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University of Essex Session 2011/12

Department of Economics Autumn Term

EC111: INTRODUCTION TO ECONOMICS

Consumer surplus

Consider the consumer choosing an amount of good X to maximise his/her utility,

and suppose that good Y is a composite of all other goods. Suppose we think of

discrete units of good X.

At PX1 the consumer will buy only one unit; his/her marginal utility from that good

is high relative to all other goods.

As the price falls the consumer becomes willing to buy more units and his marginal

valuation of the good (relative to all others) falls. This underpins our interpretation

of the demand curve as a marginal willingness to pay schedule.

Note that when the price is PX6, the total marginal valuation that the consumer

places on good X is the sum of the area of the boxes representing each unit.

The marginal valuation of the last unit is equal to the price but the consumer values

the intra-marginal units more highly.

PX

PX1

PX2

PX6

1 2 3 4 5 6 qX

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Drawing the demand curve as continuous rather than discrete.

At price PX1 the consumer’s total valuation is the area under the demand curve up

to qX1. The cost to the consumer of consuming this amount is qX1×PX1 (the area of

the box)

Consumer surplus is the difference between the consumer’s total valuation and the

total cost. It is the area under the demand curve down to the price.

Note that in principle this is measurable as a monetary value.

One interpretation of consumer surplus: The maximum lump sum payment

consumer would be willing to make (in addition to the price for each unit) in order

to be allowed to consume any of the good.

In some settings firms can exploit this to extract more revenue from the consumer

by charging an ‘entry’ fee and then a price per unit (a two-part tariff).

Q: Think of an example.

Consumer

surplus

PX

PX1

qX1 qX

Total

expenditure

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Market demand and supply

There is an analogous concept for producers. The area above the supply curve up to

the price represents the total surplus over the price at which producers would be

willing to supply each unit.

The sum of producer and consumer surplus is social surplus. It is a money-metric

measure of the welfare generated in this market.

At the equilibrium price PX1 consumers’ marginal willingness to pay is just equal to

producers opportunity cost of supplying that unit. This is where social surplus is

maximised.

Suppose that for some reason producers were able to set price PX2. Producer surplus

would increase and consumer surplus would fall but the triangle below the demand

curve and above the supply curve between QX1 and QX2 is lost. This loss of social

surplus is the deadweight loss of the ‘distortion’

Q: Economists often use the term ‘distortion’. What does it mean?

Consumer

surplus

PX

PX2

PX1

QX2 QX1 QX

Producer

surplus

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The effect of a tax (revisited)

Introducing a tax on good X drives up the price to consumers and reduces the price

to producers. QX falls as a result of the tax.

Consumer surplus falls and producer surplus falls, but the government receives tax

revenue T×QX.

Tax revenue could be redistributed to consumers and/or producers, but they could

not be fully compensated because of the deadweight loss.

The tax could be used as a method of redistributing income. But it comes at the cost

of a loss in efficiency as a result of the distortion.

T

Consumer

surplus

PX

PXC

PXC-T

QX QX

Producer

surplus

Tax

revenue

Deadweight

loss

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Uncertainty

Consider how a consumer’s utility changes with the consumer’s total income,

assuming that at each point he or she chooses the optimum combination of goods.

The individual’s utility function us described by U(m). We assume that this

relationship is concave: there is diminishing marginal utility of income.

This individual’s income varies with the ‘state of nature’. He/she gets m1 + Δ with

probability 0.5 and m1 – Δ with probability 0.5.

The individuals expected utility (ie what he/she gets on average) is:

EU = 0.5×U(m1 + Δ) + 0.5×U(m1 – Δ).

The concavity of the utility function means that this individual is risk averse. As

compared with m the downside loss in utility is greater than the upside gain.

The individual would be better off with a certain income of m1, which gives utility

U(m1), than with the uncertain income which delivers expected utility EU.

U(m)

U(m1)

EU

m1–Δ m1-s m1 m1+Δ

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Insurance

The individual would be willing to pay for an insurance contract where he she gives

up Δ on a good year and gets and additional Δ in a bad year. The individual would

be willing to pay a premium of m – s.

Problems of insurance

Adverse selection (hidden characteristics).

Insurance companies cannot observe whether the individual’s risk of loss is high or

low.

Those individuals with the highest risk of loss are most likely to want to insure.

In equilibrium the insurance premium will rise (because the insurance company

finds itself paying out a lot).

Those with low risk will not find it worthwhile to take out the (now more expensive)

insurance.

Note that this is a case of imperfect information the individual knows his or her type

(high or low risk of loss) but the insurance company does not.

Q: why not simply ask the individual about his or her type?

Moral hazard (hidden actions)

Suppose I insure my house for its full value. I know that if the house burns down I

will be fully compensated.

I will be more likely to take actions that increase the risk of the house burning down

(e.g. smoking in bed) than if I was not insured.

Insurance companies could either:

a) set a premium that allows for the increase risk, guessing how I will behave

(in which case the insurance will be more expensive), or

b) offer only part insurance, say half the value of the house, so that I still bear

some of the risk.

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Note that:

Insurance companies diversify risk by pooling a large number of insurance

contracts. If the probability of risk of loss is, is 0.1 then on average 10 percent of

policy holders will claim every year and the insurance company’s payouts will be

stable.

Some risks are undiversifiable, e.g. war, tsunami. They affect a whole population at

the same time. Insurance companies may be unwilling to offer insurance against

such events.

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THE THEORY OF THE FIRM

3 types of firms: sole traders, partnerships and companies. Sole traders are the most

numerous but they are often very small. Sole traders and partnerships have

unlimited liability. The large firms are companies that have limited liability and are

often complex organisations

Firms use factors of production, typically labour and capital to produce output.

Factors may be broadly or narrowly defined (e.g. skilled and unskilled labour)

These factors are stocks (workers, machines that) when combined can produce (and

sell) a flow of output.

The profit motive.

Profit is defined as: Total profit = Total Revenue – Total Cost.

We focus on economic profit. The distinctive feature is that costs are measured as

opportunity costs. Economic costs include purchased inputs, but are also defined to

include:

Earnings foregone by a self-employed entrepreneur

Interest foregone on any funds tied up in the firm.

Our assumption is that the overriding objective of firms is to maximise their profits.

Profit is income from the owner(s) of the firm, who want more rather than less

income.

Large (and not so large) firms are owned by shareholders but are run by boards of

directors. This divorce of ownership from control can led to a principal/agent

problem.

How can the shareholders (principals) ensure that the directors (agents) act in the

shareholders interest by maximising profit rather than in the managers interest (a

stress free comfortable life perhaps)?

Overcoming the principal/agent problem

Link managers salaries to the firm’s profit.

The discipline of the stock market discipline. Firms that fail to maximise

profits become takeover targets. A successful corporate raider will fire the

old management.

Q: can the ‘market for corporate control’ really solve the principal agent problem?

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Two general implications of profit maximisation

Cost minimisation: choosing the least cost method of producing a given

output

The MR = MC rule: choosing the level of output that generates maximum

profit.

MR: Marginal Revenue = the addition to the firm’s total revenue from selling one

more unit.

MC: Marginal Cost = the addition to the firm’s total cost from selling one more

unit.

For the firm, MR and MC vary with the level of output (sales), q.

MC cuts the MR curve from below. Profit is maximised where q*.

Intuition: consider an output less than q* . An additional unit of output adds more

to profit than to cost because MR > MC. It is worth producing that unit because it

adds to the firm’s profit.

MC,

MR

MR

MC

q* q

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Technology

A production function relates output to the minimum factor inputs needed to

produce it. This is determined by technology.

q = f(L, K, ..)

where K is capital (machines, factories) and L is labour (workers or worker hours)

Suppose we vary the amount of labour the firm uses holding the amount of capital

constant at, say K0.

Note these key points:

The production function is upward sloping.

The slope of this relationship is the Marginal Product of Labour.

MPL = Δq/ΔL (or Lq/ )

The MPL is diminishing as output increases (the curve is concave).

An increase in the amount of capital (say to K1 > K0) will shift the whole

curve upwards.

A technological improvement shifts the curve upwards for a given amount of

capital.

q

Slope = MPL Q = f(L, K0 )

L

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There is an exactly analogous relationship for capital holding constant the amount

of labour.

Any marginal change in output is the result of changes in labour and/or capital

input:

Δq = MPL × ΔL + MPK×ΔK

Setting the change in output to zero we have: ΔK/ΔL = – MPL/MPK = MRTS

This defines the slope of an isoquant The slope of an isoquant is known as the

Marginal Rate of Technical Substitution (MRTS). It is the rate at which labour can

be substituted for capital to produce the same output.

q

Slope = MPK Q = f(K, L0 )

K

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Isoquants

The isoquant map is a set of isoquants that corresponds to a given production

function. There is a strong analogy to indifference curves in consumer theory except

that here, output can be observed directly. Isoquants have the following properties.

They slope down. Starting from point A the same output, q0 can be produced

with less capital only if more labour is added (e.g. at B).

They don’t cross. At point C the firm employs the same amount of capital

and more labour than at A. This must represent a higher level of output. If

output at C exceeds output at A then it must also exceed output at B.

They are convex. This is because of diminishing marginal products of capital

and labour. The slope of an isoquant is MPL/MPK (the MRTS). Moving down

an isoquant MPL falls as more labour is employed and MPK rises as less

capital is employed. The isoquant therefore becomes flatter (its slope gets

smaller).

Note that unlike indifference curves, isoquants are in principle observable.

Q: Why the difference?

D

● C

●

●

B

A ●

q2

q1

q0

K

L

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Economies of scale

Suppose the firm increases inputs of both capital and labour, each by x percent, e.g.

the shift from point C to point D. Output has increased from q0 to q1, say by y

percent. There are three possible cases.

Output increases more than in proportion to factor inputs (y > x). Over the

range there are increasing returns to scale (or economies of scale).

Output increases by the same proportion as factor inputs (y = x) Over the

range there are constant returns to scale.

Output increases less than in proportion to factor inputs (y < x) Over the

range there are decreasing returns to scale (diseconomies of scale).

Note that:

Economies of scale are reflected in the ‘distance’ between isoquants as we

shift outwards along a ray from the origin.

There may be a range of output over which there are increasing returns and

another range where there are decreasing returns.

Q: Why should there be decreasing returns if replication is possible (i.e. the firm

builds two small plants instead of one large one)?

Short run versus long run

Short run: the period over which one factor is fixed. E.g. new capital goods take

time to build and install .

Long run: The period over which all factors are variable.

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Cost minimisation

We are considering a long run decision: both factors are variable.

Total cost is TC = wL + rK,

where w is the wage rate (the price to the firm of a unit of labour), r is the ‘user cost

of capital (the per period rental cost including depreciation and all opportunity

costs).

For a given level of total cost TC0, an isocost line is defined as: Lr

w

r

TCK 0

Note that:

The slope of the isocost line is (minus) the ratio of factor prices, – r

w .

Assuming that the firm is ‘small’, i.e. has no influence over its factor prices,

isocost curves are straight lines.

Points A and B are different combinations of capital and labour that add up

to the same total cost. Point C is on a higher isocost curve.

There is an obvious analogy with the consumer’s budget line. But there is also a

fundamental difference. Q: What is it?

TC0/r

Slope: – w/r

●

B

A ●

TC2

TC1

TC0

K

TC0/w L

C

●

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What combination of K and L minimises total cost?

Points A and B are on the q1 isoquant but are associated with total cost TC2.

The cost minimising combination is at C where q1 is produced with total cost TC1.

At cost minimising points C and d the isocost curve is tangent to an isoquant. The

cost minimising condition is:

slope of isocost line = slope of isoquant

K

L

MP

MPMRTS

r

w

ratio of input prices = ratio of marginal products

Note :

This does not tell us what level of output the firm will choose, only the

minimum-cost method of producing each output level.

The tangency condition only holds for an interior solution.

E

●

TC1 TC2

C

●

D

●

B

●

A

●

q2

q1

q0

K

L

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Cost functions.

Long run cost function: LRTC = f’(q, w, r); here all costs are variable.

For given factor prices the cost minimising total cost function is: LRTC = f’’(q).

The short run cost function holds one factor fixed (let this be capital). Short run

cost function: SRTC = g’(q, w, K0), or for a given wage, SRTC = g’’(q, K0).

Fixed cost is that associated with capital: F = rK0.

Variable cost is associated with labour: VC = wL.

Average Cost AC(q) = TC/q

Marginal Cost MC = ∆TC/∆q (or ∂TC/∂q)

Consider the short run.

SRTC = F + wL;

SRAC = (F +wL)/q = F/q + wL/q = F/q +w/APL

SRMC = w ∆L/∆q = w/MPL

Notice that marginal cost will be higher in the short run that in the long run.

In the long run moving from q1 to q2 increases costs from TC1 to TC2; i.e moving

from cost minimising factor combination C to D.

In the short run only labour can be varied; q2 can only be attained by moving from

C to E. This involves a bigger increase in cost than when both factors could be

adjusted.