Chapter Thirty 9/27/2015 1 Chapter Thirty Production Exchange Economies (revisited) No production, only endowments, so no description of how resources are converted to consumables. General...

MICROECONOMICS


Chapter Thirty 9/27/2015 1 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 ... 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. 9/27/2015 2 Robinson Crusoe’s Technology Production function Labor (hours) Coconuts 240 Robinson Crusoe’s Technology Labor (hours) Coconuts Production function 240 Feasible production plans Robinson Crusoe’s Preferences RC’s preferences: –coconut is a good – leisure is a good Robinson Crusoe’s Preferences Leisure (hours) Coconuts More preferred 240 Robinson Crusoe’s Preferences Leisure (hours) Coconuts More preferred 24 0 Robinson Crusoe’s Choice Labor (hours) Coconuts Feasible production plans Production function 240 9/27/2015 3 Robinson Crusoe’s Choice Labor (hours) Coconuts Feasible production plans Production function 240 Leisure (hours)24 0 Robinson Crusoe’s Choice Labor (hours) Coconuts Feasible production plans Production function 240 Leisure (hours)24 0 Robinson Crusoe’s Choice Labor (hours) Coconuts Feasible production plans Production function 240 Leisure (hours)24 0 Robinson Crusoe’s Choice Labor (hours) Coconuts Production function 240 Leisure (hours)24 0 C* L* Robinson Crusoe’s Choice Labor (hours) Coconuts Production function 240 Leisure (hours)24 0 C* L* Labor Robinson Crusoe’s Choice Labor (hours) Coconuts Production function 240 Leisure (hours)24 0 C* L* Labor Leisure 9/27/2015 4 Robinson Crusoe’s Choice Labor (hours) Coconuts Production function 240 Leisure (hours)24 0 C* L* Labor Leisure O u tp u t Robinson Crusoe’s Choice Labor (hours) Coconuts Production function 240 Leisure (hours)24 0 C* L* Labor Leisure MRS = MPL O u tp u t 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 =  . Isoprofit Lines Labor (hours) Coconuts 24 C wL  Higher profit;   1 2 3  Slopes = + w 3  2 1 0 Profit-Maximization Labor (hours) Coconuts Feasible production plans Production function 240 9/27/2015 5 Profit-Maximization Labor (hours) Coconuts Production function 240 Profit-Maximization Labor (hours) Coconuts Production function 240 Profit-Maximization Labor (hours) Coconuts Production function 24 C* L*0 Profit-Maximization Labor (hours) Coconuts Production function 24 C* L* Isoprofit slope = production function slope 0 Profit-Maximization Labor (hours) Coconuts Production function 24 C* L* Isoprofit slope = production function slope i.e. w = MPL 0 Profit-Maximization Labor (hours) Coconuts Production function 24 C* L* Isoprofit slope = production function slope i.e. w = MPL = 1 MPL = MRPL. 0 9/27/2015 6 Profit-Maximization Labor (hours) Coconuts Production function 24 C* L* Isoprofit slope = production function slope i.e. w = MPL = 1 MPL = MRPL.  * * * * C wLRC gets 0 Profit-Maximization Labor (hours) Coconuts Production function 24 C* L* Isoprofit slope = production function slope i.e. w = MPL = 1 MPL = MRPL. * * * C wL  * Given w, RC’s firm’s quantity demanded of labor is L*Labor demand RC gets 0 Profit-Maximization Labor (hours) Coconuts Production function 24 C* L* Isoprofit slope = production function slope i.e. w = MPL = 1 MPL = MRPL.  * Given w, RC’s firm’s quantity demanded of labor is L* and output quantity supplied is C*. Labor demand Output supply * * * C wLRC gets 0 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 C wL  * . Utility-Maximization Labor (hours) Coconuts  * 240 C wL  * . Budget constraint Utility-Maximization Labor (hours) Coconuts  * 240 C wL  * . Budget constraint; slope = w 9/27/2015 7 Utility-Maximization Labor (hours) Coconuts More preferred 240 Utility-Maximization Labor (hours) Coconuts  * 240 C wL  * . Budget constraint; slope = w Utility-Maximization Labor (hours) Coconuts  * Budget constraint; slope = w 240 C wL  * . Utility-Maximization Labor (hours) Coconuts  * 240 C wL  * .C* L* Budget constraint; slope = w Utility-Maximization Labor (hours) Coconuts  * 240 C wL  * .C* L* MRS = w Budget constraint; slope = w Utility-Maximization Labor (hours) Coconuts  * 240 C wL  * .C* L* Labor supply Budget constraint; slope = w MRS = w Given w, RC’s quantity supplied of labor is L* 9/27/2015 8 Utility-Maximization Labor (hours) Coconuts  * 240 C wL  * .C* L* Given w, RC’s quantity supplied of labor is L* and output quantity demanded is C*. Labor supply Output demand Budget constraint; slope = w MRS = w Utility-Maximization & Profit- Maximization Profit-maximization: –w = MPL –quantity of output supplied = C* –quantity of labor demanded = L* Utility-Maximization & Profit- Maximization Profit-maximization: –w = MPL –quantity of output supplied = C* –quantity of labor demanded = L* Utility-maximization: –w = MRS –quantity of output demanded = C* –quantity of labor supplied = L* Utility-Maximization & Profit- Maximization Profit-maximization: –w = MPL –quantity of output supplied = C* –quantity of labor demanded = L* Utility-maximization: –w = MRS –quantity of output demanded = C* –quantity of labor supplied = L* Coconut and labor markets both clear. Utility-Maximization & Profit- Maximization Labor (hours) Coconuts 24 C* L*  * 0 MRS = w = MPL Given w, RC’s quantity supplied of labor = quantity demanded of labor = L* and output quantity demanded = output quantity supplied = C*. Pareto Efficiency Must have MRS = MPL. 9/27/2015 9 Pareto Efficiency Labor (hours) Coconuts 240 MRS  MPL Pareto Efficiency Labor (hours) Coconuts 240 MRS  MPL Preferred consumption bundles. Pareto Efficiency Labor (hours) Coconuts 240 MRS = MPL Pareto Efficiency Labor (hours) Coconuts 240 MRS = MPL. The common slope  relative wage rate w that implements the Pareto efficient plan by decentralized pricing. First Fundamental Theorem of Welfare Economics A competitive market equilibrium is Pareto efficient if –consumers’ preferences are convex – there are no externalities in consumption or production. Second Fundamental Theorem of Welfare Economics Any Pareto efficient economic state can be achieved as a competitive market equilibrium if –consumers’ preferences are convex – firms’ technologies are convex – there are no externalities in consumption or production. 9/27/2015 10 Non-Convex Technologies Do the Welfare Theorems hold if firms have non-convex technologies? Non-Convex Technologies Do the Welfare Theorems hold if firms have non-convex technologies? The 1st Theorem does not rely upon firms’ technologies being convex. Non-Convex Technologies Labor (hours) Coconuts 240 MRS = MPL The common slope  relative wage rate w that implements the Pareto efficient plan by decentralized pricing. Non-Convex Technologies Do the Welfare Theorems hold if firms have non-convex technologies? The 2nd Theorem does require that firms’ technologies be convex. Non-Convex Technologies Labor (hours) Coconuts 240 MRS = MPL. The Pareto optimal allocation cannot be implemented by a competitive equilibrium. Production Possibilities Resource and technological limitations restrict what an economy can produce. The set of all feasible output bundles is the economy’s production possibility set. The set’s outer boundary is the production possibility frontier. 9/27/2015 11 Production Possibilities Fish Coconuts Production possibility frontier (ppf) Production Possibilities Fish Coconuts Production possibility frontier (ppf) Production possibility set Production Possibilities Fish Coconuts Feasible but inefficient Production Possibilities Fish Coconuts Feasible but inefficient Feasible and efficient Production Possibilities Fish Coconuts Feasible but inefficient Feasible and efficient Infeasible Production Possibilities Fish Coconuts Ppf’s slope is the marginal rate of product transformation. 9/27/2015 12 Production Possibilities Fish Coconuts Ppf’s slope is the marginal rate of product transformation. Increasingly negative MRPT  increasing opportunity cost to specialization. Production Possibilities  If there are no production externalities then a ppf will be concave w.r.t. the origin. Why? Production Possibilities  If there are no production externalities then a ppf will be concave w.r.t. the origin. Why? Because efficient production requires exploitation of comparative advantages. Comparative Advantage Two agents, RC and Man Friday (MF). RC can produce at most 20 coconuts or 30 fish. MF can produce at most 50 coconuts or 25 fish. Comparative Advantage F C F C RC MF 20 50 30 25 Comparative Advantage F C F C RC MF 20 50 30 25 MRPT = -2/3 coconuts/fish so opp. cost of one more fish is 2/3 foregone coconuts. 9/27/2015 13 Comparative Advantage F C F C RC MF 20 50 30 25 MRPT = -2/3 coconuts/fish so opp. cost of one more fish is 2/3 foregone coconuts. MRPT = -2 coconuts/fish so opp. cost of one more fish is 2 foregone coconuts. Comparative Advantage F C F C RC MF 20 50 30 25 MRPT = -2/3 coconuts/fish so opp. cost of one more fish is 2/3 foregone coconuts. MRPT = -2 coconuts/fish so opp. cost of one more fish is 2 foregone coconuts. RC has the comparative opp. cost advantage in producing fish. Comparative Advantage F C F C RC MF 20 50 30 25 MRPT = -2/3 coconuts/fish so opp. cost of one more coconut is 3/2 foregone fish. Comparative Advantage F C F C RC MF 20 50 30 25 MRPT = -2/3 coconuts/fish so opp. cost of one more coconut is 3/2 foregone fish. MRPT = -2 coconuts/fish so opp. cost of one more coconut is 1/2 foregone fish. Comparative Advantage F C F C RC MF 20 50 30 25 MRPT = -2/3 coconuts/fish so opp. cost of one more coconut is 3/2 foregone fish. MRPT = -2 coconuts/fish so opp. cost of one more coconut is 1/2 foregone fish. MF has the comparative opp. cost advantage in producing coconuts. Comparative Advantage F C Economy F C F C RC MF 20 50 30 25 70 55 50 30 Use RC to produce fish before using MF. Use MF to produce coconuts before using RC. 9/27/2015 14 Comparative Advantage F C Economy F C F C RC MF 20 50 30 25 70 55 50 30 Using low opp. cost producers first results in a ppf that is concave w.r.t the origin. Comparative Advantage F C Economy More producers with different opp