economics production

8/3/2019 Economics Production

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PRODUCTION ANALYSIS

• INTRODUCTION• Production is basically an activity of transformation which

transfers inputs into outputs.• Farms use land, labor, seeds and small amount of capital as

inputs to produce output like corn.• Similarly, a flour mill uses inputs like wheat, labor, capital

for machinery, factory building to produce output like wheatflour.• So, an input is the goods or services which produce an

output.

• The firm generally uses many inputs to produce an output.• Output of any firm may be the inputs of other firms, e.g.,steel is an output of the steel producer, but this steel is alsoan input of automobile or rail coach manufacturing orrefrigeration manufacturing or air-condition manufacturingindustries.



PRODUCTION ANALYSIS

• The transforming process of inputs into output can be threetypes:

• i) change in form (output should be new form compared to

inputs, for example cloth as output and thread as input)• ii) change in space (transportation)• iii) change in time (storage).

• The transformation process or production increases theconsumer usability of goods and services.



PRODUCTION ANALYSIS

• Production Function • A production function is the technical relationship between

inputs and outputs.• A commodity may be produced by various methods using

different combinations of inputs with given state of

technology.• Take the example of cloth, it may be produced by usingcotton or silk or polymer as raw materials with handloom,power loom or computerized machines.

• You can see various types of raw materials and technologyoptions will create several possible ways of producing thesame product.

• Hence, there can be several technically efficient methodsof roduction.



PRODUCTION ANALYSIS

• Production function includes all such technically efficientmethods.

• It can be said that production function is purely atechnological relationship between physical inputs and

physical outputs over a given period of time; production is afunction of inputs, their quality and quantity andinterrelation, i.e., complementarities and substitutability.

• Hence it can be said that production function is:

– Always related to a given time period

– Always related to a certain level of technology

– Depends upon relation between inputs



PRODUCTION ANALYSIS

• Production function shows the maximum quantity of thecommodity that can be produced per unit of time for each

set of alternatives inputs, and with a given level of production technology.• A given amount of output can be produced by different

combinations of inputs and each of these combinations may

be technically efficient.• Technical efficiency is defined as a situation when usingmore of one input with either the same amount or more of the other input must increase output.

• Normally a production function is written as;• Q = f (x 1, x 2,.…..x n) …………….…………(i) • Where, Q is maximum quantity of output of a good being

produced, and x 1, x 2,.… ..x n are the quantities of variousinputs used in production.



PRODUCTION ANALYSIS

• If we replace x1, x 2,.… ..x n in (i) by the factors of productiondiscussed above, then the production function may be;

• Q = f (L, K, I, R, E) ……………………… .. (ii)• Where, Q =output and the inputs are L, K, I, R, E; L=

labour, K = capital, I =land, R =raw material and E =efficiency parameter.

• In short run, some inputs like plant-size, and machineequipments cannot be changed, so a producer trying toincrease output in the short run will have to do so byincreasing only the variable inputs.

• On the contrary in the long run input options are very wide.

• On the basis of such characteristics of inputs, productionfunctions are normally divided into two broad categories:

• (i) with one variable input or variable proportion productionfunction

• (ii) with two variable inputs or constant proportionroduction function



PRODUCTION ANALYSIS• PRODUCTION FUNCTION WITH ONE VARIABLE INPUT

• In short run, producers have to optimize with only one

variable input.• Let us consider a situation in which there are two inputs,

capital and labour, capital is fixed and labour is variableinput.

• You will notice as the amount of capital is kept constant andlabour is increased to increase output, the ratio in whichthese two inputs are used will also change.

• Therefore, any change in output can be manifested onlythrough a change in labour input only.

• Such a production function is also termed as variableproportion production function; it is essentially a short termproduction function in which production is planned withvariable input.



PRODUCTION ANALYSIS• The short run production function shows the maximum output a firm

can produce when only one of its inputs can be varied, other inputsremaining fixed. It can be written as:

• Q = f (L, K 0)…………………… ..……………… (iii)• Where, Q is output, L is labor and K 0 denotes the fixed capital.• This also implies that it is possible to substitute some of the capital by

labor.

• It is easy to understand that as units of the variable input areincreased, the proportion of use between fixed input and variable inputalso changes.

• Therefore, short run production function is governed by law of variable proportions.

• To explain the concepts of average and marginal products of factorinputs consider the production function given in equation (iii),assuming capital to be constant and labor to be variable, total productis a function of labor and is given as:

• TP L = f (K 0, L) ……… .………………………… .(iv)



PRODUCTION ANALYSIS

L

Q

Q 1 = f (K 10, L)

Q 2 = f (K 20, L)

Q 3 = f (K 30, L)

Production Function with constant K; K 10< K 2

0< K 30



PRODUCTION ANALYSIS

• If instead labour is fixed in the short run, the total product of the capital function can be similarly expressed as:

• TP K = f (L 0, K) ………………………………….(v)

K

Q

Q1 = f (L 10, K)

Q2 = f (L 20, K)

Q3 = f (L 30, K)

Production Function with constant L; L 10< L 2

0<L3

0



• Average Product (AP) is total product per unit of variable

input; therefore it can be expressed as:• AP L = TP / L…………………………..(vi)

• If instead of capital, labor is fixed in the short run, average

product of the capital function (AP K) can be similarlyexpressed as:

• AP K = TP / K …………………… .…… .(vii)

• Marginal Product (MP) is defined as addition in total outputper unit change in variable input.

• Thus marginal product of labor (MP L) would be:

• MP L = dTP / dL ………………… .…… (viii)

PRODUCTION ANALYSIS



PRODUCTION ANALYSIS• PRODUCTION FUNCTION WITH TWO VARIABLE INPUTS• Most simplistic form of production function with two

variable inputs, labour (L) and capital (K), and a singleoutput, Q, is as follows;

• Q = f (L, K) ……….…………………(ix) • This production function is constructed based on the

assumption that the state of the technology is given and

output can be increased by increasing inputs.• When the state of technology changes, the production

function itself changes.• Further, it is assumed that the inputs are utilized in the best

possible way, i.e., optimum utilization of inputs.• The best utilization of any particular input combination is atechnical, not an economic problem.

• Selection of best input combination for the production of a

particular output level depends upon the input and outputprices and is subject of economic analysis.



• LAW OF VARIABLE PROPORTION OR LAW OFDIMINISHING RETURNS TO FACTORS

• The slope of the total product curve is determined from thelaw of diminishing returns.

• The law of diminishing returns, being empirical in nature,states that with a given state of technology if the quantity of one factor input increased, by equal increments, thequantities of other factor inputs remaining fixed, theresulting increment of total product will first increase andthen decrease after a particular point.

• The law is also known as diminishing returns to factors.• It states that as more and more one factor of production is

employed, other factor remaining the same, its marginal

productivity will diminishing after some time.

PRODUCTION ANALYSIS



PRODUCTION ANALYSIS

• For example, if we increase labor input and capital inputremaining the same, then the marginal productivity of laborfirst increased, reaches maximum and then decreases.

• The law of diminishing returns to factors is depending onthree assumptions.

• i) It is assumed that the state of technology is given.

• ii) It is assumed that one factor of production must alwaysbe kept constant at certain level.

• iii) This law is not applicable when two inputs are used in afixed proportion and the law is applicable only to varyingratios between the two inputs.



PRODUCTION ANALYSIS

• DIFFERENCE BETWEEN RETURNS TO A FACTOR ANDRETURNS TO SCALE

• The law of diminishing returns factors states that as moreand more one factor of production is employed, otherfactor remaining the same, its marginal productivity will

diminishing after some time, e.g., if we increase one factorof production i.e., labour and other factor of productioni.e., capital remaining the same, then the marginalproductivity of labour first increased, reaches maximum

and then decreases.• So, returns to a factor (variable factor) of production is first

increasing in the initial level of production and thendecreasing if we increase the amount of that variable factorof production.

PRODUCTION ANALYSIS



PRODUCTION ANALYSIS

• But, if we increase more and more of that variable factorthen the returns to the variable factor is negative.

• In the very first stage of production, if additional units of labour are employed, the total output increases more thanproportionately; so marginal product rises.

• In the following figure, stage I would begin from the originand continue to a point where AP L attains its maximumvalue.

• In this stage, MP L > 0, and MP L > AP L. This stage is calledas increasing returns to the variable factor.



PRODUCTION ANALYSIS

L

TP

TP L

LO

TP

Stage I Stage II Stage III

MPL

AP L

TP, AP and MP Curves



PRODUCTION ANALYSIS

• In the second stage, the total product increases but lessthan proportionate to increase in labor.

• In this stage, marginal product of labor falls and this stageis called as diminishing returns to variable factors. Here,MP L > 0 and MP L < AP L.

• The stage three is a technically inefficient stage of

production and a rational producer will never produce inthis stage. Here, MP L < 0 and total product is decreasing.• The law of returns to scale refers to the long run

analysis of production.

• It refers to the effects of scale relationships which impliesthat in the long run output can be increased by changingall factors by the same proportion, or by differentproportions.

• If the production function is Q0

= f (K, L) and we increaseall the factors of production by the same proportion p.



PRODUCTION ANALYSIS• So, the new production function is Q* = f [(p.K), (p.L)].• If Q* increases in the same proportion as the factors of production,

p, then we can say there are Constant Returns to Scale (CRS).

• If Q* increases less than proportionately with an increase in thefactors of production, p, then we can say there are DecreasingReturns to Scale (DRS).

• If Q* increases more than proportionately with an increase in thefactors of production, p, then we can say there are IncreasingReturns to Scale (IRS).

Proportion (p)O

Q

DRS

CRS

IRS

Returns to Scale (DRS, CRS & IRS

PRODUCTION ANALYSIS



PRODUCTION ANALYSIS

• ISOQUANT• An isoquant is the firm’s counterpart of the consumer’s

indifference curve.• It is a curve representing the various combinations of twoinputs that produce the same amount of output.

• It is also known as iso-product curve or equal product

curve or production indifferent curve.• It is the collection of inputs in the form of factors of

production labour (L) and capital (K), which yield thesame output.

• For a definite level of output, i.e., for Q 0, say 1000 unitsof output or for Q 1, say 2000 units of output, the equationof production function is

• Q0 = f (L, K) or Q 1 = f (L 1, K 1)• Where, Q 0 and Q 1 are parameters.

PRODUCTION ANALYSIS



PRODUCTION ANALYSIS

• The locus of all the combinations of L and K which satisfy theabove equation forms an isoquant.

• Since the production function is continuous, an indefinite number of input combinations will lie on each and every isoquant.

• The two factors of production are substitutable and can employmore of one input and less of another input to get the same level of output.

• A higher level of output is represented by a higher isoquant.• If we assume that that the marginal productivities of both the factors

of production are positive and decreasing as more of them are used,the isoquant will be downward sloping and convex to the origin.

L

K

Q0 = 1000 units of output

ISOQUANT

Q1 = 2000 units of output

ISOQUANTS



• TYPES OF ISOQUANT• Isoquants are various shapes depending on the degree or elasticity of

substitutability of inputs. These are as follows; • Linear Isoquant: This type assumes perfect substitutability between

factors of production, i.e., a given output can be produced by usingonly capital or only labor or by a large number of combinations of capital or labor.

PRODUCTION ANALYSIS

O

Isoquant

Units of Labor

Units of Capital

Perfectly Substitutability

PRODUCTION ANALYSIS



PRODUCTION ANALYSIS

• Input-Output Isoquant: It assume strict complementary orzero substitutability between the factors of production, we

get input-output isoquant.

O

Isoquant

Units of Labor

Units of Capital

Zero Substitutability

PRODUCTION ANALYSIS



PRODUCTION ANALYSIS

• Kinked Isoquant: This assume limited substitutability of capitaland labor. Since there are only a few processes available for

producing any commodity, substitutability of factors is possibleonly at kinks.

• This form is also called activity analysis isoquant or linearprogramming isoquant.

O

Isoquant

Units of Labor

Units of Capital

Linear Programming Isoquant



PRODUCTION ANALYSIS

• Smooth Convex Isoquant: This form assumes continuoussubstitutability of capital and labor only over a certain

range, beyond which factors can not be substituted for eachother. Such an isoquant appears as a smooth curve convexto the origin.

O

Isoquant

Units of Labor

Units of Capital

Continuous Substitutability



PRODUCTION ANALYSIS• CHARACTERISTICS OF ISOQUANT • Isoquants are Downward Sloping: Technological efficiency

connotes that an isoquant must slope downwards from left to right,which implies that using more of one input to produce the same levelof output must imply using less of the other input.

• Thus if more of labour is used in the production process, then less of capital must be used to produce the same level of output. Slope of the

isoquant is equal to: K/L, ratio of capital and labour.

OL

K

Q0 Q1

Q2 AB

C

Panel I O

L

K

Q1

Q2

A

CB

PanelII

PRODUCTION ANALYSIS



PRODUCTION ANALYSIS• A higher Isoquant represents a higher output• In the panel I of above figure, if we consider point A on the

curve Q 1 and the point C on Q 2, it can follow that C hasmore of both labour and capital as compared to A.• Thus as per given technology, more of both factors should

produce greater output.

• However you should learn that it is not necessary than on ahigher isoquant a point will have greater quantity of at leastone of the two inputs as in case of A and B.

• Hence a greater quantity of any one of the two inputs will

render a higher level of output.• In short, using more of both inputs and more of either of theinputs must increase output given the state of technology.

• Hence a higher isoquant Q 2 would represent a higher output

than isoquant Q 1.

PRODUCTION ANALYSIS



PRODUCTION ANALYSIS• Isoquants do not intersect each other• An isoquant represents the same level of outputs with

different units of two inputs: intersection of two isoquantswould signify single input combinations producing twolevels of output.

• This is explained by Panel II of above figure. Let A and Bbe two different points on Q 1 and Q 2 respectively.

• Suppose two isoquants Q 1 and Q 2 interested each other atpoint C. At point B and C of isoquant Q 1 the firm producesthe same level output Q 1.

• Again points A and C of isoquant Q 2 denote the same levelof output Q

2any the firm.

• Thus it follows that at points A and B, the same level of output should be produced.

• But from the fig it is clear that point A denotes a higherlevel of output than B; this is contradictory, and hence weconclude that isoquants cannot intersect each other.

PRODUCTION ANALYSIS



PRODUCTION ANALYSIS

• Convex to the origin• Given substitutability between factor inputs, as the firm

continues to employ more of one input say labour and lessof other say capital, a situation comes when it becomesdifficult to substitute labour for capital.

• Since labour and capital are not perfect substitutes, thereforeas capital (K) is kept fixed to produce additional units of outputs only by increasing laour (L), it would requiresuccessively increasing units of labour.

• This is better understood with the help of the law of themarginal technical substitution (MRTS).

• The absolute slope of the isoquant falls as we move downthe isoquant and the declining MRTSlk determining theconvexity of an isoquant.

PRODUCTION ANALYSIS



PRODUCTION ANALYSIS• ISOCOST LINE OR EQUAL COST LINE • The cost equation of the firm is C0 = w.L + r.K, where w is the cost of

labour, i.e., wages and r is the cost of another input capital, i.e., rate of

interest.• This equation will be satisfied by different combinations of L and K.

the locus of all such combinations is called the equal cost line orisocost line.

OL

K

Isocost Line

A

B

OA = C 0 / rand

OB = C 0 / w



PRODUCTION ANALYSIS

• In the above figure, if the firm spend entire amount of

money i.e., C 0 in hiring labor, the firm will get OB units of labor which is equal to C 0 / w.

• On the other hand, if the firm spends the entire money inpurchasing capital, the firm will get OA units of K which isequal to C 0 / r.

• By joining the two points A and B we get the isocost lineC0.

• With the given cost C 0 the firm can purchase anycombination of labor and / or capital on the line AB.

PRODUCTION ANALYSIS



PRODUCTION ANALYSIS

• MARGINAL RATE OF TECHNICALSUBSTITUTION

• Marginal Rate of Technical Substitution (MRTS) measuresthe reduction in per unit of one input, due to unit increase inthe other input that is just sufficient to maintain the samelevel of output.

• Thus for the same quantity of output, marginal rate of technical substitution of labour (L) for capital (K)(MRTS LK) would be willing to give up for an additional unitof labour.

• Similarly, marginal rate of technical substitution of capitalfor labour (MRTS KL) would be the amount of labour thatfirm would be willing to give up for an additional unit of capital.

PRODUCTION ANALYSIS



PRODUCTION ANALYSIS

• Consider the isoquant Q 1 of above figure, MRTS LK would measure

the downward vertical distance (representing the amount of capital

that the producer is willing to sacrifice) per unit of the horizontaldistance (representing additional units of labor).

• In other words, MRTS is expressed as the ratio between rates of

change in L and K, down the isoquant. Thus: MRTS LK = - (dK/dL)

O

L

K

Q0

Q1

Q2 AB

C

PRODUCTION ANALYSIS



PRODUCTION ANALYSIS

• MRTS of labour for capital is equal to the slope of theisoquants, it is also equal to the ratio of the marginalproduct of one input to the marginal product of other input.

• Since output along an isoquant is constant, if dL units of labour are substituted for dK units of capital, then the

increase in output due to increase in dL, i.e (dLxdK) shouldmatch with the decrease in output due to decrease in dK i.e.,(-dKx MP K).

• In other words:• dLx MP L = -dKx MP K

• Or,• MP L / MP K = -dK / dL

PRODUCTION ANALYSIS



PRODUCTION ANALYSIS

• A change in the level of output can be expressed as changein total output (Q) equals to the sum of change in labor

input (dL) times MP of labour and change in capital input(dK) times MP of capital.• In other words: Q = MP L x dL + MP K x dK• However, along a given isoquant, output remains

unchanged, ie. Q = 0.• Hence we have,• MP L x dL + MP K x dK = 0

• Or, MP L / MP K = -dK / dL• Or, MRTS LK = MP L / MP K

• So, the marginal rate of technical substitution between twoinputs is equal to the ratio of the marginal physical products

f h i

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