CHAPTER 31PRODUCTION

The Robinson Crusoe Economy One consumer and one firm; The consumer owns the firm; Preference: over leisure and coconuts; Technology: use leisure to produce coconuts; The planner’s problem:

F.O.C.,

max ( , ) s.t. ( )C lu C l C f L l L L

( )u u

f Ll C

The Robinson Crusoe economy

The Competitive equilibrium

Labor market and goods market; The consumer supplies labor and buys

consumption goods from markets; The firm hires labor and sells output in

markets; Utility maximization and profit maximization; General equilibrium on both markets; The consumer is the shareholder of the firm.

The Competitive equilibrium

The firm’s behavior:

F.O.C.

The firm’s profits:

max ( )Lf L wL

( )f L w

* * *C wL

The Competitive equilibrium The firm’s behavior

The Competitive equilibrium

The consumer’s budget constraint:

The consumer’s problem:

F.O.C.

*C wl wL

*

,max ( , ) s.t.C lu C l C wl wL

u uw

l C

The Competitive equilibrium The consumer’s behavior

The Competitive equilibrium

The competitive outcome is Pareto efficient.

( )u u

w f Ll C

The Competitive equilibrium

Different Technologies

Constant returns to scaleZero profits for the firm;The isoprofit coincides with the production

function;The budget line coincides with the isoprofit;The competitive equilibrium is Pareto efficient.

Different Technologies The competitive equilibrium exists.

Different Technologies

Increasing returns to scaleThe Pareto efficient allocation cannot be achieved

by the competitive market. The firm would be making negative profits at the Pareto

efficient allocation; Given any market price, the profit-maximization

problem has no solution.

Different Technologies The Pareto efficient allocation is not attainable.

The 1st and 2nd theorem of welfare economics Assuming convexity and closedness, the

competitive equilibrium exists; The competitive equilibrium is Pareto

efficient; Assuming convexity, any Pareto efficient

allocation can be achieved by a competitive equilibrium.

Production possibilities

One input, multiple output; Production possibility set: set of feasible

outputs; Production possibility frontier: set of efficient

outputs; Marginal rate of transformation: the rate at

which the economy substitutes one output for another.

Production possibilities

Comparative Advantage

Robinson Crusoe: FC/10+CC/2010;

Friday: FF/20+CF/1010;

Robinson has a comparative advantage in coconuts and Friday has a comparative advantage in fish.

Comparative Advantage

Comparative Advantage

Joint production possibility set:

10; 10.10 20 20 10C C F FF C F C

3300 300 if 0;

2 23

300 300 if 0.2 2

C C

F F

FC F F

CF C C

Comparative Advantage

Pareto efficiency

Given total output (x1, x2), the competitive equilibrium is given by MRSA=MRSB.

We must have MRSA=MRSB=MRT; The slope of indifference curves at the

competitive equilibrium must equal the slope of the PPF at (x1, x2).

Pareto efficiency

Competitive Equilibrium

Assuming inelastic supply of labor: LC+LF=L;

The firm’s problem:

F.O.C.,

max C FC F

p C p F L

F

C

pMRT

p

Competitive Equilibrium The firm chooses a point on the PPF that maximizes

its profits given prices.

Competitive Equilibrium

The consumer’s problem:

F.O.C.

,max ( , ) s.t. C FC Fu C F p C p F wL

F

C

pMRS

p