CHAPTER 31 PRODUCTION. The Robinson Crusoe Economy One consumer and one firm; The consumer owns the...
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Transcript of CHAPTER 31 PRODUCTION. The Robinson Crusoe Economy One consumer and one firm; The consumer owns the...
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 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 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
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
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.
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.
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
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
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).
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.