CHAPTER 31
PRODUCTION
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:

max u (C , l ) s.t. C  f ( L) l  L  L
C, l
 F.O.C.
u
l
u
 f ( L)
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:
max f ( L)  wL
L
 F.O.C.

f ( L)  w
The firm’s profits:
*  C *  wL*
The Competitive equilibrium
The Competitive equilibrium

The consumer’s budget constraint:
C  wl  wL  *

The consumer’s problem:
max u (C , l ) s.t. C  wl  wL  
C ,l
 F.O.C.
u
l
u
w
C
*
The Competitive equilibrium
The Competitive equilibrium

The competitive outcome is Pareto efficient.
u
l
u
 w  f ( L)
C
The Competitive equilibrium
Different Technologies

Constant returns to scale
 Zero
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 scale
 The
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/2010;
 Friday: FF/20+CF/1010;
 Robinson has a comparative advantage in
coconuts and Friday has a comparative
advantage in fish.

Comparative Advantage
Comparative Advantage

Joint production possibility set:
FC CC

 10;
10 20
FF CF

 10.
20 10
F
3
C   300  FC  300 if
2
2
C
3
F   300  CF  300 if
2
2
FC  0;
CF  0.
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:

max pC C  pF F  L
C,F
 F.O.C.
pF
MRT  
pC
Competitive Equilibrium

The firm chooses a point on the PPF that maximizes
its profits given prices.
Competitive Equilibrium

The consumer’s problem:
max u(C, F ) s.t. pC C  pF F  wL  
C, F
 F.O.C.
pF
MRS  
pC