Chapter Thirty. Production. Exchange Economies (revisited). No production, only endowments, so no description of how resources are converted to consumables. General equilibrium: all markets clear simultaneously. 1st and 2nd Fundamental Theorems of Welfare Economics. Now Add Production.
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Exchange Economies (revisited) • No production, only endowments, so no description of how resources are converted to consumables. • General equilibrium: all markets clear simultaneously. • 1st and 2nd Fundamental Theorems of Welfare Economics.
Now Add Production ... • Add input markets, output markets, describe firms’ technologies, the distributions of firms’ outputs and profits …
Now Add Production ... • Add input markets, output markets, describe firms’ technologies, the distributions of firms’ outputs and profits … That’s not easy!
Robinson Crusoe’s Economy • One agent, RC. • Endowed with a fixed quantity of one resource -- 24 hours. • Use time for labor (production) or leisure (consumption). • Labor time = L. Leisure time = 24 - L. • What will RC choose?
Robinson Crusoe’s Technology • Technology: Labor produces output (coconuts) according to a concave production function.
Robinson Crusoe as a Firm • Now suppose RC is both a utility-maximizing consumer and a profit-maximizing firm. • Use coconuts as the numeraire good; i.e. price of a coconut = $1. • RC’s wage rate is w. • Coconut output level is C.
Robinson Crusoe as a Firm • RC’s firm’s profit is = C - wL. • = C - wL C = + wL, the equation of an isoprofit line. • Slope = + w . • Intercept = .
Profit-Maximization Isoprofit slope = production function slope Coconuts Production function C* L* 24 0 Labor (hours)
Profit-Maximization Isoprofit slope = production function slope i.e. w = MPL Coconuts Production function C* L* 24 0 Labor (hours)
Profit-Maximization Isoprofit slope = production function slope i.e. w = MPL = 1 MPL = MRPL. Coconuts Production function C* L* 24 0 Labor (hours)
Profit-Maximization Isoprofit slope = production function slope i.e. w = MPL = 1 MPL = MRPL. Coconuts Production function C* L* 24 0 Labor (hours) RC gets
Profit-Maximization Isoprofit slope = production function slope i.e. w = MPL = 1 MPL = MRPL. Coconuts Production function C* Given w, RC’s firm’s quantity demanded of labor is L* Labor demand L* 24 0 Labor (hours) RC gets
Profit-Maximization Isoprofit slope = production function slope i.e. w = MPL = 1 MPL = MRPL. Coconuts Production function C* Output supply Given w, RC’s firm’s quantity demanded of labor is L* and output quantity supplied is C*. Labor demand L* 24 0 Labor (hours) RC gets
Utility-Maximization • Now consider RC as a consumer endowed with $* who can work for $w per hour. • What is RC’s most preferred consumption bundle? • Budget constraint is
Utility-Maximization Coconuts MRS = w Budget constraint; slope = w C* L* 24 0 Labor (hours)
Utility-Maximization Coconuts MRS = w Budget constraint; slope = w C* Given w, RC’s quantity supplied of labor is L* Labor supply L* 24 0 Labor (hours)
Utility-Maximization Coconuts MRS = w Budget constraint; slope = w C* Output demand Given w, RC’s quantity supplied of labor is L* and output quantity demanded is C*. Labor supply L* 24 0 Labor (hours)
