Microeconomics 2

John Hey

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.• Price-offer curves.• The contract curve.• Competitive equilibrium.• Paretian efficiency and inefficiency.• And, of course, the connections between these.

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.

• (Interlude : chapter 16, estimation of demand and supply and a policy check)

Chapter 10: Technology

• 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.

• This chapter catalogues the technologies that we are going to use in the future.

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)• where q1,q2 are the quantities of the goods

• Firms• Buy inputs and

produce output…• …depends on the

technology…• …which we can

represent with isoquants ..

• …in the space (q1,q2)• where q1,q2 are the quantities of the inputs

The only difference?

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

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

utility/happiness 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 (the analogue of an indifference curve)

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

• Is usually downward sloping, because if the firm has less of one input it needs more of the other.

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

Can isoquants (indifference curves) cross?

Two dimensions of technology

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

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

Substitution

• Marginal Rate of Substitution (MRS) ...

• ... the slope of the isoquants: dq2/dq1 along an isoquant.

• Constant for Perfect Substitutes• The Elasticity of Substitution ... “how quickly the

marginal rate of substitution changes as we move along an isoquant”

• ... d[ln(q2)]/d[ln(q1)] = [dq2/dq1]/[q2/q1]

• Constant for CES.

Returns to scale

• Tells you how output changes affect the scale of production:

• Suppose we double both inputs...• ... if output is less than double, then we have

decreasing returns to scale...• ... if output is exactly double, then we have

constant returns to scale...• ... if output is more than double, then we have

increasing returns to scale.

Technologies

• We are going to consider

• Perfect substitutes

• Perfect complements

• Cobb-Douglas

• Stone-Geary

• CES (Constant Elasticity of Substitution)

• They differ in terms of the substitutability between the inputs.

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

• Or more generally

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

Stone-Geary with parameters a and b and ‘subsistence levels’ of the two inputs s1 and s2

• an isoquant: (q1-s1)a (q2-s2)b = constant

• y = A (q1-s1)a (q2-s2)b

• a+b<1 decreasing returns to scale

• a+b=1 constant returns to scale

• a+b>1 increasing returns to scale

CES (Constant Elasticity of Substitution)

• an isoquant: (c1q1-ρ+ c2q2

-ρ)-s/ρ = constant

• y = A (c1q1-ρ+ c2q2

-ρ)-s/ρ

• s<1 decreasing returns to scale

• s=1 constant returns to scale

• s>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!