eco lecture notes 20

7/28/2019 Eco Lecture Notes 20

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Lecture 1 & 2:Introduction toEconomics & the Market Economy

Objectives

After working through this topic you should be able to:

Explain the concepts of scarcity and opportunity cost

Identify the basic choices facing any economy

Describe the essential structure of a market economy/system Explain and use the supply and demand model.

Identify and explain the role of prices in the market system

Key Concepts

scarcity supply

opportunity cost equilibriumallocation of resources equilibrium price

circular flow model comparative statics

demand role of prices

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Scarcity, Choice & Cost

Virtually all resources (i.e. land, labour, capital) are scarce - i.e.there are not enough to satisfy all the wants of all people in anygiven period. Hence:

Choices have to be made amongst all the alternative uses of theresources - all the goods that could be produced

Such choice inevitably involves a cost in terms of the foregonealternatives - the opportunity cost

Opportunity cost = value of the most highly valued foregonealternative = value of the resource in its next best alternative use

Allocation of Resources

Because of scarcity, every economy/society has to have some meansof organising the allocation of resources such that three majordecisions are made:

1. What to Produce - what goods & in what quantities

2. How to produce the goods - the methods of production

3. Who gets the output - a fair distribution

Now try seminar question 1

Economic Systems

An economic system is the method of organising the allocation ofresources. Two polar cases are:

Market system - a mode of organisation in which resourceallocation is determined by the independentdecisions and actionsofindividualconsumers and producers.

Centrally planned economy - a mode of organisation in whichall resource allocation is determined by the decisions ofgovernment bodies

The UK, in common with most other industrial societies, reliesprimarily on a market system. However, there is also somegovernment direction of resource allocation - the UK is an exampleof a mixed economy.

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The Workings of a Market Economy

Structure

The following diagram shows the basic structure of a market system

(ignoring the role of government)

Product

Markets

Factor

Markets

Households Firms

Revenue

Expenditure

Goods

demandedGoods

supplied

Costs

Inputs

demanded

Inputs

supplied

Incomes

Flow of goods and services

Flow of money

Figure 1-1: The Circular Flow Model

Firms sell goods to households and buy inputs from households.

Households buy goods from firms and sell inputs to firms

The demand and supply in product and factor markets determinethe prices of goods and inputs respectively.

Demand and Supply Model

How are all the individual buying and selling decisions taken in amarket system co-ordinated? Answer - viaprice changes.

Prices are determined by and, in turn, co-ordinate buying and selling(i.e. demand and supply) decisions in markets. The demand andsupply model shows how prices fulfil this crucial co-ordinating role

DemandA demand function for a good A can be written as follows:

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( )D F P Y P P TA A s C= , , , ,

i.e. the demand for a good A (DA) depends upon:

Price of the good (PA)

Income of consumers (Y) Prices of related goods - complements (PC) and substitutes (PS)

Tastes (T) - preferences of consumers

A demand schedule shows the relation between the market price (PA)and the quantity demanded of a good during a given time period, allother determinants held constant (ceteris paribus)

Numerical example: Demand Schedule

Pri

cepe

r

uni

t

Q

uanti

ty

pe

r

pe

ri

od

2 19

4 18

6 17

8 16

10 15

12 14

0

2

4

6

8

10

12

14

0 10 20 30

Quantity per period

Priceperunit

D

If the price changes - a movement along the demand curve

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If another variable changes - a shift in the demand curve

e.g. an increase in income shifts the demand curve to the right(normal good) or to the left (inferior good)


Supply

A supply function for a good A can be written as follows:

( )S F P P T A A F= , ,

i.e. the supply of a good A (SA) depends upon:

Price of the good (PA)

Prices of inputs (factors) (PF)

Technology - the available production methods

A supply schedule shows the relation between the market price (PA)and the quantity of a good firms are willing to supply in a given

period of time, all other determinants held constant (ceteris paribus)

Numerical example: Supply Schedule

Pri

ce

per

uni

t

Q

ua

ntity

pe

r

pe

ri

od

2 4

4 8

6 12

8 16

10 20

12 24

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0

2

4

6

8

10

12

14

0 10 20 30

Quantity per period

Pricepe

runit

S

If the price changes - a movement along the supply curve

If another variable changes - a shift in the supply curve

e.g. if the wage rate paid to labour increases, the supply curve shiftsto the left.


Equilibrium

The concept of equilibrium is central to microeconomic models.Equilibrium is a position of balance, which persists because there isno incentive for anyone to change their behaviour.

Market equilibrium exists when demand = supply; i.e. when theamount consumers want to buy at a particular price equals theamount firms want to sell at that price. The price which equatesdemand and supply (i.e. clears the market) is the equilibrium price.

Numerical example: Market equilibrium

Pri

ce

pe

runi

t

Qua

ntity

dem

anded

per

peri

od

Qua

ntity

supp

liedper

perio

d

2 19 4

4 18 8

6 17 12

8 16 16

10 15 20

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12 14 24

0

2

4

6

8

10

12

14

0 10 20 30

Quantity per period

Priceperunit

S

D

16

The equilibrium price is 8 and the equilibrium quantity traded is 16

If price is above equilibrium - excess supply (glut) - price falls

If price is below equilibrium - excess demand (shortage) - pricerises

Comparative Statics

What happens if one of the held constant variables determiningdemand and/or supply changes? Clearly, a new equilibrium price

and quantity will occur.Numerical example: Decrease in Income

Suppose that consumers incomes decrease (and the good is normal)- the demand curve shifts to the left as less is demanded at every

price. Assume that demand falls by 5.

Pri

ce

pe

r

uni

t

Ol

d

Qu

ant

ity

dema

nd

ed

pe

r

pe

rio

d

Ne

w

Qu

ant

ity

dema

nd

ed

pe

r

pe

rio

d

Q

u

a

n

ti

ty

s

u

p

p

li

e

d

p

e

r

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p

e

ri

o

d

2 19 14 4

4 18 13 8

6 17 12 12

8 16 11 16

10 15 10 20

12 14 9 24

0

2

4

6

8

10

12

14

0 10 20 30

Quantity per period

Priceperunit

S

D1

16

D2

12

The new equilibrium price is 6 and quantity traded is 12; i.e. bothquantity and price fall.

Now try seminar questions 4 & 5

The Role of Prices

The demand and supply model clarifies the fundamental role ofprices in the market system. Specifically, prices perform thefollowing essential functions:

Prices convey information - about relative scarcity or abundance

of goods and inputs to households and firms Prices ration scarce resources - by equating demand and supply

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Prices determine incomes - a households income from themarket depends on the prices of the inputs it supplies to themarket.

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The Market Economy: Seminar Questions

1. Evaluate each of the following statements:

a) A society can always produce more automobiles if it chooses todo so. Hence, there can never be any real scarcity of automobiles.

b) Governments have the power to raise all the money they want bytaxation. Hence, scarcity is not a problem for governments.

c) Citizens of Sweden are lucky because they have free health care,while citizens of the United States have to pay for it.

2. Explain what happens to the demand curve for a good when thefollowing changes occur, ceteris paribus.

a) A rise in the price of a substitute good

b) A rise in the price of a complementary good

c) A fall in the price of the good

3. Explain what happens to the supply curve for a good when the followingchanges occur, ceteris paribus

a) A fall in the price of components used to make the good

b) An improvement in the productivity of the labour producing thegood

c) A rise in the price of the good.

4. Suppose that the market demand curve for haircuts in some town is:

D P I= +80 2 5

where D is quantity demanded per month, P is price per haircut, and I isconsumer income (in tens of thousands of pounds). The supply curve is:

S P= 2

where Sis the quantity supplied per month.

a) According to this model, are haircuts a normal or inferior good?

b) SupposeI= 3. find the equilibrium price and quantity of haircuts.

c) Because of a recession, I falls to 2. What happens in the haircutmarket?

5. In the late 1980s, improvements in technology led to a dramatic loweringin the price of fax machines. Use a supply and demand model to predictthe impact of this development on the overnight document-delivery

business. Use the diagram to predict changes in the number of pieces ofovernight mail, and the price per piece.

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Lecture 3 & 4 : Consumer Choice

Objectives


Describe the fundamental axioms of consumer preferences

Explain the concept of an ordinal utility function

Define and explain the properties of indifference curves

Define and explain the consumers budget constraint Predict the effects of changes in prices and/or income on the budget

line

Describe and explain the conditions for consumer equilibrium

Key Concepts

completeness marginal rate of substitution

consistency/transitivity budget line

non-satiation relative prices

ordinal utility function consumer equilibrium

indifference curve utility maximisation

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U(A) > U(B) simply means that A is preferred to B, but we cannotsay by how much; utility is ordinalnot cardinal.

Assuming 2 goods, X and Y, in each bundle we can write the utilityfunction as:

( )U U X Y = ,where: X = units of good X

Y = units of good YU = utility of bundle X, Y

Indifference Curves

An indifference curve shows the bundles of two goods (e.g. X andY) which have the same level of utility: i.e.

( )U U X Y = ,

where U is fixed at some chosen level of utility.

The axioms of preferences imply that indifference curves have thefollowing important properties:

1. Negatively-sloped - this follows from the assumption of non-satiation. See the diagram below.

Good X

Good Y

U

E

More

preferredregion

Less

preferred

region

Consider the bundle of X and Y shown by point E. All bundles tothe north east must be preferred to E as they include more of at

least one of the goods (or more of both). All bundles to the southwest must be less preferred to E as they include less of at leastone of the goods (or less of both). Hence, only bundles in theother two quadrants (which include more of one good and less ofthe other) can be indifferent to E. Thus, the indifference curve Umust be negatively sloped.

The slope of an indifference curve is called the Marginal Rate ofSubstitution (MRS)

MRS = the amount of one good the individual is willingto give up for an additional unit of the other good whilst

remaining as well off (i.e. on the same indifference curve)

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MRSY

XY X, =

The MRS can also be expressed in a different way as thefollowing shows:

Given the utility function:

( )U U X Y = ,

the change in utility (U) is as follows:

U MU X MU Y X Y= +

i.e. the change in utility equals the marginal utility of good X

(MUX) times the change in units of X (X) plus the marginalutility of good Y (MUY) times the change in units of Y (Y)

Marginal utility is the increase in total utility gained fromconsumption of one more unit of the good

Now, along an indifference curve U = 0 (by definition). Hence,

MU X MU YX Y + = 0

and, finally, rearranging this expression gives the following:

=

Y

X

MU

MU

X

Y

Thus, we can see that the MRS is equal to the ratio of the

marginal utilities; i.e.

MRSMU

MUY X

X

Y

, =

2. Convex to the origin - this property results from the assumptionthat theMRS diminishes as we move along an indifference curve.See the following diagram.

Good X

Good Y

U1

U2

U2 > U1

1

1

2

0.5

When the individual has a relatively large amount of good Yhe/she is willing to give up 2 units of Y in return for one more

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unit of good X and still feel as well off. However, as we movedown the indifference curve, the individual will only sacrificeless of Y (e.g. 0.5 units) for one more unit of X as he/she beginsto have to relatively more of X than Y.

3. More utility the further from the origin - because of non-satiation, indifference curves further from the origin (with moreof both goods) must represent higher levels of utility. (Seediagram above where U2 > U1)

4. Cannot intersect - the axiom of transitivity implies thatindifference curves cannot intersect each other.


Budget Constraint

The individuals consumption possibilities depend on his/her income(I) and the prices of the two goods (PX & PY). Together these three

parameters determine the budget constraint.

The budget line shows the maximum amounts of each good thatcould be purchased by spending allthe income.

Budget Line

The equation of the budget line is as follows:P X P Y IX Y+ =

i.e. the amount spent on good X (= price per unit of X times thenumber of units bought) plus the amount spent on Y (= price per unitof Y times the number of units bought) must equal the total incomeavailable.

Numerical example: Budget Constraint

Assume: I = 20, PX = 4, PY = 2

U

n

i

t

s

o

f

X

U

n

i

t

s

o

f

Y

0 1

0

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1 8

2 6

3 4

4 2

5 0

A Budget Line

0

2

4

6

8

10

12

0 1 2 3 4 5 6Good X

GoodY

Note that the two endpoints of the budget line are equal to incomedivided by the respective price (I / P), as they represent the units

bought of one good when all income is spent on that good

Slope of the Budget Line

The slope (gradient) of the budget line can be deduced as follows:

( ) ( )Absolute SlopeY

X

IP

IP

P

P

Y

X

X

Y

= = =

i.e. theslope of the budget line equals the relative price of good X togood Y.

In other words, the slope tells us the rate at which the individual cantrade off one good for the other - e.g. the amount of Y that has to beforegone in order to purchase one more unit of X

Numerical example

The gradient of the budget line above is:

P

P

X

Y

= =4

22

i.e. two units of Y have to given up in order to buy one more unit ofX

Shifts in the Budget Line

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Any change in one or more of the parameters of the budget line(income and prices) will clearly result in a shift in its position.

A change in income shifts the budget line parallel to the originalline - relative prices are unchanged.

A change in the price of one good shifts the budget line andchanges its slope - relative prices are different.

An equal percentage change in the price of both goods shifts thebudget line parallel to the original - relative prices areunchanged

Numerical example

Assume that the price of good Y rises to 4, so that the parameters ofthe budget line are now:

I = 20, PX = 4, PY = 4

Units of X Units of Y

(Old)

Units of Y

(New)

0 10 5

1 8 4

2 6 3

3 4 2

4 2 1

5 0 0

A Budget Line

0

2

4

6

8

10

12

0 1 2 3 4 5 6Good X

G

oodY

Old

New

A rise in the price of good Y, ceteris paribus, swivels the budget lineinwards. The relative price of good Y to good X is now equal to one.


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Consumer Equilibrium

The rational consumer wants to maximise his/her utility subject totheir preferences and budget constraint; i.e. he/she will choose fromthe affordable bundles of goods the one which gives them the most

utility.

Utility Maximisation

Specifically, the consumer chooses the point on the budget linewhich is on the highest attainable indifference curve - point E in thefollowing diagram.

Good X

Good Y

U1

U2

At point E

MRS = PX / PY

E

A

B

X*

Y*

C

D

At E, utility is maximised subject to the budget constraint. Why?

Because any other point on the budget line (e.g. points A & B) orwithin it (e.g. point D) is on a lower indifference curve. Bundles

beyond the budget line (e.g. point C) are, of course, unobtainable. Atpoint E the consumer is in equilibrium as they have no incentive toconsume another bundle given their preferences and budgetconstraint.

Equilibrium Conditions

Looking at the diagram it is clear that two conditions characterise theoptimum point E:

1. All income is spent - the individual must choose a point on thebudget line not within it.

2. The slope of indifference curve (U2) equals the (absolute)slope ofthe budget line: i.e.

MRSP

PY X

X

Y

, =

In other words, at the equilibrium bundle, the rate at which theconsumer is willing to trade good X for good Y (MRS) is exactlyequal to the rate at which he/she can trade good X for Y (relative

price). Why should this be so?

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Consider point A. Here the MRS > relative price; e.g. the consumeris willing to give up, say, 2 units of Y to get one extra unit of X,whilst the actual trade off (relative price) is, say, 1:1. The consumercan thus increase utility by buying more of X and less of Y; e.g. buy2 units less of Y and buy 2 units of X instead. But at point A only

one more unit of X would have compensated for giving up 2 units ofY - getting 2 units of X means the consumer is better off. Thus at

point A the consumer was not maximising utility. Only when theMRS = relative price will a reallocation of expenditure between thetwo goods produce no further gains in utility.


Note: We can express the consumer equilibrium condition in another

way. Remember that the MRS equals the ratio of the marginalutilities; Hence we can write the (second) equilibrium condition as:

MU

MU

P

P

X

Y

X

Y

=

i.e. in equilibrium, the ratio of the marginal utilities equals the ratioof the prices.

Alternatively, we can rearrange this condition to read:

MU

P

MU

P

X

X

Y

Y

=

This tells us that, in equilibrium, the marginal utility of the lastpound spent is the same for each good.


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Consumer Choice: Seminar Questions

1. A computer expert is offered a choice between 10 floppy disks and 5

software manuals, or 9 floppy disks and 20 software manuals. All youknow about the persons preferences for disks and manuals is that theysatisfy the three axioms. On the basis of this information alone, can you

predict which bundle the person will choose?

2. Explain why indifference curves cannot intersect.

3. What would the indifference curves look like for the following types ofgoods:

a) Perfect substitutes?

b) Perfect complements?

c) Good X much more preferred to good Y by an individual?

4. Given the following information about an individuals consumptionpossibilities between two goods, X and Y.

I = 100; PX = 10; PY = 5

a) Calculate and draw the individuals budget line

b) Show what happens to the budget line when:

i) Income decreases by 20%

ii) PY rises by 40%

iii) Both prices fall by 10%

Start from the original budget line in each case

5. Explain why the consumer would not be in equilibrium at point B in thefollowing diagram. What should the consumer do?

Good X

Good Y

U1

U2

E

B

X*

Y*

6. Explain why consumer equilibrium requires that the marginal utility perlast pound spent on each good must be equal. (Hint: explain why the

rational consumer would change his/her expenditure if they were notequal.)

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7. The following table gives four indifference curves of an individual.

U1 U2 U3 U4X Y X Y X Y X Y

A 3 12 6 12 8 15 10 13

B 4 7 7 9 9 12 12 10C 6 4 9 6 11 9 14 8

F 9 2 12 4 15 6 18 6.4

G 14 1 15 3 19 5 20 6

a) Using graph paper, plot the four indifference curves on the sameset of axes. Label the points A, B, C, F & G on U1.

b) Calculate the marginal rate of substitution between the variouspoints on U1

c) Can we tell how much better off is the individual on U2 than onU1?

d) Suppose that the individual has an income (I) of 15 per timeperiod, the price of good X (PX) is 1 and the price of good Y (PY)is also 1.

i) What is the equation of the budget line of this individual?

ii) What is its slope?

iii) Draw the budget line on your graph.

e) Where is the individual maximising utility? (Label it point E)

How much of X and Y should he/she purchase at the optimum?What are the general conditions for utility maximisation subject tothe budget constraint?

f) Why is the individual not maximising utility at point A? At pointG?

g) Why cant the individual reach U3 or U4?

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Lecture 5 & 6 :Comparative Statics &Demand

Objectives


Derive the individuals demand curve for a good

Show the effects of a change income on consumption of normal and

inferior goods Define and calculate price elasticity of demand

Explain the relationship between price elasticity and total expenditure

Explain how price elasticity varies along a linear demand curve

Define and calculate income elasticity of demand

Define and calculate cross-price elasticity of demand

Key Concepts

price consumption curve point elasticity

individual demand curve arc elasticity

income consumption curve total expenditure

Engel curve linear demand curve

market demand curve income elasticity of demand

price elasticity of demand cross-price elasticity of demand

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Price Change: Derivation of Demand Curve

A change in the price of one of the goods, ceteris paribus, willclearly change the position (and slope) of the budget line leading to anew equilibrium bundle. Hence the amount consumed of each goodwill change. The following diagram shows how to derive theindividuals demand curve for good X.

Good X

Good Y

U1

U2

E3

X1 X3X2

DX

Price of

good X

Qty of Good X

U0

E2E1 PCC

As PX falls the optimum point changes. The line drawn through theoptimum points is called aprice consumption curve (PCC)

As PX falls the quantity the individual would like to consume ofgood X rises. Hence, in the bottom half of the diagram, we canderive the individuals demand curve for good X given income,

price of good Y and preferences. The model of rational consumerchoice predicts that an individuals demand curve for a good isdownward-sloping (the reasons why this is generally the case arediscussed more explicitly in the next topic - see income andsubstitution effects)

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Income Change

When the persons income changes, ceteris paribus, the budget linewill shift parallel to the original. Note that as the prices of the goodsare constant this represents a change in both nominal and real

income.

Normal Good

For a normal good a rise in income will lead to a rise in theconsumption of the good. The diagram below illustrates this case.

Good X

Good Y

U1

U2

E2

X2

Y2 E1Y1

X1

ICC

Both goods here are normal - as income increases, consumption ofboth goods rises. The line connecting the points of equilibrium is

called an income consumption curve (ICC).

Inferior Good

Some goods are inferior - i.e. when income increases, ceterisparibus, consumption of the good falls. A possible explanation isthat consumers regard these goods as being of low quality comparedto other alternatives - once their income has risen sufficiently theyswitch their expenditure to the alternative goods. Possible examplesof inferior goods include tobacco, coal, bread & cereals, black &white T.V.s.


Deriving an Engel Curve

An Engel curve shows the relationship between income and theamount consumed of a commodity, ceteris paribus. It can easily bederived via the income consumption curve, as the following diagramshows:

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Good X

Good Y

U1

U2

E2

X2

E1

X1

ICC

X3 Qty of Good X

Income

E3

Engel

curve

I3

I2

I1

This shows the Engel curve for good X - as X is normal, the Engelcurve will be positively sloped.


Market Demand Curve

Above we derived an individuals demand curve for a commodity.

When looking at the market for a particular commodity, we are moreconcerned with the total market demand for the commodity - i.e. thetotal demand for the good at each price.

The market demand curve of a good shows the relationshipbetween the price and the quantity demanded by all marketparticipants, ceteris paribus.

To derive the market demand curve we simply add up at each pricethe amount demanded by each individual - as quantity is measuredon the horizontal axis, this is referred to as the horizontal summationof the individual demand curves. (See Katz & Rosen, p 71, Figure

3.13)

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Elasticity of Demand

Elasticity of demand measures the responsiveness of the quantitydemanded of a good to a change in one of its determinants, ceteris

paribus. It tells us how much demand changes when own-price,

income or the price of another good changes, ceteris paribus.

Elasticity usespercentage changes - it is unit free

Elasticity tells us how many times greater the percentage changein quantity demanded is compared to the percentage change in

price etc.

Three demand elasticities can be calculated - (own-)price,income, cross(-price)

Price Elasticity of DemandPrice elasticity of demand () measures the percentage change in thequantity demanded per period with respect to the percentage changein the price of the good, ceteris paribus (i.e. assuming income and

prices of other goods remain constant). The formula is as follows:

= ( )%

%

X

P

where %X is the percentage change in the quantity demanded ofgood X and %P is the percentage change in the price per unit ofgood X

Because demand curves slope downwards, the percentagechanges in quantity and price have opposite signs, and their ratiois negative. Hence the minus sign at the front simply makes theelasticity a positive number. This is OK as it is the magnitude (notthe direction) of the change in demand which we are concernedwith.

Calculation of Price Elasticity

There are two ways to compute the value of price elasticitydepending on whether small or large changes in price are beingconsidered:

1. Point Elasticity - this is used when the price change is small. It iscalculated as follows:

=

=

( )/

/

( )

X X

P P

X

P

P

X

where Xand P represent the initial quantity and price respectively.Note that the second line of the formula indicates that point elasticity

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can be calculated by multiplying the inverse of the slope of the

demand curve (X/P) at a particular point by the correspondingratio ofPtoX- hence the term point elasticity.

Numerical example

Calculate the price elasticity of demand for good X when pricechanges from 20 to 20.50 and quantity demanded changes from300 units to 290 units per month.

X= 290 - 300 = -10; P= 20.5 - 20 = 0.5X= 300; P= 20

Hence,

=

=

=

=

( )/

/

( )

/

. /

( )

X X

P P

10 300

05 20- 0.033

0.025

1.32

2. Arc Elasticity - this is used when the price change is relativelylarge. It is calculated using the following formula:

= ( )/

/

X X

P P

where X-bar and P-bar are the average quantity and average pricerespectively; i.e.

( )

( )

XX X

PP P

=

+

=

+

1 2

1 2

2

2

Numerical example

Calculate the price elasticity of demand for good X when pricechanges from 20 to 25 and quantity demanded changes from 300

units to 220 units per month.

X= 220 - 300 = -80; P= 25 - 20 = 5

X =+

=

=

300 220

2260

P =20+25

222.5

Hence,

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=

=

=

( )/

/

( )/

/ .

( )

X X

P P

80 260

5 22 5

- 0.3080.222

= 1.387


Range & Meaning of Elasticity

Price elasticity can range between a value of zero and infinity. The

values of zero, one and infinity are special cases. In general,elasticity will be either less or greater than one.

Inelastic demand ( < 1). A given % change in price leads to asmaller% change in demand.

Elastic demand ( > 1). A given % change in price leads to alarger% change in demand.

Perfectly inelastic ( = 0). A given % change in price leads to nochange in demand - a verticaldemand curve.

Unit elastic ( = 1). A given % change in price leads to an equal% change in demand.

Perfectly elastic ( = ). Any increase in price (however small)leads to zero demand. Hence, a horizontal demand curve -consumers will purchase as much as they want at the going price,

but only at that price.

Determinants of Price Elasticity

What makes the demand for some goods elastic and the demand forothers inelastic? The main determinants of price elasticity of demandare as follows:

Substitutability - the ease with which one good can besubstituted for another. The more and closer substitutes availablefor a good, the more elastic the demand tends to be. Hence,narrower categories of good tend to have a higher elasticity than

broader categories (see figures below)

Commodity share - the proportion of income spent on the good.In general, the larger the % of income absorbed by the good, thehigher the elasticity, ceteris paribus.

Time - demand tends to be more elastic in the long-run asconsumers often need time to adjust their spending patterns (e.g.find substitutes)

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Empirical Estimates of UK Demand

The following table gives some estimates of price elasticity ofdemand for various categories of good in the UK.

Category of Good Pric

eElas

ticit

y

Fuel & Light 0.47

Food 0.52

Alcohol 0.83

Durables 0.89

Services 1.02Dairy Produce 0.05

Bread & Cereals 0.22

Entertainment 1.40

Expenditure abroad 1.63

Catering 2.61


Price Elasticity & Total Expenditure

An important relationship exists between the price elasticity ofdemand and the total expenditure by consumers on a good.

Total expenditure is the total amount of money spent byconsumers on a commodity. It is computed as the price per unit

(P) times the number of units purchased (X); i.e.Total expenditure = PxX

On a diagram, total expenditure is shown by an area under thedemand curve, as indicated below:

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Qty per period

Price per

unit

D

P1

X1

Totalexpenditure

As the price of a commodity falls, the quantity demanded rises(ceteris paribus) - i.e. they move in opposite directions. But as total

expenditure is price times quantity its clear that total expendituremay either rise or a fall depending on which is the largest change,the price fall or the quantity increase. The former tends to reduceexpenditure, the latter to increase it. (Obviously, the sameconsiderations apply for a price rise/quantity fall).

The size of the change in price and quantity must be measured inpercentage terms, not absolute units (as different units give differentanswers). And, of course, price elasticity tells whether the

percentage change in price or quantity is the largest. Hence we candeduce the results shown in the following table:

If demand is and price then total expenditure

Elastic rises falls

falls rises

Inelastic rises rises

falls falls


Linear Demand Curve

By definition a linear (i.e. straight line) demand curve has a constantslope, where the slope is the ratio of the absolute change in quantityto the absolute change in price. But remember elasticity is defined asthe ratio of the percentage changes. Thus, price elasticity and theslope of a demand curve, although connected, are not the same. And,a linear demand curve will not have a constant elasticity at each

point.

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To see how elasticity varies along a linear demand curve, we can usethe relationship between price elasticity and total expenditure.Consider the following example:

Price per

unit

Quantity demanded

per week

Total

expenditure

2 50 100

4 45 180

6 40 240

8 35 280

10 30 300

12 25 300

14 20 280

16 15 240

Here we have a linear demand curve (with a slope equal to -5/2).Note that when price rises from 2 through to 10 total expenditure isrising - i.e. for that price range, demand is price inelastic. As pricerises from 12 up to 16 (and above), total expenditure is falling -hence in this price range demand is price elastic. The conclusion isthat along a linear demand curve, elasticity is less than one atrelatively low prices, and greater than one at relatively high prices.

And thus at some price in the middle elasticity must be equal to one.From the table, its clear that = 1 at price = 11


The following diagram neatly shows how price elasticity variesalong a linear demand curve.

Qty per period

Price per

unit

D

= 1

< 1

> 1

=

= 0

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Income Elasticity of Demand

Income elasticity (I) measures the percentage change in the quantitydemanded with respect to the percentage change in consumersincome, ceteris paribus. Its is calculated using the following

formula:

=%

%

X

I

where %X is the percentage change in the quantity demanded ofgood X and %I is thepercentage change in income

Range & Meaning

Income elasticity can be eitherpositive (normal good) or negative

(inferior good). If 0 < I < 1, then quantity demanded rises bysmaller percentage than income implying that consumers do notspend much of any increase in income on this particular good; ifI >1 then quantity demanded rises by larger percentage than incomeimplying that quantity demanded is quite responsive to changes inincome. The former goods are often called necessities and the latterluxury goods. The following table summarises this information.

If income elasticity is the good is

Negative Inferior

Positive (and < 1) Normal & a Necessity

Positive (and > 1) Normal & a Luxury

Empirical Estimates

The following table gives some estimates of income elasticity ofdemand for various commodity groups in the UK.

Category of Good Income

Elasticity

Tobacco -0.50

Fuel & Light 0.30

Food 0.45

Alcohol 1.14

Clothing 1.23

Durables 1.47

Services 1.75

Coal -2.02

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Bread & Cereals -0.50

Dairy Produce 0.53

Vegetables 0.87

Travel abroad 1.14

Recreational goods 1.99

Wines & spirits 2.60


Cross-Price Elasticity of Demand

Cross-price elasticity (xy) measures the percentage change in thequantity demanded of good X with respect to the percentage changein the price of good Y, ceteris paribus. Its is calculated using thefollowing formula:

xy =%

%

X

PY

where %X is the percentage change in the quantity demanded ofgood X and %PY is thepercentage change in the price of good Y.

Range & Meaning

Cross-price elasticity can be eitherpositive ornegative. Ifxy > 0, thetwo goods aresubstitutes for each other as an increase in the price ofY induces a rise in the quantity demanded of good X. Conversely, if

xy < 0, the two goods are complements. Also, the greater theabsolute value of the cross elasticity the greater the degree ofsubstitutability or complementarity between the two goods. Thefollowing table summarises these results.

If cross-price elasticity is the goods are

Negative Complements

Positive Substitutes

Empirical Estimates

The following table gives some estimates of cross-price elasticity ofdemand for various commodity groups in the UK.

With respect to a 1% change in priceof

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Comparative Statics & Demand: Seminar Questions

1. Draw a diagram to illustrate the effect on the individuals utility

maximising choice of an increase income such that good Y is an inferiorgood.

2. Read pages 72 to 74 in Katz & Rosen and then answer the followingquestions;

a) Consider an individual who spends his/her weekly income onfood and all other goods, whose current equilibrium position inshown in the diagram below.

Food

All

other

goods

U1

E1

X1

Y1

Suppose the government gives the individual an in-kind transfer of food(which cannot be resold by the individual). Show the effect on the

budget line

b) Suppose that instead of an in-kind transfer the government givesthe individual a cash transfer equal to the market value of the foodtransfer. Show the effect on the initial budget line.

c) Add indifference curves to show the cases where:

i) the individual prefers the cash transferii) the individual is indifferent between the cash and in-kind

transfers

d) What difference does it make if the in-kind transfer of food can beresold by the individual?

3. Calculate price elasticity of demand in the following cases using the mostappropriate method.

a) When the price of good Z falls from 3000 to 2500, the quantitydemanded rises from 4 million to 5 million units per year.

b) When the price of good Y rises from 50 to 51, the quantitydemanded falls from 120 to 110.

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4. Referring to the empirical estimates of price elasticity shown in the table:

a) How would you explain the estimates shown in the table?

b) If the price of alcoholic drinks increased by 5%, ceteris paribus,what would happen to the quantity demanded

c) If the government (for energy conservation reasons) wanted toreduce consumption of fuel and light by 20%, how much would ithave to raise the price?

5. The diagram below provides information on Maries consumption ofcake before and after an increase in the price of cake. According to thediagram, is Maries price elasticity of demand for cake greater, less than,or equal to one?

Cake

All

other

goods

6. Confirm the change in elasticity along a linear demand curve bycalculating the price elasticities for the following price and quantitychanges taken from the demand schedule in the text.

a) Price rises from 4 to 6, quantity falls from 45 to 40

b) Price rises from 12 to 14, quantity falls from 25 to 20

c) Price rises from 10 to 12, quantity falls from 30 to 25

7. Between 1980 and 1987 the percentage share of total consumersexpenditure in the UK taken by spending on food fell from 15.4% to13.3%, whilst the share of services increased from 26.4% to 29.4%. Howcan the empirical estimates of the income elasticities of food and serviceshelp explain this data?

8. Referring to the empirical estimates of cross-price elasticity of demandshown in the table:

a) what are the figures in the diagonal (from top left to bottomright)?

b) Are food and clothing substitutes or complements?

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c) Which commodity group has the highest cross-price elasticity?What would happen to the quantity demanded of this commodityif the price of the other good increased by 10%, ceteris paribus.

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Lecture 7 & 8 : Price Changes &Consumer Welfare

Objectives


Distinguish between the income and substitution effects of a pricechange

Illustrate the income and substitution effects diagrammatically

Distinguish between an inferior good and a Giffen good

Explain and illustrate the concepts of compensating and equivalentvariation

Explain and apply the concept of consumer surplus as a monetarymeasure of the change in consumer welfare.

Key Concepts

substitution effect equivalent variation

income effect marginal valuation

inferior good willingness to pay

Giffen good consumer surplus

compensating variation

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Income & Substitution Effects

As we deduced in the last topic, the model of rational consumerchoice predicts that when the price of a good changes, ceteris

paribus, the consumer will consumer more of the good (hence thedownward sloping individual demand curve). Can we say moreabout the reasons why this negative relationship exists (and when itmight not)? The answer is yes, if we consider exactly what happensto the consumers budget line when the price of one good changes,ceteris paribus.

The budget line moves position implying that the consumers realincome has changed (remember nominal income is assumedconstant)

The slope of the budget line changes implying a change in therelative prices of the two goods.

This means that we can separate (analytically) the effect of a changein the price of one good (the total price effect) into its twocomponents:

1. SUBSTITUTION EFFECT - the effect on consumption of agood resulting only from the change in its relative price (i.e. theslope of the budget line)

2. INCOME EFFECT - the effect on consumption of a goodresulting only from the change in real income (i.e. the position ofthe budget line)

Example: A Fall in the Price of a Normal Good

The following diagram shows to separate the income andsubstitution effects of a fall in the price of good X, ceteris paribus.

Good X

All

other

goods

(Y)

U1

U2

E3

X3

Y3 E2

E1Y1

Y2

X1 X2

Substitution effect:

E1 to E2

Income effect:

E2 to E3

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The consumer is initially maximising utility at point E1. When theprice of good X falls, the consumer moves to point E3, consumingmore of good X (and less of all other goods). To separate out theincome and substitution effects we employ the following technique

Draw a budget line parallel to the new budget line which is

tangential to the indifference curve the consumer was originallyon.

Using this method we get the line going through point E 2. What wehave effectively done is to take away from the consumer the increasein real income brought about by the fall in the price of good X, sothat he/she is back at their original level of utility but with the new

set of relative prices.

E1 to E2 is the pure substitution effect resulting from the change inrelative price alone. It is always negative as the consumer will

always consume more of the good whose relative price has fallen. E2 to E3 is the pure income effect - it is negative for normal goods

(as in this case) but positive (i.e. a price fall leads to lessconsumption) forinferiorgoods.

Hence in this example of a normal good the substitution and incomeeffects reinforce each other to produce a downward sloping demandcurve.


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Inferior & Giffen Goods

If a good is inferior then the income effect will be positive and willcounteract the substitution effect. Two possibilities therefore canoccur:

1. The positive income effect is less than the negative substitutioneffect and the good still has a downwardsloping demand curve.

2. The positive income effect is greater than the negativesubstitution effect and the good has an upwardsloping demandcurve (as price falls, so does demand). This exceptional case iscalled a Giffen good.


Compensating & Equivalent Variations

A price fall (increase) makes the individual better (worse) off. Canwe measure how much better or worse off? Comparing utility levelsis invalid because utility numbers are arbitrary (remember that utilityis ordinal not cardinal). Hence we need a monetary measure ofwelfare change. Our indifference curve analysis suggest two possiblemeasures.

Compensating Variation (CV) - the minimum (maximum)amount of money that has to be given to (taken away from) anindividual to make them as well off as before the price rise (fall)

Equivalent Variation (EV) - the minimum (maximum) amountof money which would have to be given to (taken away) anindividual to make them as well off as they would have been afterthe price fall (rise)

The following diagram illustrates these two measures for an increasein the price of good X, ceteris paribus.

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Good X

All other

goods

(Y)

U1

U2

E1EV

E2

EC

Y2

Y3

Y1

CV = Y2 - Y1EV = Y1 - Y3

Compensating Variation

When the price of good X rises, the consumers equilibrium movesfrom point E1 to E2. To compensate him/her for this price rise weneed to move the new budget line back till it touches the originalindifference curve U2 - at point EC. Hence the compensatingvariation is given by the amount (Y2 - Y1)

Equivalent Variation

To compute the EV we need to measure the (maximum) amount ofmoney we would need to take away from the individual to makethem as worse off as they would be when the price of good X rises.So, move the original budget line back till it just touchesindifference curve U1 - at point EV. The EV is then the loss ofincome given by amount (Y1 - Y3).

Comparing the CV & EV

Note that the CV and EV measures of welfare change are not equal.The reason why is that each one is measured at different relative

prices.

CV is measured at the new relative price ratio

EV is measured at the originalrelative price ratio

Now try seminar questions 4, 5 & 6

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Consumer Surplus

Although useful concepts for accurately measuring welfare change,both CV and EV require knowledge of the individuals indifferencemap. This is difficult to obtain, so an alternative, more practical (but

less accurate) measure of changes in consumer welfare is needed.The most commonly used measure is ordinary (Marshallian)consumer surplus.

Consumer surplus is the difference between what a consumer iswilling to pay for a good and what he/she has to pay. It ismeasured as the area under the demand curve and above the

going price

To see why consumer surplus is derived from the demand curve, weneed to interpret a demand curve as a marginal valuation (orwillingness to pay) schedule.

The Demand Curve as a Marginal Valuation Schedule

The standard interpretation of a demand curve is that it shows theamount the consumer would buy at each particular price (ceteris

paribus). But we can also view the relationship between price andquantity the other way round; i.e. the demand curve shows themaximum price the individual is willing to pay for each additional

unit. Now the price represents what the consumer is willing to giveup of other goods, i.e. the value placed on each extra unit, so thedemand curve can also be seen as a marginal valuation curve - it

shows the value placed on each additional unit by the consumerwhere value is measured as the maximum price he/she is willing to

pay.

The following diagram illustrates the concept of marginal valuationfor a good which is consumed in discrete units.

Qty per

period

Price per

unit

0 1 2 3 4

10

40

24

15

MV1 = 40

MV2 = 24

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The consumer is willing to pay a maximum price of 40 for the firstunit, 24 for the second unit, etc. Hence the marginal valuation(MV) of the first unit is 40, MV of the second unit is 24 and so on.

Note that the MVs are given by the areas under the demand curve -hence the total value (willingness to pay) for any given number of

units is measured by the total area under the demand curve up tothat number of units.


Consumer Surplus

To calculate consumer surplus we need to know the actual goingprice paid by the consumer for each unit. The diagram below shows

the consumer surplus when the market price is 15 per unit.

Qty per

period

Price per

unit

0 1 2 3 4

10

40

24

15

CS1 = 25

CS2 = 9

At price 15, the consumer buys 3 units per period. But on the firsttwo units he is willing to pay more than 15. Hence he/she receivesa consumer surplus of 25 (40 - 15) on the first unit, and 9 (24 -15) on the second unit. A total CS of 34. Its clear from this that

the total consumer surplus of a given number of units all bought atthe going market price is the area under the demand curve and

above the going price.


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Smooth Demand Curve

When the demand curve is a continuous curve rather than a stepfunction the same principles for measuring marginal and totalwillingness to pay and consumer surplus still apply.

The marginal value placed on a particular unit is the verticaldistance from the horizontal axis up to the demand curve.

The total willingness to pay is the area under the demand curve.

Consumer surplus is the area under the demand curve and abovethe market price

The two diagrams below illustrates these concepts.

Qty per period

Price per

unit

P1

X1

D

Total value of

consuming X1 units

MV of X1 st unit = P1

The total value of (or willingness to pay for) X1 units is equal to theshaded area. The MV of the X1st unit is equal to price P1.

Qty per period

Price per

unit

P1

X1

D

Consumer surplus

of consuming X1units

The total consumer surplus gained from consuming X1 units of thecommodity per period is equal to the shaded area in the diagram.

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Using CS to measure Welfare Change

Finally, we can use the CS to measure the effect on the consumerswelfare of a change in the price of the good, ceteris paribus.Consider the diagram below which shows the effect of a rise in the

price of a good from P1 to P2.

Qty per period

Price per

unit

P1

X1

D

Loss in consumer

surplus created by

the price increase

P2

X2

Clearly, when the price rises from P1 to P2 the area of consumersurplus falls. The loss in consumer surplus (shown by the darkershaded area) is a monetary measure of the loss in welfare suffered bythe consumer. More generally,

When the price of a commodity changes from P1 to P2, the areabehind the demand curve and between the two prices is a moneymeasure of the resulting change in welfare.


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Price Changes & Consumer Welfare: Seminar

Questions

1. Draw a diagram to show the income and substitution effects of a RISE inthe price of a good, ceteris paribus.

2. This question continues on from question 7 in seminar 2.

a) Assume the price of good X rises to 2. Draw the new budget lineon your graph. What is the new optimum point? How much of Xand Y is consumed at this point?

b) On the diagram separate out the substitution and income effects ofthis price rise. Is either X or Y an inferior good?

c) Finally, assume the price of good X falls to 0.50 (PY still 1, I

still 15). Add this new budget line to your graph. What is theoptimum combination of X and Y with this budget line? (Label it

point H).

d) From your diagram, derive the price-consumption curve and theindividuals demand curve for good X. (You will need to draw aseparate diagram for the demand curve).

3. Draw appropriate diagrams to show the income and substitution effectsof a fall in the price of good X, ceteris paribus, where:

a) X is an inferior good but not a Giffen good

b) X is a Giffen good.4. The local swimming pool charges non-members 10 per visit. If you join

the pool, you can swim for 5 per visit, but you have to pay an annual feeof F. Use an indifference curve diagram to find the value of F thatwould make it just worthwhile for you to join the pool. Suppose that the

pool charged you exactly that value. Would you swim more or less thanyou did before joining? Use income and substitution effects to explainyour answer.

5. Read pages 107 to 110 in Katz & Rosen and then answer the followingquestions;

a) Assume that low income households are choosing between food(measured in calories per week) and consumption of all othergoods (measured in pounds). Show the equilibrium position on adiagram.

b) Now suppose that the government agrees to subsidise these poorerhouseholds by paying 50% of their food bills. How will the

budget line change? Show the new equilibrium.

c) Show on the same diagram the minimum amount of incomesupplement the government would have to give households

instead of subsiding their food bills to make them as well off asthey were in situation (b).

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d) Which policy is cheaper? Which should the government choose?

6. Read pages 110 to 114 in Katz & Rosen and then answer the followingquestions:

a) Explain the difference between an ideal cost of living index and a

Laspeyres index.b) Calculate the Laspeyres index for the following data showing an

individuals consumption of food and fuel in 1990 and 1991 andthe prices of the two commodities in those years.

1990 1992

Quantity of food 60 40Quantity of fuel 100 50Price of food 3 4Price of fuel 10 12

c) Why does compensation for a price increase according to aLaspeyres index overcompensate the individual?

7. What is the MV of the 3rd unit? The 4th unit. What is the totalwillingness to pay for 4 units?

8. If the market price is 10, what is the CS on the 1st, 2nd, 3rd & 4th units?Calculate the total CS.

9. Using the following diagram, calculate the change in welfare when theprice rises from 12 to 15.

Qty per period

Price per

unit ()

12

80

D

15

70

10. Boriss demand curve for tennis games, D, is shown below. At the localtennis club, the cost per tennis game for member is Pt pounds. In order to

become a member, one must pay an annual fee. Show on the diagram thelargest fee that Boris would be willing to pay.

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Lecture 9 & 10 : The Firm & its Goals

Objectives


Identify the firms goal and define economic profit

Distinguish between economic profit and accounting profit

Define and calculate the user cost of capital

Use the total revenue and total cost curves to calculate the maximumprofit output level

Explain and apply the marginal output rule to determine the maximumprofit output level

Explain the shut-down rule

Key Concepts

economic profit marginal revenue

total revenue marginal cost

economic cost marginal output rule

user cost of capital shut-down rule

economic depreciation

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Firms Objective: Profit Maximisation

All firms which operate in markets buy inputs to produce outputs tosell. A firm has to decide:

1. What to produce

2. How to produce the output

3. How much to sell and at what price

4. How to promote the product.

To determine solutions to these four decisions the firm needs to havea goal (objective). Hence, to predict firm behaviour we need to beclear about the objective of a firm. The standard assumption inmicroeconomic theory of the firm is that:

The firms goal is to maximise its economic profit

Economic Profit

Economic profit is defined as follows:

Economic Profit = Total Revenue - Total Economic Cost

Total revenue is the sum of the payments the firm receives fromthe sale of its output.

What about economic cost? The following distinctions between the

economists and the accountants concept of cost must be borne inmind when calculating a firms economic cost:

Economic costs are opportunity costs - i.e. the value of inputs intheir best alternative use.

Economic cost is generally not equal to accounting cost

Economic cost may begreaterorless than accounting cost.

Sunk expenditures are noteconomic costs. A sunk expenditureis a factor expenditure that, once made, cannot be recovered.

Examples1. The owner(s) of a firm must include the opportunity cost of their

labour as part of total economic cost, otherwise total accountingcost will understate total economic cost

2. Suppose that four years ago a firm leased a machine for five yearsat a rent of 2000 per year. What is the economic cost of usingthe machine for one more year? 2000? This is the accountingcost but not necessarily the economic cost. The economic costdepends on the value of the machine in its best alternative use. Ifthe firm cannot sublet the machine then the opportunity

(economic) cost is zero. And the 2000 rental payment is a sunkexpenditure - it cannot be recovered by the firm. Thus, where the

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firm has sunk expenditures, accounting cost will tend to overstatetotal economic cost.


User Cost of Capital

What is the economic (i.e. opportunity) cost to a firm of owning andusing an asset (also known as the user cost of capital)? To calculatethis we need to consider what the firm foregoes by using the assetrather than selling it now.

The total economic cost of using an asset is the sum of theeconomic depreciation and the foregone interest.

Economic depreciation is the difference between the currentvalue of the asset and the value at the end of the period i.e. it isthe fall in the value of the asset over a given period of time. Inother words, it is the amount the firm foregoes by not selling theasset now.

The forgone interest is the amount that could be earned by sellingthe asset now and investing the proceeds in the next bestalternative use.

The value of the user cost of capital will depend on whether the firmis considering purchasing an asset, or whether it already owns it. The

reason for the difference is that in the latter case some of theexpenditure on the asset may be sunk (i.e. unrecoverable)

Example 1: A firm is considering buying a machine for 10,000. Atthe end of one years use it could sell the machine for 4,000. The

best alternative use for the 10,000 is to invest it in governmentstock which yield 10% per annum.

Economic depreciation = 10,000 - 4,000 = 6,000

Foregone interest = 10,000 x 10% = 1,000

User cost of machine = 6,000 + 1,000 = 7,000

Example 2: A firm owns a machine that originally cost 10000, butnow has a market value of 7000. At the end of the another yearsuse it could be sold for 3000. The best alternative use for money isto invest it in government stock which yield 10% per annum. Theeconomic cost is the foregone interest on the 7000 that could beraised by selling it now, plus the economic depreciation (i.e. fall inmarket value). Thus:

Economic depreciation = 7000 - 3000 = 4000

Foregone interest = 7000 x 10% = 700

User cost of machine = 4000 + 700 = 4700

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N.B. The difference between the original (historic) cost of themachine (10000) and the current market value (7000) is a sunkexpenditure which therefore does not represent an economic cost.


The Profit-Maximising Level of Output

As weve seen, economic profit is the difference between totalrevenue and total economic cost. Hence, to determine how the firmchooses output so as to maximise profit we need first to considerhow total revenue and cost vary with the level of output

Total RevenueTotal revenue is the amount the firm receives from selling its output.This can be calculated by multiplying the units of output by themaximum price at which each unit can be sold. How can wedetermine the maximum price per unit for each level of output?From thefirms demand curve. (N.B. not the market demand curve.)

Numerical Example: Firms Demand & Total Revenue

Outputperweek(000s)

Priceperunit()

TotalRevenue

per week(000)

1 20 20

2 18 36

3 16 48

4 14 56

5 12 60

6 10 60

7 8 56

8 6 48

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Total Revenue Curve

0

10

20

30

40

50

60

70

0 2 4 6 8 10Output per week (000)

000perweek

R

The first two columns show the firms demand curve for its product.The third column shows the total revenue the firm would receivefrom selling each particular level of output. Clearly, it is calculated

by multiplying the level of output by the corresponding (maximum)price per unit at which the firm can sell all that output (i.e. columnone times column two)

The diagram graphs total output against total revenue to show thefirms total revenue curve. Note that it has an inverted U-shape.

Total (Economic) Cost

How does the firms total economic cost vary with the level ofoutput? (This will be discussed in more detail in topic 7.) Thefollowing points can be made:

Total cost will varypositively with output - to produce more unitsof output the firm will need to use more inputs, hence the totalcost will be higher.

Total cost represents the minimum expenditure on the inputsnecessary to produce the output

Total cost depends on the prices of the inputs and the firms

technology - these are assumed to be constant.

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Numerical Example: Firms Total Cost

Output per week (000s) Total Cost per week(000)

0 0

1 10

2 18

3 24

4 26

5 30

6 38

7 50

8 70

Total Cost Curve

0

10

20

30

40

50

60

70

80

0 2 4 6 8 10Output per w eek (000)

000p

erweek

C

Note that as output rises initially total cost rises at a decreasing rate(the curve gets flatter). But as output continues to rise, total coststarts to go up much more quickly (the curve gets steeper). The

reason for this particular relationship between total cost and outputwill examined in topic 7.

Total Economic Profit

Given the information on the firms total revenue and total cost wecan calculate total profit and hence determine the output whichmaximises profit. Remember that:

Economic Profit = Total Revenue - Total Economic Cost

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Numerical Example: Total Profit

Output perweek (000s)

TotalRevenue perweek (000)

Total Cost perweek (000)

Total Profit perweek (000)

0 0 0 0

1 20 10 10

2 36 18 18

3 48 24 24

4 56 26 30

5 60 30 30

6 60 38 22

7 56 50 68 48 70 -22

Total Profit Curve

-30

-20

-10

0

10

20

30

40

0 1 2 3 4 5 6 7 8

Ouput per w ee k (000)

000perweek

Maximising ProfitIts clear that, in the example above, total profit is maximised at aoutput level of 4000 (or 5000) units per week. This gives a total

profit of 30,000 per week. As profit is equal to revenue minus cost,profit is maximised at the output level where the difference betweenrevenue and cost is at its greatest; i.e. where the vertical distancebetween the total revenue and total cost curves is greatest. This isillustrated in the following diagram.

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Profit Maximisation

0

10

20

30

40

50

60

70

80

0 1 2 3 4 5 6 7 8

Ouput per week (000)

000perweek

C

R

Profit


Alternative Approach

The problem with finding the maximum profit output level using thetotal revenue and cost is that the firm needs to look at its entirerevenue and cost curves all at once. This requires a lot ofinformation which the firm may not have. An alternative, more

useful approach is to divide the decision into two parts:

1. If the firm is in business, how much should it produce?

2. Should the firm be in business at all, or should it shut down?

The Marginal Output Rule

Assume the firm is producing some given level of output. Does thisoutput level maximise profit? The answer is no if producing more(or less) output would increase profit. And profit would rise if the

increase in output added more to total revenue that it did to totalcost. So we need to look at the change in revenue and cost whenoutput changes - i.e. the concepts of marginal revenue and marginalcost.

Marginal Revenue

Marginal Revenue (MR) is the change in revenue due to the saleof one more unit of output. It is calculated by dividing the changein revenue by the change in output: i.e.

MRR

Q=

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Numerical Example: Marginal Revenue

Outputperweek(000s)

TotalRevenue

per week(000)

MarginalRevenue(000)

0 0

20

1 20

16

2 36

12

3 48 8

4 56

4

5 60

0

6 60

- 4

7 56

- 8

8 48

Marginal Revenue Curve

-10

-5

0

5

10

15

20

0 1 2 3 4 5 6 7 8

Ouput per w ee k

000

MR

Marginal Cost

Marginal Cost (MC) is the change in total cost due to theproduction of one more unit of output. It is calculated by dividingthe change in cost by the change in output: i.e.

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MRC

Q=

Numerical Example: Marginal Cost

Outputperweek(000s)

TotalCost perweek(000)

MarginalCost(000)

0 0

10

1 10

8

2 186

3 24

2

4 26

4

5 30

8

6 38

12

7 5020

8 70

Marginal Cost Curve

0

2

4

6

8

10

12

14

16

18

20

0 1 2 3 4 5 6 7 8

Ouput per we ek

000

MC

Marginal Output Rule

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The change in profit when the firm produces one more unit of outputequals marginal revenue minus marginal cost. Hence if MR > MCthe firm should produce the additional unit as its total profit will rise.In other words, at the current output level it could not have beenmaximising profit. On the other hand, if MR < MC then the firm

should not produce the additional unit as doing so would reduce totalprofit. So, to maximise profit a firm should raise production whilstMR > MC and continue to do so until on the next additional unit ofoutput MR < MC. Logically, this implies that to maximise profit thefirm should produce at the output level where MR = MC.

Numerical Example: Profit Maximisation

Out

put

perweek(000s)

Tota

lCost

perweek(000)

MarginalCo

st(000)

TotalReve

nue

perweek(000)

MarginalRe

venue(000)

TotalProfit

perweek(000)

0 0 0

10 20

1 1

0

20 10

8 16

2 18

36 18

6 12

3 24

48 24

2 8

4 26

56 30

4 45 3 60 30

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0

8 0

6 38

60 22

12 - 4

7 50

56

20 - 8

8 70

48 - 22

Profit Maximisation

-10

-5

0

5

10

15

20

0 1 2 3 4 5 6 7 8

Ouput per we ek

000

MC

MR

Both the table and diagram show that MR > MC on the first 4 unitsof output - hence the firm can raise profit by producing these units ofoutput. On the fifth unit MR = MC hence the change in profit iszero, and profit remains at 30,000. But, if the firm produced 6 units

per week profit would be lower because MR < MC on the sixth unit.Hence the firm will maximise profit by producing 5 units of output

per week; i.e. where MR = MC. This gives the marginal output ruleas follows:

Marginal Output Rule: If the firm does not shut down, then itshould produce output at a level where marginal revenue is equalto marginal cost.

Note:

1. Because, in our example, output is measured in discrete singleunits, profit is also maximised at 4 units of output. For the samereason, MR does not cross the MC curve at 5 units of output inthe diagram (they cross instead at 4.5 - the midpoint between 4and 5 units). However, if output can vary continuously so that theMR and MC curves are smooth curves, then Profit will bemaximised at a single level of output where MR=MC. See the

diagram below.

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MC

MR

Ouput per period

per

period

2. The marginal output rule is perfectly general. Although theprecise shapes of the MR and MC curves depend on the

particulars of the market in which the firm operates, the rule thatthe firm should produce at a point where MR = MC is valid forany profit-maximising firm.


Shut-Down Decision

How does a firm decide whether or not to be in business at all? Itshould compare its economic profit when it does produce with theeconomic profit it would earn if its shut down instead.

If a firm shuts down and sells no output total revenue is obviouslyzero. But total economic cost will also be zero. Why? becauseeconomic cost equals opportunity cost - the amount the firm loses

by not using its inputs in their best alternative use. If the firmshuts down the inputs will actually be put to their best alternativeuse. hence the opportunity/economic cost of the inputs is zero.Thus if revenue and cost are both zero, economic profit is zero.

A firm should therefore shut down if it makes less than zeroeconomic profit by producing output; i.e. if it makes economiclosses.

Shut-Down Rule

When will the firm make an economic loss? Clearly when totalrevenue is less than total cost at every level of output. We can alsostate this condition for making an economic loss in terms of averagerevenue and average cost

Average revenue (AR) is total revenue divided by the units ofoutput produced: i.e. it is the revenue earnedper unit

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ARR

Q=

Average cost (AC) is total cost divided by the units of outputproduced: i.e. it is the costper unit.

ACC

Q=

When total cost is less than total revenue, then AR < AC. Usingthese concepts we can therefore state the shut down rule as follows:

Shut-Down Rule: If for every choice of output level the firmsaverage revenue is less that its average cost, the firm should shutdown.

The following diagram shows the case of a firm which should shutdown.

AC

AR

Ouput per period

per

period

M

H

Q1

Total revenue of output Q1 is equal to shaded area H. Total cost isequal to area H + M. Hence total economic loss is shown by area M.Since AC lies above AR for all levels of output, the firm cannotmake an economic profit by producing and hence would do better byshutting down.


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The Firm & its Goals: Seminar Questions

1. Suppose that a young chef opened his own restaurant. To do so, he quit

his job, which was paying 28,000 per year; cashed in a 5000 certificateof deposit that was yielding 5% (to purchase equipment); and took over abuilding owned by his wife which had been rented out for 1000 permonth. His expenses for the first year amounted to 50,000 for food,40,000 for extra help, and 4000 for utilities.

The chef is trying to decide whether he would have been better off not being inbusiness last year. He knows how to calculate his revenues, but he needshelp with the cost side of the picture. What were the chefs economiccosts?

2. A firm is considering borrowing 50000 from the bank at 8% p.a. to buy

a machine. At the end of one years use they estimate it could be sold for35000.

a) Calculate the user cost of the machine for the first year.

b) What would be the economic cost of the machine if it wasworthless to anyone else but this firm?

c) Would the answer to part (b) be the same if the firm had alreadypurchased the machine?

3. Given below are some data on total revenue and total cost for a firm

Total output per

month

Total revenue () Total Cost ()

0 0 0

1 15 7

2 29 14

3 41 22

4 51 31

5 60 42

6 66 55

7 70 70

a) Plot the total revenue and total cost curves on the same graph

b) Calculate total profit and plot the total profit curve on a separategraph

c) What is the output level that maximises profit

4. Using the data given in question 3:

a) Calculate the firms marginal cost and marginal revenue curvesand plot them on the same graph.

b) Indicate the profit-maximising level of output

5. Many firms incur a one-time set-up cost to begin production. Forinstance, whether to sell one copy of a word-processing program or a

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thousand, a company needs to write the basic computer code one time.As a result of set-up costs, the marginal cost of the first unit may beextremely high - going from 0 to 1 unit of output triggers the need to bearthe entire set-up cost. More generally, costs may be such that marginalcost initially is greater than marginal revenue. The figure below

illustrates a firm whose marginal cost curve crosses its marginal revenuecurve at two different points.

Ouput per year

per

unit

MR

MCA

B

a) How much output, if any, should this firm plan to produce?

b) How is your answer affected by the relative sizes of areas A andB?

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Lecture 11 & 12 : Production

Objectives


Explain the concepts of a firms technology and associated productionfunction

Distinguish between the short run and long run production periods

Define an isoquant and explain its properties

Explain the concept of returns to scale and distinguish between thethree possible cases.

Derive a short run production function.

Explain and calculate the marginal physical product of an input.

Distinguish between increasing, constant and diminishing returns to afactor

Derive and explain the relationship between the MRTS and the MPP

of the inputs

Key Concepts

technology marginal rate of technical substitution

production function returns to scale

short run marginal physical product

long run increasing and constant returns

isoquant diminishing returns

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Technology: The Production Function

A firm options for combining inputs into outputs is called itstechnology. The firms technology is summarised by its productionfunction

A production function shows the maximum output that can beproduced from any given combination of inputs:

( )Q F L K = ,

where Q = units of outputL = units of labour inputK= units of capital input

Why maximum output? Because it is assumed that only

technologically efficientmethods are used by the firm - this impliesthat using more of one input and either the same amount or more ofthe other input must increase output.

Numerical Example: Production Function

Unit

s of

Lab

our

per

day

Unit

s of

Capi

tal

per

day

O

u

t

p

u

t

pe

r

d

a

y

500 300 160

1000 200 160

1300 170 160

500 350 180

1000 220 18

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0

1300 190 180


Long Run & Short Run

The production possibilities available to a firm depend on the timehorizon over which the firm makes its input choices. In general, themore time a firm has to make its decisions, the more input choices it

has. In particular, an important distinction exists between the longrun and short run production periods.

The short run is defined as the period of time during which thequantity of only one of the firms inputs can be varied - all theothers are fixed.

The long run is defined as the period of time long enough for thequantity ofallthe firms inputs to be varied.

Note: An input (factor) whose level can be varied over the relevanttime period is known as a variable factor. An input which cannot bevaried is called a fixed factor.

Long Run Production Function

The long run production function shows the maximum output thefirm can produce when all its inputs can be varied. Assuming twoinputs, capital and labour, we can write this using the same notationas before: i.e.

( )Q F L K = ,

The numerical example shown above is a long-run productionfunction given that both capital and labour can be freely varied bythe firm. To graph the long run production function we need to makeuse of the concept of an isoquant.

Isoquants

An isoquant shows the combinations of the two inputs (e.g.,capital and labour) which produce the same level of output.

The production function shown above illustrates two isoquants - onefor 160 units of output per day, and another for 180 units. Lets look

at the input combinations which produce 160 units per day.Numerical Example: An Isoquant

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Units of Labour

per day

Units of Capital

per day

Output per

day

500 300 160

1000 200 160

1300 170 160

An Isoquant

0

50

100

150

200

250

300

350

400

450

0 250 500 750 1000 1250 1500 1750

Labour per day

Ca

pitalperday

160

Marginal Rate of Technical Substitution

The slope of an isoquant is called the marginal rate of technicalsubstitution (MRTS). It shows the rate at which one input (e.g.capital) can be substituted for one more unit of the other (labour)whilst the level of output remains constant. The MRTS is equal tothe (absolute) ratio of the change in capital input to the change inlabour input: i.e.

MRTSK

LK L, ( )=

Example: Referring to the isoquant in the diagram above, if the firmchanges from using 500 units of labour and 300 units of capital tousing 1000 units of labour and 200 units of capital, the MRTS is:

MRTSK L, ( ) .=

=100

5000 2

This tells us that for every extra unit of labour input the firm uses 0.2units less of capital input.


Properties of Isoquants

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The following diagram shows a set of isoquants (known as anisoquant map) which describes the firms production function (i.e. itstechnology). The diagram illustrates the key properties of isoquants:

Units of

Labour

Units of

capital

1

1

2

0.5Q3

Q2

Q1

A

B

CD

1. Negatively-sloped. Technological efficiency implies that anisoquant must slope downwards from left to right - using more ofone input to produce the same level of output must imply usingless of the other input.

2. Convex to the origin. The MRTS is not constant, it diminishes asthe firm moves along an isoquant: e.g. as the firm uses more andmore units of one input (e.g. labour) and less of the other (e.g.capital), the amount of the other input that can be foregone

diminishes.For example in the diagram, when the firm has a relatively large

amount of capital to labour (point A) then if it uses one more unitof labour, it can afford to use two units less of capital and still

produce the same output. Further down the isoquant, we see thatas the firm continues to substitute more labour for less capital, theamount of capital that can be foregone decreases; e.g. the secondexample in the diagram shows that when the firm has a relativelysmall amount of capital to labour (point C) then using one moreunit of labour to produce the same output implies giving up only0.5 units of capital.

Why does the MRTS diminish? To answer this question properly,we need to invoke the concept of marginal product, which isdescribed in detail later in this topic. For the moment, we canargue that when, as at point A, the firm has a relatively largeamount of capital to labour it can afford to give up a lot of capitalin return for more labour and still maintain its output level. At

point D, the situation is reversed. Here labour is the relativelymore plentiful input - hence the firm could afford to give up a lotof labour in return for a bit more capital.

3. The further the isoquant from the origin, the higher the levelof output. This is obviously the case as using more of both inputsmust increase output. Hence, Q3 > Q2 > Q1.

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Returns to Scale

Another important property of a long run production function is theconcept of returns to scale. This refers to what happens to outputwhen the quantity of all inputs is increased by a certain proportion.There are three possibilities:

Increasing Returns: output increases by a largerpercentage thanthe increase in inputs

Constant Returns: output increases by the same percentage asthe increase in inputs

Decreasi

eco lecture notes 20

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