MicroeconomicsCorso E

John Hey

Summary of Chapter 8• The contract curve shows the allocations that

are efficient in the sense of Pareto.• There always exist the possibility of mutually

advantageous exchange if preferences are different and/or endowments are different (unless the endowment point is on the contract curve).

• Perfect competitive equilibrium (with both individuals taking the price as given) always leads to a Pareto efficient allocation.

• If one of the individuals chooses the price the allocation is not Pareto efficient.

The competitive equilibrium depends on the preferences and the endowments.

• If one individual changes his or her preferences in such a way that he or she now prefers more a particular good than before...

• ... the relative price of that good rises.• If an individual is endowed with more of a

good than before...• ... the relative price of that good falls.

Part 1 and Part 2

• Part 1: an economy without production...• ... just exchange

• Part 2: an economy with production...• ... production and exchange.

Part 1• Reservation prices.• Indifference curves.• Demand and supply curves.• Surplus.• Exchange.• The Edgeworth Box.• The contract curve.• Competitive equilibrium.• Paretian efficiency and inefficiency.

Part 2

• Chapter 10: Technology.• Chapter 11: Minimisation of costs and factor

demands.• Chapter 12: Cost curves.• Chapter 13: Firm’s supply and profit/surplus.• Chapter 14: The production possibility frontier.• Chapter 15: Production and exchange.

Chapter 10

• Firms produce...• ...they use inputs to produce outputs.• In general many inputs and many outputs.• We work with a simple firm that produces

one output with two inputs...• ...capital and labour.• The technology describes the possibilities

open to the firm.

Chapter 5 Chapter 10

• Individuals• Buy goods and

‘produce’ utility…• …depends on the

preferences…• …which we can

represent with indifference curves..

• …in the space (q1,q2)

• Firms• Buy inputs and

produce output…• …depends on the

technology…• …which we can

represent with isoquants ..

• …in the space (q1,q2)

The only difference?

• We can represent preferences with a utility function ...

• ... but this function is not unique...• ... because/hence we cannot measure the utility

of an individual.• We can represent the technology of a firm with a

production function ... • ... and this function is unique…• …because we can measure the output.

An isoquant

• In the space of the inputs (q1,q2) it is the locus of the points where output is constant.

• (An indifference curve – the locus of the points where the individual is indifferent. Or the locus of points for which the utility is constant.)

Two dimensions

• The shape of the isoquants: depends on the substitution between the two inputs.

• The way in which the output changes form one isoquant to another – depends on the returns to scale.

Perfect substitutes 1:1

• an isoquant: q1 + q2 = constant• y = A(q1 + q2) constant returns to scale

• y = A(q1 + q2)0.5 decreasing returns to scale

• y = A(q1 + q2)2 increasing returns to scale

• y = A(q1 + q2)b returns to scale decreasing (b<1) increasing (b>1)

y = q1 + q2 : perfect substitutes 1:1 and constant returns to scale

y = (q1 + q2)2 : perfect substitutes 1:1 and increasing returns to scale

y = (q1 + q2)0.5 : perfect substitutes 1:1 and decreasing returns to scale

Perfect Substitutes 1:a

• an isoquant: q1 + q2/a = constant

• y = A(q1 + q2/a) constant returns to scale

• y = A(q1 + q2/a)b returns to scale decreasing (b<1) increasing (b>1)

Perfect Complements 1 with 1

• an isoquant: min(q1,q2) = constant

• y = A min(q1,q2) constant returns to scale

• y = A[min(q1,q2)]b returns to scale decreasing (b<1) increasing (b>1)

y = min(q1, q2): Perfect Complements 1 with 1 and constant returns to scale

y = [min(q1, q2)]2 Perfect Complements 1 with 1 and increasing returns to scale

Y = [min(q1, q2)]0.5: Perfect Complements 1 with 1 and decreasing returns to scale

Perfect Complements 1 with a

• an isoquant: min(q1,q2/a) = constant

• y = A min(q1,q2/a) constant returns to scale

• y = A[min(q1,q2/a)]b returns to scale decreasing (b<1) increasing (b>1)

y = q10.5 q2

0.5: Cobb-Douglas with parameters 0.5 and 0.5 – hence

constant returns to scale

y = q1 q2: Cobb-Douglas with parameters 1 and 1 – hence increasing returns to scale

y = q10.25 q2

0.25: Cobb-Douglas with parameters 0.25 and 0.25 – hence

decreasing returns to scale

Cobb-Douglas with parameters a and b

• an isoquant: q1a

q2b = constant

• y = A q1a

q2b

• a+b<1 decreasing returns to scale• a+b=1 constant returns to scale• a+b>1 increasing returns to scale

Chapter 5 Chapter 10

• Individuals• The preferences are

given by indifference curves

• …in the space (q1,q2)• .. can be represented

by a utility function u = f(q1,q2)…

• …which is not unique.

• Firms• The technology is

given by isoquants • …in the space (q1,q2)• ..can be represented

by a production function …

y = f(q1,q2)…• … which is unique .

Chapter 10

• Goodbye!