INTMIC9.jpg Chapter 33 Production Exchange Economies (revisited) uNo production, only endowments, so no description of how resources are converted to consumables. uGeneral equilibrium: all markets clear simultaneously. u1st and 2nd Fundamental Theorems of Welfare Economics. u Now Add Production ... uAdd input markets, output markets, describe firms’ technologies, the distributions of firms’ outputs and profits … Now Add Production ... uAdd input markets, output markets, describe firms’ technologies, the distributions of firms’ outputs and profits … That’s not easy! Robinson Crusoe’s Economy uOne agent, RC. uEndowed with a fixed quantity of one resource -- 24 hours. uUse time for labor (production) or leisure (consumption). uLabor time = L. Leisure time = 24 - L. uWhat will RC choose? Robinson Crusoe’s Technology uTechnology: Labor produces output (coconuts) according to a concave production function. Robinson Crusoe’s Technology Production function Labor (hours) Coconuts 24 0 Robinson Crusoe’s Technology Labor (hours) Coconuts Production function 24 0 Feasible production plans Robinson Crusoe’s Preferences uRC’s preferences: –coconut is a good –leisure is a good Robinson Crusoe’s Preferences Leisure (hours) Coconuts More preferred 24 0 Robinson Crusoe’s Preferences Leisure (hours) Coconuts More preferred 24 0 Robinson Crusoe’s Choice Labor (hours) Coconuts Feasible production plans Production function 24 0 Robinson Crusoe’s Choice Labor (hours) Coconuts Feasible production plans Production function 24 0 Leisure (hours) 24 0 Robinson Crusoe’s Choice Labor (hours) Coconuts Feasible production plans Production function 24 0 Leisure (hours) 24 0 Robinson Crusoe’s Choice Labor (hours) Coconuts Feasible production plans Production function 24 0 Leisure (hours) 24 0 Robinson Crusoe’s Choice Labor (hours) Coconuts Production function 24 0 Leisure (hours) 24 0 C* L* Robinson Crusoe’s Choice Labor (hours) Coconuts Production function 24 0 Leisure (hours) 24 0 C* L* Labor Robinson Crusoe’s Choice Labor (hours) Coconuts Production function 24 0 Leisure (hours) 24 0 C* L* Labor Leisure Robinson Crusoe’s Choice Labor (hours) Coconuts Production function 24 0 Leisure (hours) 24 0 C* L* Labor Leisure Robinson Crusoe’s Choice Labor (hours) Coconuts Production function 24 0 Leisure (hours) 24 0 C* L* Labor Leisure MRS = MPL Robinson Crusoe as a Firm uNow suppose RC is both a utility-maximizing consumer and a profit-maximizing firm. uUse coconuts as the numeraire good; i.e. price of a coconut = $1. uRC’s wage rate is w. uCoconut output level is C. Robinson Crusoe as a Firm uRC’s firm’s profit is p = C - wL. up = C - wL Û C = p + wL, the equation of an isoprofit line. uSlope = + w . uIntercept = p . Isoprofit Lines Labor (hours) Coconuts 24 Higher profit; Slopes = + w 0 Profit-Maximization Labor (hours) Coconuts Feasible production plans Production function 24 0 Profit-Maximization Labor (hours) Coconuts Production function 24 0 Profit-Maximization Labor (hours) Coconuts Production function 24 0 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 Profit-Maximization Labor (hours) Coconuts Production function 24 C* L* Isoprofit slope = production function slope i.e. w = MPL = 1´ MPL = MRPL. 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* 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 RC gets 0 Utility-Maximization uNow consider RC as a consumer endowed with $p* who can work for $w per hour. uWhat is RC’s most preferred consumption bundle? uBudget constraint is Utility-Maximization Labor (hours) Coconuts 24 0 Budget constraint Utility-Maximization Labor (hours) Coconuts 24 0 Budget constraint; slope = w Utility-Maximization Labor (hours) Coconuts More preferred 24 0 Utility-Maximization Labor (hours) Coconuts 24 0 Budget constraint; slope = w Utility-Maximization Labor (hours) Coconuts Budget constraint; slope = w 24 0 Utility-Maximization Labor (hours) Coconuts 24 0 C* L* Budget constraint; slope = w Utility-Maximization Labor (hours) Coconuts 24 0 C* L* MRS = w Budget constraint; slope = w Utility-Maximization Labor (hours) Coconuts 24 0 C* L* Labor supply Budget constraint; slope = w MRS = w Given w, RC’s quantity supplied of labor is L* Utility-Maximization Labor (hours) Coconuts 24 0 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 uProfit-maximization: –w = MPL –quantity of output supplied = C* –quantity of labor demanded = L* Utility-Maximization & Profit-Maximization uProfit-maximization: –w = MPL –quantity of output supplied = C* –quantity of labor demanded = L* uUtility-maximization: –w = MRS –quantity of output demanded = C* –quantity of labor supplied = L* Utility-Maximization & Profit-Maximization uProfit-maximization: –w = MPL –quantity of output supplied = C* –quantity of labor demanded = L* uUtility-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 uMust have MRS = MPL. Pareto Efficiency Labor (hours) Coconuts 24 0 MRS ¹ MPL Pareto Efficiency Labor (hours) Coconuts 24 0 MRS ¹ MPL Preferred consumption bundles. Pareto Efficiency Labor (hours) Coconuts 24 0 MRS = MPL Pareto Efficiency Labor (hours) Coconuts 24 0 MRS = MPL. The common slope Þ relative wage rate w that implements the Pareto efficient plan by decentralized pricing. First Fundamental Theorem of Welfare Economics uA 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 uAny 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. – Non-Convex Technologies uDo the Welfare Theorems hold if firms have non-convex technologies? Non-Convex Technologies uDo the Welfare Theorems hold if firms have non-convex technologies? uThe 1st Theorem does not rely upon firms’ technologies being convex. Non-Convex Technologies Labor (hours) Coconuts 24 0 MRS = MPL The common slope Þ relative wage rate w that implements the Pareto efficient plan by decentralized pricing. Non-Convex Technologies uDo the Welfare Theorems hold if firms have non-convex technologies? uThe 2nd Theorem does require that firms’ technologies be convex. Non-Convex Technologies Labor (hours) Coconuts 24 0 MRS = MPL. The Pareto optimal allocation cannot be implemented by a competitive equilibrium. Production Possibilities uResource and technological limitations restrict what an economy can produce. uThe set of all feasible output bundles is the economy’s production possibility set. uThe set’s outer boundary is the production possibility frontier. 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. Production Possibilities Fish Coconuts Ppf’s slope is the marginal rate of product transformation. Increasingly negative MRPT Þ increasing opportunity cost to specialization. Production Possibilities uIf there are no production externalities then a ppf will be concave w.r.t. the origin. uWhy? Production Possibilities uIf there are no production externalities then a ppf will be concave w.r.t. the origin. uWhy? uBecause efficient production requires exploitation of comparative advantages. Comparative Advantage uTwo agents, RC and Man Friday (MF). uRC can produce at most 20 coconuts or 30 fish. uMF 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. 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. 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. costs “smooth out” the ppf. Coordinating Production & Consumption uThe ppf contains many technically efficient output bundles. uWhich are Pareto efficient for consumers? Coordinating Production & Consumption Fish Coconuts Output bundle is Coordinating Production & Consumption Fish Coconuts Output bundle is and is the aggregate endowment for distribution to consumers RC and MF. Coordinating Production & Consumption Fish Coconuts ORC OMF Output bundle is and is the aggregate endowment for distribution to consumers RC and MF. Coordinating Production & Consumption Fish Coconuts ORC OMF Allocate efficiently; say to RC Coordinating Production & Consumption Fish Coconuts ORC OMF Allocate efficiently; say to RC and to MF. Coordinating Production & Consumption Fish Coconuts ORC OMF Coordinating Production & Consumption Fish Coconuts ORC OMF Coordinating Production & Consumption Fish Coconuts ORC OMF Coordinating Production & Consumption Fish Coconuts ORC OMF MRS ¹ MRPT Coordinating Production & Consumption Fish Coconuts ORC OMF O’MF Instead produce Coordinating Production & Consumption Fish Coconuts ORC OMF O’MF Instead produce Coordinating Production & Consumption Fish Coconuts ORC OMF O’MF Instead produce Give MF same allocation as before. Coordinating Production & Consumption Fish Coconuts ORC OMF O’MF Instead produce Give MF same allocation as before. MF’s utility is unchanged. Coordinating Production & Consumption Fish Coconuts ORC OMF O’MF Instead produce Give MF same allocation as before. MF’s utility is unchanged Coordinating Production & Consumption Fish Coconuts ORC OMF O’MF Instead produce Give MF same allocation as before. MF’s utility is unchanged Coordinating Production & Consumption Fish Coconuts ORC OMF O’MF Instead produce Give MF same allocation as before. MF’s utility is unchanged, RC’s utility is higher Coordinating Production & Consumption Fish Coconuts ORC OMF O’MF Instead produce Give MF same allocation as before. MF’s utility is unchanged, RC’s utility is higher; Pareto improvement. Coordinating Production & Consumption uMRS ¹ MRPT Þ inefficient coordination of production and consumption. uHence, MRS = MRPT is necessary for a Pareto optimal economic state. Coordinating Production & Consumption Fish Coconuts ORC OMF Decentralized Coordination of Production & Consumption uRC and MF jointly run a firm producing coconuts and fish. uRC and MF are also consumers who can sell labor. uPrice of coconut = pC. uPrice of fish = pF. uRC’s wage rate = wRC. uMF’s wage rate = wMF. Decentralized Coordination of Production & Consumption uLRC, LMF are amounts of labor purchased from RC and MF. uFirm’s profit-maximization problem is choose C, F, LRC and LMF to Decentralized Coordination of Production & Consumption Isoprofit line equation is Decentralized Coordination of Production & Consumption Isoprofit line equation is which rearranges to Decentralized Coordination of Production & Consumption Isoprofit line equation is which rearranges to Decentralized Coordination of Production & Consumption Fish Coconuts Higher profit Slopes = Decentralized Coordination of Production & Consumption Fish Coconuts The firm’s production possibility set. Decentralized Coordination of Production & Consumption Fish Coconuts Slopes = Decentralized Coordination of Production & Consumption Fish Coconuts Profit-max. plan Slopes = Decentralized Coordination of Production & Consumption Fish Coconuts Profit-max. plan Slope = Decentralized Coordination of Production & Consumption Fish Coconuts Profit-max. plan Slope = Competitive markets and profit-maximization Þ Decentralized Coordination of Production & Consumption uSo competitive markets, profit-maximization, and utility maximization all together cause the condition necessary for a Pareto optimal economic state. Decentralized Coordination of Production & Consumption Fish Coconuts ORC OMF Competitive markets and utility-maximization Þ Decentralized Coordination of Production & Consumption Fish Coconuts ORC OMF Competitive markets, utility- maximization and profit- maximization Þ