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:  F.O.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:

The Competitive equilibrium The firm’s behavior

The Competitive equilibrium The consumer’s budget constraint: The consumer’s problem:  F.O.C.

The Competitive equilibrium The consumer’s behavior

The Competitive equilibrium The competitive outcome is Pareto efficient.

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 1 st and 2 nd 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: F C /10+C C /20  10; Friday: F F /20+C F /10  10; Robinson has a comparative advantage in coconuts and Friday has a comparative advantage in fish.

Comparative Advantage

Joint production possibility set:

Comparative Advantage

Pareto efficiency Given total output (x 1, x 2 ), the competitive equilibrium is given by MRS A =MRS B. We must have MRS A =MRS B =MRT; The slope of indifference curves at the competitive equilibrium must equal the slope of the PPF at (x 1, x 2 ).

Pareto efficiency

Competitive Equilibrium Assuming inelastic supply of labor: L C +L F =L; The firm’s problem:  F.O.C.

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.