amount of the private costs passed through to the consumer is determined

by the market structure, and the elasticities of demand, supply, and income. Once the prices,

quantities, and elasticities are known, the process of calculating changes in producer and

consumer surpluses is also theoretically straight forward.

If the imposition of real-resource compliance costs leads to an increase in the price of the good,

this will lead consumers to either buy less or switch to substitutes, thereby leading to a fall in the

consumer surplus. The amount of the private costs passed through to the consumer is determined

by the market structure, and the elasticities of demand, supply, and income. Once the prices,


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quantities, and elasticities are known, the process of calculating changes in producer and

consumer surpluses is also theoretically straightforward.Transitional effects vary depending on

the length of the time period examined; therefore, social cost analyses should be explicit about

the time frame being studied. In the short run, the private annualized costs of compliance, both

for consumers and producers will be higher relative to the annualized long-run costs. This is

because the short run analysis will not provide for possible adjustments in the production

process, or allow consumers to find substitutes. Some workers may become unemployed in the

short run, but will almost certainly find other jobs in the long run.

However, over time the impact of a policy can easily spread out to a variety of markets and result

in a number of unanticipated adverse effects. Therefore, it is not always appropriate to assume

that social costs arising in the short run as a consequence of transitional effects will be resolved

in the long run. For EPA economic analyses, the four transitional effects most frequently

considered include:

i) plant closings and resultant unemployment,

ii) resources shifting to other markets,

iii) transactions costs associated with setting up incentive-based programs, and

iv) disruption of production.

Firm closings and unemployment:

In the simplest static models, the time frame is assumed to be a period of time in the near future

(e.g., the first year after a new policy is promulgated). Surplus-based measures of social cost are

therefore short-run estimates. But as time passes, adjustments are likely to occur. Workers who


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suffer transitional unemployment will usually find new jobs, and new plant and equipment

installed in the future might require relatively less costly pollution control. These long-run

changes should be considered as the yearly social costs of a policy are calculated into the future.

In most cases, involuntary unemployment and plant closings are consequences that are difficult

to model using a conventional partial equilibrium framework (which will be discussed in the

following section on modeling tools). Predicting these specific consequences would require far

more detailed analysis and data than are usually available for practical assessments.

Unemployment rates for each group of workers, the duration of unemployment, and the cost of

job training programs are just some of the factors that need to be taken into account when

estimating how the transitional costs decline over time. These temporary effects are typically

assessed and reported as part of an "economic impact" of the policy, and are incorporated into

the development of the social cost section of an economic analysis.

Shifts of resources to other markets:

These shifts occur when the payments to factors of production (labor, land, and capital) are

reduced. These shifts are partly responsible for the decreased output level of the product or

service. Those that remain earn less than before, at least in the short run, which is reflected in the

lower net price received by producers for the good or service. Some of the resources no longer

employed in producing this good or service might even become unemployed for a while, such as

labor, or be permanently and prematurely scrapped, such as plant and equipment. These and

other real world phenomena can change the position and slope of the supply functions in other

markets. Likewise, consumers of the product either pay more for thesame good or purchase


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substitutes that are less suitable or more costly, which can change the position and slope of

several demand functions.

Transaction costs:

These costs are encountered with incentive-based policies, such as with a tradable permits

program. A market must be established so that the efficiency gains from trading permits are

maximized, and rules for trading are developed that enable the market to function under the rules

of perfect competition. Therefore, initial short-run costs associated with setting up the market

will be high, but are expected to diminish over time as the created

market begins to function with less government oversight. The private cost of buying and selling

permits will then become similar to the purchase of any other resource needed to produce a good

or service.

Disruptions in production:

This may take place when new equipment is installed or new production processes or inputs are

applied. These costs can be estimated as the amount of time the production line is stopped or

slowed down to allow for the necessary changes to comply with the new policy regulations.

However, if the changes are made during previously scheduled down-time or required

maintenance, then downward adjustments should be made to the estimated costs to reflect this.

To conclude, in many cases transitional costs are considered to be small enough that their

inclusion in the overall social cost estimate would not appreciably alter the quantitative

conclusions. However, when these are expected to be significant, the costs should be estimated.

For example, lost wages and job search costs during the time workers are unemployed can be


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used as a proxy for this transitional social cost. Similarly, the value of prematurely retired plant

and equipment can be calculated and added to the plus-based social cost estimates to capture this

transitional effect, as long as this is not reflected already in thesupply and demand framework.

3.4.2 General Equilibrium (Indirect) Effect

Other possible components of social costs, such as effects on product quality, productivity,

innovation, and market structure, can require fairly complex dynamic models to quantify.

Although most individual regulatory policies will not have such dramatic effects, these costs can

be quite significant in certain instances, such as when a policy's requirements delay industrial

projects or affect new product development. Such policy effects have implications for future

social costs but are difficult to measure and express in social cost terms. However, an effort

should be made to qualitatively describe these factors and look at approaches that can quantify

these effects when data and resources can support this level of detailed analysis of social costs.

Changes in market structure may occur if the expense of pollution control is sufficiently high

that it drives out enough firms to cause changes in the market concentration and competitiveness

of firms remaining in the industry. Such a change often results in shifts of both firm and industry

supply curves, which can lead to changes in output and prices in several markets affecting both

producer and consumer surpluses..

Labor and capital productivity may decrease under new regulations. For example, the

administrative costs of monitoring emissions and filing reports with regulatory agencies may

require firms to hire more workers whose labor does not increase productivity (as measured by

labor employed relative to produced output). Pollution control devices or restrictions on the use


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of products may cause lower levels of output relative to unconstrained production processes. For

example, placing restrictions on pesticide use may reduce the yield of crops susceptible to pest

damage, holding other factors of production (e.g., labor, fertilizer) constant. In each case,

however, private costs are captured by changes in the supply and demand curves of the product,

and therefore care should be taken to insure that social costs associated with productivity losses

are not double counted with other social cost estimates.

Discouraged investment may occur if research and development funds are reallocated to meet

additional compliance costs. This may result in decreases in technological innovation and

product quality. The latter can be modeled as the reduced amount consumers are willing to pay

for the low quality good, relative to what they were willing to pay for the original, higher quality

good. In practice, changes in technological innovations are not commonly analyzed in most

economic models used in benefit-cost analyses of individual regulations and policies.

3.4.3 Other Issues Arising in Presentation of Social Costs

Four additional issues to note arise in the organization and presentation of social costs, several of

which have also been raised earlier in this document in connection with the measurement of

social benefits. These issues discussed here on social costs include:

i) discounting,

ii) difficulties valuing some social cost categories,

iii) conducting sensitivity analysis

iv) simplifying market effects.


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Discounting:

For purposes of computing the social costs of environmental policies, costs should be discounted

using the methods and social discount rates discussed in the chapter. This is the case regardless

of the methods used to estimate social costs. Social costs can be estimated in detail year-by year,

or estimated using growth rates, or merely assumed to be constant. These streams of social costs

can then be adjusted to yield: (1) discounted present value, (2) future value, or (3) the annualized

cost of the policy. All three approaches are different ways to express the same concept and

choosing which method to present the results will depend on the method that most effectively

allows comparisons among the options and the measurement of net benefits.

Difficulties of valuing social costs:

Some consequences of environmental policies are difficult to represent in the definitive,

quantitative terms of conventional social cost analysis. Irreversible environmental impacts,

substantial changes in economic opportunities for certain segments of the population, social costs

that span very long time horizons, socioeconomic effects on communities, and poorly understood

effects on large-scale ecosystems are difficult to summarize in a quantitative benefit cost

analysis. Some alternative techniques for measuring and presenting these effects to policy

makers are reviewed in section 7.6.3 of the benefits chapter that discusses measuring ecological

benefits. The relative significance of social cost categories that are not quantified—or are

quantified but not valued—should be described in the analysis.Sensitivity analysis: The estimates

in the social cost analysis will not be known with certainty. In fact, some data and models will

likely introduce substantial uncertainties into the estimations of social costs. Numerous

assumptions are made in regard to the baseline, predicting responses to policy, and the number of


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affected markets. Therefore, the conclusions drawn in the benefit-cost analysis will be sensitive

to the degree of uncertainty present and the assumptions that were made. Reporting the

uncertainty of the data, the assumptions used, and how the uncertainty and assumptions affect the

results are important components of the presentation of social cost.

Simplifying market effects:

Given the complexity of modern economies, measuring and predicting all of the consequences of

a particular action would involve a significant effort. The central question explored in this

section is whether some or all markets indirectly affected by a policy must be analyzed to obtain

a measure of social costs suitable for a benefit-cost analysis, or whether the calculation of social

costs can be limited to an assessment of the directly affected markets without introducing

unacceptable biases and errors into the analysis.

In general, the social cost of a policy can be measured exclusively by changes that occur in the

markets directly targeted by a policy, as long as significant net changes in social welfare are not

generated in indirectly affected markets. If price changes in other markets generate both gainers

and losers among the producers and consumers, then they may offset each other in a social cost

analysis as transfers. However, if there are strong reasons to believe that conditions in other

related markets might generate important net social welfare consequences, these should be

examined. If a policy indirectly increases or decreases the quantity of a good that is consumed,


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whose production or consumption involves an externality, then this results in net social welfare

effects that may be worth considering when calculating total social costs (and benefits).

3.5 Modeling Tools

The following section first focuses on the basic framework common to all models used to

estimate social costs, while the remaining sections examine the models commonly used: (1)

direct compliance cost methods, (2) partial equilibrium models, (3) multi-market models, and (4)

computable general equilibrium models. used:

3.5.1The Basic Framework

Benefit-cost models must predict what actions firms are likely to choose when attempting to

comply with a new policy and what the compliance costs of those actions will be. Normally,

these are based on engineering or process cost models that examine firms' alternative compliance

methods. Engineering cost estimates typically specify the capital, operating, and maintenance

costs that are likely to occur in adopting different pollution control strategies.

When possible, these initial engineering cost estimates should include the expected level of

compliance costs, as well as reasonable lower and upper bounds for purposes of sensitivity

analysis.

In addition to the preliminary engineering or other estimates of the social costs of various

compliance strategies, other costs may be significant. As noted earlier, for some market-based

approaches, transaction costs can often be substantial. For example, when setting up the market

for a permit trading system, determining how many permits to purchase or sell can involve

detailed cost modeling and forecasting, in addition to the social costs associated with


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operating the trading system. When these costs are likely to be significant, they should be

estimated in addition to the basic private real-resource costs of capital and the operating costs of

alternative compliance methods.

3.5.2 The Direct Compliance Cost Method

In some cases, social costs are estimated using the direct compliance cost method. This is the

simplest approach used in estimating social costs. Under this approach, the social cost for a

policy is simply set equal to the initial engineering or other compliance cost estimates for the

compliance options the firms are likely to adopt; no additional modeling is undertaken. If only

compliance costs are calculated, the private (compliance) costs are likely to be overestimated.

This is because private costs are computed for the pre-policy level of output under the implicit

assumption that there is no substitution away from the affected products or activities into other

relatively less expensive ones. That is, firms do not make any capital orlabor adjustments in their

production processes. In addition, when the resulting changes in consumer surplus are calculated

at the new higher prices, consumer welfare losses are also likely to be overestimated since

changes in consumer behavior will not be taken into account.

Nevertheless, using direct compliance costs as an approximation of actual social costs may be

reasonable for a policy when price and quantity changes are small, and there are few indirect

effects. However, if consumers can easily switch to substitute goods, this adjustment will make

the actual social cost of the policy significantly less than indicated by the direct compliance cost

estimates. Likewise, if firms can find less costly substitutes for their inputs or production


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processes, which have been made more expensive by the new regulations, then compliance costs

will be an overestimate of the actual social costs.

3.5.3 Partial Equilibrium Analysis

Because of the limitations of using direct compliance costs as a measure of social costs, an

alternative approach is to model the economic effects of these compliance costs on producers and

consumers using a partial equilibrium supply and demand model of the affected markets. This

allows for a more complete analysis of social costs and their incidence. "Partial" equilibrium

refers to the fact that the supply and demand functions are modeled for just one or a few isolated

markets and that conditions in other markets are assumed either to be unaffected by a policy or

unimportant for social cost estimation. For example, if using a partial equilibrium supply and

demand framework, a new environmental policy that increases production costs will cause a

change in the supply function. The demand function, the old and new supply functions, prices,

and quantities can then be used to compute changes in producer and consumer surpluses. If the

relevant markets are evolving over time, this technique can be applied in each future time period

using new supply and demand functions. This makes it possible to estimate the changing

distribution of social costs over time.

The practical difference between the results of the partial equilibrium supply and demand-based

modeling and the direct compliance costs approach depends on the nature of the policy and the

magnitude of its effects. For small compliance costs, price and quantity movements are likely to

be minimal, so the social cost estimates derived from the partial equilibrium model framework


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will not be significantly different from the results obtained from the directcompliance cost

method.

For policies with larger compliance costs, price and quantity movements could be more

substantial. The estimated social costs using the supply and demand framework in these cases

may be considerably less than those suggested by the simpler direct compliance cost approach.

Moreover, policies that effectively ban products or activities cause the loss of all producer and

consumer surpluses in these markets. Therefore, it is difficult to calculate social costs of these

policies without an explicit supply and demand framework. Analyzing the effects of a policy

using a partial equilibrium model of the directly affected markets is appropriate when the

ramifications in indirectly affected markets do not generate net social costs. It is also a

reasonable framework as long as the social costs imposed by a policy are small and do not

significantly alter other markets or produce measurable macroeconomic effects (e.g., changes in

national unemployment levels).

In most cases, a conventional partial equilibrium framework comparing the pre-policy baseline

with the expected results of a new environmental policy will suffice for an economic analysis.

For analyzing environmental policies that pose very large consequences for the economy,

computable general equilibrium modeling is an alternative technique that is particularly useful.

The partial equilibrium framework is a commonly used theoretical tool for modeling and

measuring the social costs of environmental policies. In theory, a variety of social costs can be

observed and calculated using this technique. Even transitional effects that result in short run

social costs, such as premature capital equipment retirement and relatively brief spells of

involuntary unemployment, can be modeled and estimated using this framework. Thus, the


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approach offers a theoretically sound, if limited, method for conceptualizing the consequences of

an environmental policy and measuring their social costs.

Deriving the supply and demand functions is the foundation of benefit-cost analysis and is

necessary in all economic models used to analyze social costs and benefits. However, because of

its importance and the uncertainties associated with estimating supply and demand functions, it

may be useful to evaluate key assumptions with sensitivity analyses and develop a range of

estimated social costs.

The typical analysis is performed assuming a competitive market, although unusual

circumstances may require relaxing this assumption. Even should competitive market conditions

fail to hold, partial equilibrium analysis can be adapted to analyze varying market conditions that

may more closely reflect real-world conditions. It is useful to indicate when social benefits or

social costs have been overestimated or underestimated because of biases caused by market

distortions. However, the principles underlying partial equilibrium analysis can serve as a useful

model to evaluate the real-resource costs of many of EPA's regulations

and policies. models are needed for regulatory policies that may have large economic effects on

several sectors of the economy.

3.5.4 Multi-Market Models

Multi-market models go beyond partial equilibrium analysis by extending the inquiry to more

than just a single market. Multi-market analysis attempts to capture at least some of the

interactions between markets. However, unlike the general equilibrium models discussed in the


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next section, multi-market models do not attempt to incorporate a representation of the entire

economy.

An example of the use of a multi-market model for environmental policy analysis is contained in

a report prepared for EPA on the regulatory impact of controls on asbestos and asbestos products

(EPA, 1989). The model developed for the study describes the interactions between the asbestos

fiber market and markets for the goods that use the fiber as an intermediate input. The collective

demands for final goods that use asbestos create a derived demand for asbestos fiber. The price

of the fiber is determined through the interaction between the demand and supply schedules for

asbestos. Changes in this price in turn influence the prices and demands for the downstream

goods.

The specification of the links between the input and output markets is especially important for

simulating alternative regulatory policies, including interventions in both the input market (caps

on the usage of asbestos fiber) and in the output market (bans on some of the goods that use

asbestos as an input), as well as combinations of the two.

The model was then used to compare the efficiency losses under various regulatory scenarios.

3.5.5 General Equilibrium Analysis

Although the use of a partial equilibrium or multi-market model may be appropriate when

policies are likely to affect a limited number of markets, they are not able to capture interactions

between a large numbers of sectors. Many environmental policies, such as energy taxes, can be

expected to impact a large number of sectors both directly where the policy is applied, and

indirectly through spillover and feedback effects on those and other sectors.


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A strength of general equilibrium models is their ability to account consistently for the linkages

between all sectors of the economy. Three types of general equilibrium models that have been

used for the analysis of social costs are input-output models, linear programming models, and

computable general equilibrium (CGE) models.

3.5.6 Input-Output (I/O) Models

The central idea underlying I/O analysis is that in modern economies, production activities are

closely interrelated. An input-output table represents the flow of goods and services through the

economy, usually measured as transactions occurring over the course of a year. In addition to the

primary factors of capital, labor, and land, most productive sectors use many different

intermediate inputs. In an I/O table, the column associated with a particular sector

lists the value of the individual intermediate and primary inputs consumed by that sector. The

row associated with an individual sector lists the value of that sector's output purchased as both

intermediate inputs and final demand. For each sector in a table, the column sum represents the

total costs of production and the row sum represents total expenditure on that sector's output. A

key feature of I/O tables is that, by definition, for every sector, total costs must equal total

expenditures during the year.

An I/O table can be turned into a simple linear model through a series of matrix operations. The

intermediate inputs matrix defines a matrix of technical coefficients, based on the assumption

that inputs to production are consumed in fixed proportions to output and that there are constant

returns to scale. The model is manipulated by making exogenous changes to the vector of final

demands. The model will then calculate how much of each of the intermediate goods is required


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to produce the new final demand vector. The sum of the intermediate inputs required plus final

demand is equal to total output for the year.

I/O models have a long history in environmental policy analysis. Leontief (1970) showed how it

was possible to augment the basic I/O model with an additional set of coefficients for pollution

generation and/or abatement.

When a set of pollution coefficients has been defined, an I/O model can then produce an estimate

of the quantity of pollution that would be generated along with a given amount of final demand

or total output. The quantity of pollution generated may be specified in either monetary terms (as

damages) or in physical units.

Some economic research firms use I/O models to provide upper bound estimates on price effects.

Others use I/O models to look at the related markets and their potential significance prior to

adopting a partial or general equilibrium model. The I/O approach has also been extended further

to include non-market, ecological commodities such as ecosystem services.

Although I/O models can be a useful as a consistency check or a first-order approximation, they

have a number of shortcomings that limit their applicability as a predictive tool:

1. Given that prices are normally assumed to be fixed and do not adjust to indicate

scarcity, there is nothing to ensure that the total demands generated by

manipulation of the model are consistent with the actual productive capacity of

the economy.

2. The fixed coefficients assumption leaves no scope for substitution of inputs in

production.


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3. Since there is no producer or consumer behavior built into I/O models, simulation

of policy interventions that would affect those agents is of limited value.

4. Because the construction of an input-output table is a costly and time-consuming

process, usually requiring a specialized survey, the application of input-output

analysis to environmental policy making will normally only be possible when an

appropriate table already exists. More importantly, since input-output tables are

used in linear programming and computable general equilibrium models, this last

shortcoming is shared by these models as well.

3.6.7 Linear Programming (LP) Models

I/O models are driven by exogenous changes in final demand. Since they do not contain an

objective function, I/O models are difficult to use for decision making among multiple

alternatives. However, it is possible to extend the basic I/O model into a LP model by

incorporating an explicit objective function and a set of inequality constraints.

In addition to the usual economic variables, the objective function may be specified to include a

number of environmental variables, such as the discharge of air or water pollutants.

The specification of multiple inequality constraints allows for a great deal of flexibility in the

application of LP model (because of this flexibility, EPA's Office of Air and Radiation has used

linear programming models for many years). Shadow prices generated in the dual

form of LP models have a limited relationship to market prices and may sometimes be useful as

indicators of the importance of the individual constraints. Sensitivity analysis can be conducted

by varying key parameters in the model.


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The flexibility in the specification of LP models is also something of a liability of the approach.

The problem is that the selection of the constraints used is often ad hoc and may influence the

model solution. As with many linear models, there is often a tendency towards unrealistic

solutions, such as excessive specialization in production or trade. Finally, the lack of realistic

consumer and producer behavior is carried over from I/O models.

3.6.8 Computable General Equilibrium (CGE) Models

As discussed in the previous sections on I/O and LP models, these approaches have

shortcomings that make them less than ideal tools for policy analysis in modern market

economies. In particular, in both I/O and LP models, the behavior of producers and consumers

does not reflect the independent optimizing behavior that is usually assumed to be a

characteristic of agents in a market economy.

Without the specification of realistic producer and consumer behavior, model-based policy

simulations will be unable to correctly account for the reactions agents may have to policies that

impact them. Computable general equilibrium (CGE) models incorporate more realistic

behavioral specifications of the agents into the model and are thus able to provide a better

laboratory for many types of policy analysis. CGE models have been used to analyze a wide

variety of policy interventions, including issues in public finance, international trade,

development, and increasingly, the environment.

Most policies meant to protect the environment, ranging from those relying on market-based

instruments, such as effluent taxes, to command and control regulations, induce changes in the

behavior of consumers and producers. These changes may occur directly where the intervention


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takes place or indirectly as the effects of the intervention are passed through the economy.

Because they focus on both trying to model more accurately the expected reactions of consumers

and producers to policy interventions and on the interactions between various actors in the

economy, for some problems CGE models may be the most appropriate tool for the analysis of

social costs. CGE models are particularly good at examining questions of static resource

allocation, such as the effects the imposition of a tax may have on sectoral output, income, and

employment. Under certain specifications, CGE models may also be useful for assessing impacts

on overall measures of economic performance, such as aggregate output, employment, and

various measures of welfare.

In almost all cases, CGE models start from the framework and data of an input-output table,

which provides a basic set of accounting identities for the production sectors. Producers are

assumed to maximize their profits through their choice of productive inputs, typically labor,

capital, and intermediate goods, and sometimes land. Consumers, or in many cases a

representative consumer, are assumed to maximize their utility by choosing their consumption

bundles, subject to a budget constraint. Although not usually specified as an optimizing agent,

most CGE models also include a government sector that collects a variety of taxes to pay for its

purchases of goods and services. The domestic demand for imports and the supply of exports are

determined based on the relative prices of domestic and foreign goods.

CGE models may be categorized across a number of dimensions. These can include

(1) the method by which the parameters of the model are specified (through calibration

or econometric estimation),


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(2) the time horizon of the model (static or dynamic), and

(3) the scope of the model (single- or multi-country). Most CGE models are calibrated to a

single base year, which is assumed to be in equilibrium. After the specification of a subset of

elasticities and other data obtained through a literature search (or using informed judgments) the

rest of the parameters can be determined by working backward from a social accounting matrix

(SAM) for the base year. An alternative to the calibration approach is econometric estimation.

General equilibrium econometric estimation allows models to incorporate the representation of

more sophisticated producer and consumer behavior than would normally be possible through

calibration. However, econometric estimation requires a consistent set of multi-sector time series

data and this data is usually not available for developing countries.

CGE models can also be differentiated by the time horizon of the analysis. The majority of CGE

models are "static," meaning that no explicit dynamics are incorporated and the time frame for

the attainment of a new equilibrium following a policy or external shock is indeterminate. In

conducting simulations, an exogenous shock is introduced or a variable, such as a tax rate, is

altered. The model is then allowed to search for a solution until a new set of prices is found

which again equilibrates the system. The new prices in turn determine a new set of factor

demands, outputs, and incomes. The values from this new solution are then compared with the

values from the original equilibrium. Dynamic models, on the other hand, incorporate an explicit

updating of time dependent variables, such as the labor supply, capital stock, technology, and

demand patterns. In conducting a simulation, a baseline case is first run with a given set of

assumptions about the time dependent variables. Next, an alternative or counterfactual

simulation is run with the same set of assumptions, but with a policy or external shock. The


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values resulting from the alternative solution are then compared with the original baseline. These

values may be compared at different points in time or discounted to estimate present values, or to

evaluate changes in welfare.

Another dimension along which CGE models may be classified is by scope:

(1) single country or single region models,

(2) multi-country or multi-region models, and

(3) global models encompassing all countries and regions.

Although models representing a single country or region are the most common, multi-country or

multi-region models are being developed in increasing numbers. Because trade is inherently a

multi-country phenomenon, multi-country models are generally the best suited for examining

issues that involve the flow of goods, services, and capital across national boundaries. CGE

models have been applied to an expanding array of environmental policy issues. Most recently,

they have been used for the analysis of policies designed to avert or slow global climate change,

such as those proposed in the Kyoto Protocol. Both single country and multi-country CGE

models have been used for these simulations, with multi country models able to assess policies

like global emissions trading. Because they are able to incorporate taxes and other existing

distortions, CGE models have been used to explore the potential for a "double dividend"—a

reduction in pollution plus a reduction in the inefficiencies of the tax system—from substituting

taxes on pollutants for pre-existing taxes on output, income, or wages. In addition, CGE models

have been used to perform retrospective analyses of the economic costs of a number of

environmental regulations.


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While CGE models have a number of advantages as tools for policy analysis, they also have

serious drawbacks:

i) Although the costs have been reduced in recent years, the construction of a CGE

model can be still be time consuming and expensive.

ii) In addition to an appropriate input-output table, a considerable amount of data on

national accounts, trade, elasticities, and environmental externalities must be

collected and made consistent with the sectors chosen to be part of the analysis.

iii) Dynamic models also require that forecasts be made for many exogenous variables.

Many environmental policies only affect a small part of what may be a highly aggregated

sector in an input output table. Sometimes it will be possible to separate these smaller sectors

out, but sufficient data is often not available at that level of detail.

3.7 Estimating the Social Costs of Alternative Policy Approaches

This section discusses the methods of estimating the social costs for several alternative

regulatory and non- regulatory policy approaches, which are divided into three categories:

i) direct controls,

ii) incentive-based controls, and

iii) voluntary actions taken to reduce environmental risks.

The discussion focuses on the significant features of each regulatory approach that must be

examined in either partial equilibrium, multi-market, or CGE models. In addition to the


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private compliance costs, transactions costs may be significant. Therefore, the associated

changes in the prices of goods and services will alter producer and consumer surplus and

must be calculated to estimate the total social costs. Independent of the method used, the

social cost analysis should explain how the uncertainties and assumptions in the data and

models affect the results. Since much of the data used is not known with certainty and many

assumption must be made to develop the necessary analytical models, social cost estimates

can never be known with total certainty. Another difficulty is that private (compliance) cost

bounds in one project may be based on the

intuition of a single engineer, but the private cost bounds in another sector may be developed

based on adequate data permitting the estimation of confidence intervals.

Aggregating these into a single study may conceal important uncertainties rather than

enlightening the decision making process.

3.7.1 Direct (or Standards Based) Controls

In general, direct or standards-based controls rely on different types of standards that

mandate a level of performance intended to achieve an environmental objective.

3.7.1.1 Technology Standards

Estimating the private compliance costs of standards-based regulations is relatively

straightforward compared to incentive-based approaches. Technology standards often require

Best Available Technology (BAT) or Best Practicable Technology (BPT). Since these

technologies already exist, their costs and the number of firms required to use themare often


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well documented. Additional compliance costs include expenditures on maintenance and

training costs associated with installing and operating the equipment.

However, estimating the private compliance costs is not always simple, especially for

proposed regulations. For example, unanticipated scaling effects, as well as unforeseen

bottlenecks in construction and implementation may occur, resulting in differences between

the anticipated bids for a project, the bids received, and the actual construction cost.

The private real-resource costs, when discounted over time, correspond to the sum of

investment costs and discounted annual costs (operating and maintenance and other annual

regulatory costs) that will be incurred by firms to comply with the regulation. Thus, the real

resource costs of regulation can be approximated, in most instances, by methodologies

routinely used by other EPA

ITQ

Mention five basic components of social cost.

ITA

The five basic components of total social costs are listed here in the general order of relative ease

of estimation, and hence inclusion, in most social cost analyses of environmental policies. They

include:

Real-resource compliance costs:

These direct costs are the principal component of total social costs and are associated with:

(ii) purchasing, installing, and operating new pollution control equipment;


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iii) changing the production process by using different inputs or different mixtures of

inputs;

iv) capturing the waste products and selling or reusing them. (The last two options

can actually result in negative compliance costs.)

These real-resource costs should also include unpriced resources that have opportunity costs

associated with them, such as unpaid labor diverted from other productive uses, and extra

administrative costs associated with compliance. However, the pre-tax compliance costs do not

include any transfers, such as emissions taxes, licensing fees, or subsidies (which are included in

the firm's private costs).

Government regulatory costs:

These include the monitoring, administrative, and enforcement costs associated with new

regulations. This also includes the cost of setting up a new market when incentive based

regulations are established, such as tradable permits.

Social welfare losses

These are the losses in consumer and producer surpluses associated with the rise in the price (or

decreases in the output) of goods and services that occurs as a result of an environmental policy.

Transitional costs:

These include the value of resources that are displaced because of regulation induced reductions

in production, and the private real-resource costs of reallocating those resources. Offsetting these


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costs, in theory, are regulation induced increases in resource use in both primary and related

markets (e.g., more workers and equipment are needed for pollution control).

Indirect costs:

These other costs include the adverse effects policies may have on product quality, productivity,

innovation, and changes in markets indirectly affected by the environmental policy, all of which

may have impacts on net levels of measured consumer and producer surplus.

3.8 Activity: Advanced Microeconomics 1V

Activity Timing

Allow: 10 minutes

Activity Text:

Meet a colleague and discuss methods of estimating social cost.

3.9 Summary of Study Session II


1 to define Social Cost

2 how to illustrate examples of social cost and externalities

3 how to discuss the general approach to social cost analysis

4 about model tools used in measuring social cost

5 to estimate social costs of alternative policy approach


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2.10 SAQ

1. SAQ (LO 1 & 2): Define Total Social cost

2. SAQ (LO 2): With the aid of a diagram explain consumer and producers’ surplus

with externalities.

3. SAQ (LO 3): What are the challenges in developing an estimate for a social cost

of environmental pollution?

4. SAQ (LO 4): What determines the usage of econometric tools in measuring social

costs?

5. SAQ (LO 5): Explain why Estimating the private compliance costs of standards-based

regulations is relatively easier as compared to incentive-based approach.

3.11 References

Arnold, F.S. 1995. Economic Analysis of Environmental Policy and Regulation. New York,

NY: John Wiley and Sons, Inc.

Dervis, K., J. de Melo, and S. Robinson. 1982. General Equilibrium Models for Development

Policy. New York, NY: Cambridge University Press.

Friedman, L. E. 1984. Microeconomic Policy Analysis.: New York, NY: McGraw-Hill


Friedman, L. E. 1984. Microeconomic Policy Analysis.: New York, NY: McGraw-Hill. .


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Solutions to SAQs

Study Session 1:

SAQ (LO I):

A production function can be defined as the specification of the minimum input requirements

needed to produce designated quantities of output.) Assuming that maximum output is obtained

from given inputs allows economists to abstract away from technological and managerial

problems associated with realizing such a technical maximum, and to focus exclusively on the

problem of allocative efficiency, associated with the economic choice of how much of a factor

input to use, or the degree to which one factor may be substituted for another. In the production

function itself, the relationship of output to inputs is non-monetary; that is, a production function

relates physical inputs to physical outputs, and prices and costs are not reflected in the function.

SAQ (LO 2) Stages of Production

In Stage 1 (from the origin to point B) the variable input is being used with increasing output per

unit, the latter reaching a maximum at point B (since the average physical product is at its

maximum at that point). Because the output per unit of the variable input is improving

throughout stage 1, a price-taking firm will always operate beyond this stage.

In Stage 2, output increases at a decreasing rate, and the average and marginal physical

product are declining. However, the average product of fixed inputs (not shown) is still rising,

because output is rising while fixed input usage is constant. In this stage, the employment of

additional variable inputs increases the output per unit of fixed input but decreases the output per


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unit of the variable input. The optimum input/output combination for the price-taking firm will

be in stage 2, although a firm facing a downward-sloped demand curve might find it most

profitable to operate in Stage 1. In Stage 3, too much variable input is being used relative to the

available fixed inputs: variable inputs are over-utilized in the sense that their presence on the

margin obstructs the production process rather than enhancing it. The output per unit of both the

fixed and the variable input declines throughout this stage. At the boundary between stage 2 and

stage 3, the highest possible output is being obtained from the fixed input.

SAQ ( LO 3)


The procedure for formulating different objective functions, in terms of the production model, is

introduced here. In the income formation from production the following objective functions can

be identified:

i) Maximizing the real income

ii) Maximizing the producer income

iii) Maximizing the owner income.

iv) Objective function formulations can be expressed in a single calculation which concisely

illustrates the logic of the income generation, the income distribution and the variables to

be maximized.

v) The calculation resembles an income statement starting with the income generation and

ending with the income distribution. The income generation and the distribution are

always in balance so that their amounts are equal. In this case it is 58.12 units. The


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income which has been generated in the real process is distributed to the stakeholders

during the same period. There are three variables which can be maximized. They are the

real income, the producer income and the owner income. Producer income and owner

income are practical quantities because they are addable quantities and they can be

computed quite easily. Real income is normally not an addable quantity and in many

cases it is difficult to calculate.

SAQ (LO 4)

There are two principal duopoly models, Cournot’s duopoly and Bertrand’s duopoly:

1. The Cournot’s model, which shows that two firms assume each other's output and treat


2. The Bertrand’s model, in which, in a game of two firms, each one of them will assume

that the other will not change prices in response to its price cuts.

Study Session III

SAQ (LO 1)

Total Social Cost

The total social cost is the sum of the opportunity costs incurred by society because of a new

regulatory policy; the opportunity costs are the value of the goods and services lost by society

resulting from the use of resources to comply with and implement the regulation, and from

reductions in output. These costs, however, do not take into account any of the health,

environmental, safety, or other benefits which offset the social welfare costs.


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SAQ (LO 2)

Fig 1 Producer and Consumer Surplus with an External Cost

The producer surplus is indicated by the area of triangle P1GP3 and the consumer surplus is

measured as the area of triangle P1GP4, but the total social damage is indicated by the area of

P3GF P2. Therefore, the deadweight loss to society (DWL) is equal to the area of triangle EFG.

If producers have to pay for the damage caused by the pollution, their producer surplus is

reduced to area of triangle P2HP1 minus the area of triangle HGF. In this case the firm would be

making negative profits since the area of triangle HGF is larger than their producer surplus. Net

social welfare in this case would be the area of triangle P2EP4 less the area of triangle EFG (the

deadweight loss).


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If, however, the optimal amount of the product is produced (i.e., where MR equals MSC), then

the firm's output is Q* at a price of P*. In this case, consumer surplus is equal to the area of

triangle P4EP* and producer surplus is the area of triangle P2EP*. Since there is no deadweight

loss to society, net social welfare has increased and is equal to the area of triangle P2EP4.

Suppose that producers can do nothing to reduce the pollution damages other than decrease the

amount of output supplied. If the government places a tax equal to the MSD on each unit of

pollution, this would increase private production costs (but not private real-resource costs) by the

amount of the MSD, which would cause a rise in consumer (taxpayer) welfare. This occurs

because of the reduction in adverse health effects. Depending on the revenue policy of the

government, it could lead to a possible reduction in consumer taxes, since producers are now

paying an additional tax. Although there is a decrease in the producer surplus (and the obvious

consumer surplus), the overall social welfare has increased because of the reduction in the

externality costs.2 Adding all of these surplus changes together, and subtracting the transfers to

the government (i.e., taxes), yields the net social cost of the policy.

SAQ (LO 3)

Challenges in developing an estimate for a social cost for environmental pollution

The challenge in developing an estimate of the social cost of an environmental policy is to

consider the market(s) being affected by the policy, assess the available data and analytic

methods, and adopt an analytic approach that will yield an estimate suitable for use in the

benefit-cost analysis. An important requirement in measuring social costs is to characterize the

supply and demand equations of the regulated market or behavior.


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SAQ (LO 4)

General equilibrium econometric estimation allows models to incorporate the representation of

more sophisticated producer and consumer behavior than would normally be possible through

calibration. However, econometric estimation requires a consistent set of multi-sector time

series data and this data is usually not available for developing countries.

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