© 2010 W. W. Norton & Company, Inc. 32 Production

© 2010 W. W. Norton & Company, Inc. 2 Exchange Economies (revisited) u No production, only endowments, so no description of how resources are converted to consumables. u General equilibrium: all markets clear simultaneously. u 1st and 2nd Fundamental Theorems of Welfare Economics.

© 2010 W. W. Norton & Company, Inc. 3 Now Add Production... u Add input markets, output markets, describe firms’ technologies, the distributions of firms’ outputs and profits …

© 2010 W. W. Norton & Company, Inc. 4 Now Add Production... u Add input markets, output markets, describe firms’ technologies, the distributions of firms’ outputs and profits … That’s not easy!

© 2010 W. W. Norton & Company, Inc. 5 Robinson Crusoe’s Economy u One agent, RC. u Endowed with a fixed quantity of one resource hours. u Use time for labor (production) or leisure (consumption). u Labor time = L. Leisure time = 24 - L. u What will RC choose?

© 2010 W. W. Norton & Company, Inc. 6 Robinson Crusoe’s Technology u Technology: Labor produces output (coconuts) according to a concave production function.

© 2010 W. W. Norton & Company, Inc. 7 Robinson Crusoe’s Technology Production function Labor (hours) Coconuts 24 0

© 2010 W. W. Norton & Company, Inc. 8 Robinson Crusoe’s Technology Labor (hours) Coconuts Production function 24 0 Feasible production plans

© 2010 W. W. Norton & Company, Inc. 9 Robinson Crusoe’s Preferences u RC’s preferences: –coconut is a good –leisure is a good

© 2010 W. W. Norton & Company, Inc. 10 Robinson Crusoe’s Preferences Leisure (hours) Coconuts More preferred 24 0

© 2010 W. W. Norton & Company, Inc. 11 Robinson Crusoe’s Preferences Leisure (hours) Coconuts More preferred 240

© 2010 W. W. Norton & Company, Inc. 12 Robinson Crusoe’s Choice Labor (hours) Coconuts Feasible production plans Production function 24 0

© 2010 W. W. Norton & Company, Inc. 13 Robinson Crusoe’s Choice Labor (hours) Coconuts Feasible production plans Production function 24 0 Leisure (hours) 240

© 2010 W. W. Norton & Company, Inc. 14 Robinson Crusoe’s Choice Labor (hours) Coconuts Feasible production plans Production function 24 0 Leisure (hours) 240

© 2010 W. W. Norton & Company, Inc. 15 Robinson Crusoe’s Choice Labor (hours) Coconuts Feasible production plans Production function 24 0 Leisure (hours) 240

© 2010 W. W. Norton & Company, Inc. 16 Robinson Crusoe’s Choice Labor (hours) Coconuts Production function 24 0 Leisure (hours) 240 C* L*

© 2010 W. W. Norton & Company, Inc. 17 Robinson Crusoe’s Choice Labor (hours) Coconuts Production function 24 0 Leisure (hours) 240 C* L* Labor

© 2010 W. W. Norton & Company, Inc. 18 Robinson Crusoe’s Choice Labor (hours) Coconuts Production function 24 0 Leisure (hours) 240 C* L* LaborLeisure

© 2010 W. W. Norton & Company, Inc. 19 Robinson Crusoe’s Choice Labor (hours) Coconuts Production function 24 0 Leisure (hours) 240 C* L* LaborLeisure Output

© 2010 W. W. Norton & Company, Inc. 20 Robinson Crusoe’s Choice Labor (hours) Coconuts Production function 24 0 Leisure (hours) 240 C* L* LaborLeisure MRS = MP L Output

© 2010 W. W. Norton & Company, Inc. 21 Robinson Crusoe as a Firm u Now suppose RC is both a utility- maximizing consumer and a profit- maximizing firm. u Use coconuts as the numeraire good; i.e. price of a coconut = $1. u RC’s wage rate is w. u Coconut output level is C.

© 2010 W. W. Norton & Company, Inc. 22 Robinson Crusoe as a Firm u RC’s firm’s profit is  = C - wL. u  = C - wL  C =  + wL, the equation of an isoprofit line. u Slope = + w. u Intercept = .

© 2010 W. W. Norton & Company, Inc. 23 Isoprofit Lines Labor (hours) Coconuts 24 Higher profit; Slopes = + w 0

© 2010 W. W. Norton & Company, Inc. 24 Profit-Maximization Labor (hours) Coconuts Feasible production plans Production function 24 0

© 2010 W. W. Norton & Company, Inc. 25 Profit-Maximization Labor (hours) Coconuts Production function 24 0

© 2010 W. W. Norton & Company, Inc. 26 Profit-Maximization Labor (hours) Coconuts Production function 24 0

© 2010 W. W. Norton & Company, Inc. 27 Profit-Maximization Labor (hours) Coconuts Production function 24 C* L* 0

© 2010 W. W. Norton & Company, Inc. 28 Profit-Maximization Labor (hours) Coconuts Production function 24 C* L* Isoprofit slope = production function slope 0

© 2010 W. W. Norton & Company, Inc. 29 Profit-Maximization Labor (hours) Coconuts Production function 24 C* L* Isoprofit slope = production function slope i.e. w = MP L 0

© 2010 W. W. Norton & Company, Inc. 30 Profit-Maximization Labor (hours) Coconuts Production function 24 C* L* Isoprofit slope = production function slope i.e. w = MP L = 1  MP L = MRP L. 0

© 2010 W. W. Norton & Company, Inc. 31 Profit-Maximization Labor (hours) Coconuts Production function 24 C* L* Isoprofit slope = production function slope i.e. w = MP L = 1  MP L = MRP L. RC gets 0

© 2010 W. W. Norton & Company, Inc. 32 Profit-Maximization Labor (hours) Coconuts Production function 24 C* L* Isoprofit slope = production function slope i.e. w = MP L = 1  MP L = MRP L. Given w, RC’s firm’s quantity demanded of labor is L* Labor demand RC gets 0

© 2010 W. W. Norton & Company, Inc. 33 Profit-Maximization Labor (hours) Coconuts Production function 24 C* L* Isoprofit slope = production function slope i.e. w = MP L = 1  MP L = MRP L. 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

© 2010 W. W. Norton & Company, Inc. 34 Utility-Maximization u Now consider RC as a consumer endowed with $  * who can work for $w per hour. u What is RC’s most preferred consumption bundle? u Budget constraint is

© 2010 W. W. Norton & Company, Inc. 35 Utility-Maximization Labor (hours) Coconuts 24 0 Budget constraint

© 2010 W. W. Norton & Company, Inc. 36 Utility-Maximization Labor (hours) Coconuts 24 0 Budget constraint; slope = w

© 2010 W. W. Norton & Company, Inc. 37 Utility-Maximization Labor (hours) Coconuts More preferred 24 0

© 2010 W. W. Norton & Company, Inc. 38 Utility-Maximization Labor (hours) Coconuts 24 0 Budget constraint; slope = w

© 2010 W. W. Norton & Company, Inc. 39 Utility-Maximization Labor (hours) Coconuts Budget constraint; slope = w 24 0

© 2010 W. W. Norton & Company, Inc. 40 Utility-Maximization Labor (hours) Coconuts 24 0 C* L* Budget constraint; slope = w

© 2010 W. W. Norton & Company, Inc. 41 Utility-Maximization Labor (hours) Coconuts 24 0 C* L* MRS = w Budget constraint; slope = w

© 2010 W. W. Norton & Company, Inc. 42 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*

© 2010 W. W. Norton & Company, Inc. 43 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

© 2010 W. W. Norton & Company, Inc. 44 Utility-Maximization & Profit- Maximization u Profit-maximization: –w = MP L –quantity of output supplied = C* –quantity of labor demanded = L*

© 2010 W. W. Norton & Company, Inc. 45 Utility-Maximization & Profit- Maximization u Profit-maximization: –w = MP L –quantity of output supplied = C* –quantity of labor demanded = L* u Utility-maximization: –w = MRS –quantity of output demanded = C* –quantity of labor supplied = L*

© 2010 W. W. Norton & Company, Inc. 46 Utility-Maximization & Profit- Maximization u Profit-maximization: –w = MP L –quantity of output supplied = C* –quantity of labor demanded = L* u Utility-maximization: –w = MRS –quantity of output demanded = C* –quantity of labor supplied = L* Coconut and labor markets both clear.

© 2010 W. W. Norton & Company, Inc. 47 Utility-Maximization & Profit- Maximization Labor (hours) Coconuts 24 C* L* 0 MRS = w = MP L Given w, RC’s quantity supplied of labor = quantity demanded of labor = L* and output quantity demanded = output quantity supplied = C*.

© 2010 W. W. Norton & Company, Inc. 48 Pareto Efficiency u Must have MRS = MP L.

© 2010 W. W. Norton & Company, Inc. 49 Pareto Efficiency Labor (hours) Coconuts 24 0 MRS  MP L

© 2010 W. W. Norton & Company, Inc. 50 Pareto Efficiency Labor (hours) Coconuts 24 0 MRS  MP L Preferred consumption bundles.

© 2010 W. W. Norton & Company, Inc. 51 Pareto Efficiency Labor (hours) Coconuts 24 0 MRS = MP L

© 2010 W. W. Norton & Company, Inc. 52 Pareto Efficiency Labor (hours) Coconuts 24 0 MRS = MP L. The common slope  relative wage rate w that implements the Pareto efficient plan by decentralized pricing.

© 2010 W. W. Norton & Company, Inc. 53 First Fundamental Theorem of Welfare Economics u A competitive market equilibrium is Pareto efficient if –consumers’ preferences are convex –there are no externalities in consumption or production.

© 2010 W. W. Norton & Company, Inc. 54 Second Fundamental Theorem of Welfare Economics u 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.

© 2010 W. W. Norton & Company, Inc. 55 Non-Convex Technologies u Do the Welfare Theorems hold if firms have non-convex technologies?

© 2010 W. W. Norton & Company, Inc. 56 Non-Convex Technologies u Do the Welfare Theorems hold if firms have non-convex technologies? u The 1st Theorem does not rely upon firms’ technologies being convex.

© 2010 W. W. Norton & Company, Inc. 57 Non-Convex Technologies Labor (hours) Coconuts 24 0 MRS = MP L The common slope  relative wage rate w that implements the Pareto efficient plan by decentralized pricing.

© 2010 W. W. Norton & Company, Inc. 58 Non-Convex Technologies u Do the Welfare Theorems hold if firms have non-convex technologies? u The 2nd Theorem does require that firms’ technologies be convex.

© 2010 W. W. Norton & Company, Inc. 59 Non-Convex Technologies Labor (hours) Coconuts 24 0 MRS = MP L. The Pareto optimal allocation cannot be implemented by a competitive equilibrium.

© 2010 W. W. Norton & Company, Inc. 60 Production Possibilities u Resource and technological limitations restrict what an economy can produce. u The set of all feasible output bundles is the economy’s production possibility set. u The set’s outer boundary is the production possibility frontier.

© 2010 W. W. Norton & Company, Inc. 61 Production Possibilities Fish Coconuts Production possibility frontier (ppf)

© 2010 W. W. Norton & Company, Inc. 62 Production Possibilities Fish Coconuts Production possibility frontier (ppf) Production possibility set

© 2010 W. W. Norton & Company, Inc. 63 Production Possibilities Fish Coconuts Feasible but inefficient

© 2010 W. W. Norton & Company, Inc. 64 Production Possibilities Fish Coconuts Feasible but inefficient Feasible and efficient

© 2010 W. W. Norton & Company, Inc. 65 Production Possibilities Fish Coconuts Feasible but inefficient Feasible and efficient Infeasible

© 2010 W. W. Norton & Company, Inc. 66 Production Possibilities Fish Coconuts Ppf’s slope is the marginal rate of product transformation.

© 2010 W. W. Norton & Company, Inc. 67 Production Possibilities Fish Coconuts Ppf’s slope is the marginal rate of product transformation. Increasingly negative MRPT  increasing opportunity cost to specialization.

© 2010 W. W. Norton & Company, Inc. 68 Production Possibilities u If there are no production externalities then a ppf will be concave w.r.t. the origin. u Why?

© 2010 W. W. Norton & Company, Inc. 69 Production Possibilities u If there are no production externalities then a ppf will be concave w.r.t. the origin. u Why? u Because efficient production requires exploitation of comparative advantages.

© 2010 W. W. Norton & Company, Inc. 70 Comparative Advantage u Two agents, RC and Man Friday (MF). u RC can produce at most 20 coconuts or 30 fish. u MF can produce at most 50 coconuts or 25 fish.

© 2010 W. W. Norton & Company, Inc. 71 Comparative Advantage F C F C RC MF

© 2010 W. W. Norton & Company, Inc. 72 Comparative Advantage F C F C RC MF MRPT = -2/3 coconuts/fish so opp. cost of one more fish is 2/3 foregone coconuts.

© 2010 W. W. Norton & Company, Inc. 73 Comparative Advantage F C F C RC MF 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.

© 2010 W. W. Norton & Company, Inc. 74 Comparative Advantage F C F C RC MF 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.

© 2010 W. W. Norton & Company, Inc. 75 Comparative Advantage F C F C RC MF MRPT = -2/3 coconuts/fish so opp. cost of one more coconut is 3/2 foregone fish.

© 2010 W. W. Norton & Company, Inc. 76 Comparative Advantage F C F C RC MF 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.

© 2010 W. W. Norton & Company, Inc. 77 Comparative Advantage F C F C RC MF 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.

© 2010 W. W. Norton & Company, Inc. 78 Comparative Advantage F C Economy F C F C RC MF Use RC to produce fish before using MF. Use MF to produce coconuts before using RC.

© 2010 W. W. Norton & Company, Inc. 79 Comparative Advantage F C Economy F C F C RC MF Using low opp. cost producers first results in a ppf that is concave w.r.t the origin.

© 2010 W. W. Norton & Company, Inc. 80 Comparative Advantage F C Economy More producers with different opp. costs “smooth out” the ppf.

© 2010 W. W. Norton & Company, Inc. 81 Coordinating Production & Consumption u The ppf contains many technically efficient output bundles. u Which are Pareto efficient for consumers?

© 2010 W. W. Norton & Company, Inc. 82 Coordinating Production & Consumption Fish Coconuts Output bundle is

© 2010 W. W. Norton & Company, Inc. 83 Coordinating Production & Consumption Fish Coconuts Output bundle is and is the aggregate endowment for distribution to consumers RC and MF.

© 2010 W. W. Norton & Company, Inc. 84 Coordinating Production & Consumption Fish Coconuts O RC O MF Output bundle is and is the aggregate endowment for distribution to consumers RC and MF.

© 2010 W. W. Norton & Company, Inc. 85 Coordinating Production & Consumption Fish Coconuts O RC O MF Allocate efficiently; say to RC

© 2010 W. W. Norton & Company, Inc. 86 Coordinating Production & Consumption Fish Coconuts O RC O MF Allocate efficiently; say to RC and to MF.

© 2010 W. W. Norton & Company, Inc. 87 Coordinating Production & Consumption Fish Coconuts O RC O MF

© 2010 W. W. Norton & Company, Inc. 88 Coordinating Production & Consumption Fish Coconuts O RC O MF

© 2010 W. W. Norton & Company, Inc. 89 Coordinating Production & Consumption Fish Coconuts O RC O MF

© 2010 W. W. Norton & Company, Inc. 90 Coordinating Production & Consumption Fish Coconuts O RC O MF MRS  MRPT

© 2010 W. W. Norton & Company, Inc. 91 Coordinating Production & Consumption Fish Coconuts O RC O MF O’ MF Instead produce

© 2010 W. W. Norton & Company, Inc. 92 Coordinating Production & Consumption Fish Coconuts O RC O MF O’ MF Instead produce

© 2010 W. W. Norton & Company, Inc. 93 Coordinating Production & Consumption Fish Coconuts O RC O MF O’ MF Instead produce Give MF same allocation as before.

© 2010 W. W. Norton & Company, Inc. 94 Coordinating Production & Consumption Fish Coconuts O RC O MF O’ MF Instead produce Give MF same allocation as before. MF’s utility is unchanged.

© 2010 W. W. Norton & Company, Inc. 95 Coordinating Production & Consumption Fish Coconuts O RC O MF O’ MF Instead produce Give MF same allocation as before. MF’s utility is unchanged

© 2010 W. W. Norton & Company, Inc. 96 Coordinating Production & Consumption Fish Coconuts O RC O MF O’ MF Instead produce Give MF same allocation as before. MF’s utility is unchanged

© 2010 W. W. Norton & Company, Inc. 97 Coordinating Production & Consumption Fish Coconuts O RC O MF O’ MF Instead produce Give MF same allocation as before. MF’s utility is unchanged, RC’s utility is higher

© 2010 W. W. Norton & Company, Inc. 98 Coordinating Production & Consumption Fish Coconuts O RC O MF O’ MF Instead produce Give MF same allocation as before. MF’s utility is unchanged, RC’s utility is higher; Pareto improvement.

© 2010 W. W. Norton & Company, Inc. 99 Coordinating Production & Consumption u MRS  MRPT  inefficient coordination of production and consumption. u Hence, MRS = MRPT is necessary for a Pareto optimal economic state.

© 2010 W. W. Norton & Company, Inc. 100 Coordinating Production & Consumption Fish Coconuts O RC O MF

© 2010 W. W. Norton & Company, Inc. 101 Decentralized Coordination of Production & Consumption u RC and MF jointly run a firm producing coconuts and fish. u RC and MF are also consumers who can sell labor. u Price of coconut = p C. u Price of fish = p F. u RC’s wage rate = w RC. u MF’s wage rate = w MF.

© 2010 W. W. Norton & Company, Inc. 102 Decentralized Coordination of Production & Consumption u L RC, L MF are amounts of labor purchased from RC and MF. u Firm’s profit-maximization problem is choose C, F, L RC and L MF to

© 2010 W. W. Norton & Company, Inc. 103 Decentralized Coordination of Production & Consumption Isoprofit line equation is

© 2010 W. W. Norton & Company, Inc. 104 Decentralized Coordination of Production & Consumption Isoprofit line equation is which rearranges to

© 2010 W. W. Norton & Company, Inc. 105 Decentralized Coordination of Production & Consumption Isoprofit line equation is which rearranges to

© 2010 W. W. Norton & Company, Inc. 106 Decentralized Coordination of Production & Consumption Fish Coconuts Higher profit Slopes =

© 2010 W. W. Norton & Company, Inc. 107 Decentralized Coordination of Production & Consumption Fish Coconuts The firm’s production possibility set.

© 2010 W. W. Norton & Company, Inc. 108 Decentralized Coordination of Production & Consumption Fish Coconuts Slopes =

© 2010 W. W. Norton & Company, Inc. 109 Decentralized Coordination of Production & Consumption Fish Coconuts Profit-max. plan Slopes =

© 2010 W. W. Norton & Company, Inc. 110 Decentralized Coordination of Production & Consumption Fish Coconuts Profit-max. plan Slope =

© 2010 W. W. Norton & Company, Inc. 111 Decentralized Coordination of Production & Consumption Fish Coconuts Profit-max. plan Slope = Competitive markets and profit-maximization 

© 2010 W. W. Norton & Company, Inc. 112 Decentralized Coordination of Production & Consumption u So competitive markets, profit- maximization, and utility maximization all together cause the condition necessary for a Pareto optimal economic state.

© 2010 W. W. Norton & Company, Inc. 113 Decentralized Coordination of Production & Consumption Fish Coconuts O RC O MF Competitive markets and utility-maximization 

© 2010 W. W. Norton & Company, Inc. 114 Decentralized Coordination of Production & Consumption Fish Coconuts O RC O MF Competitive markets, utility- maximization and profit- maximization 