Production 1 Exchange Economies revisited No production only

Production 1

Exchange Economies (revisited) No production, only endowments, so no description of how resources are converted to consumables. n General equilibrium: all markets clear simultaneously. n 2

Now Add Production. . . n Add input markets, output markets, describe firms’ technologies, the distributions of firms’ outputs and profits … That’s not easy! 3

Robinson Crusoe’s Economy One agent, Robinson Crusoe (RC) n Endowed with a fixed quantity of one resource -- 24 hours. n Use time for labor (production) or leisure (consumption). n Labor time = L. Leisure time = 24 - L. n What will RC choose? n 4

Robinson Crusoe’s Technology n Technology: Labor produces output (coconuts) according to a concave production function. 5

Robinson Crusoe’s Technology Coconuts Production function Feasible production plans 0 24 Labor (hours) 6

Robinson Crusoe’s Preferences n RC’s preferences: ¨ coconut is a good ¨ leisure is a good 7

Robinson Crusoe’s Preferences Coconuts More preferred 0 24 Leisure (hours) 8

Robinson Crusoe’s Choice Coconuts More preferred Production function Feasible production plans 0 24 24 0 Labor (hours) Leisure (hours) 9

Robinson Crusoe’s Choice Coconuts = Production function C* 0 24 Output Labor L* Leisure 24 0 Labor (hours) Leisure (hours) 10

Robinson Crusoe as a Firm Now suppose RC is both a utilitymaximizing consumer and a profitmaximizing firm. n Use coconuts as the numeraire good; i. e. price of a coconut = $1. n RC’s wage rate is w. n Coconut output level is C. n 11

Robinson Crusoe as a Firm RC’s firm’s profit is = C - w. L. n = C - w. L …………………. . …, the equation of an isoprofit line. n Slope = + w. n Intercept = . n 12

Isoprofit Lines Coconuts Higher profit; ……………… Slopes = + w 0 24 Labor (hours) 13

Profit-Maximization Coconuts Isoprofit slope = production function slope i. e. w = …………………. Production function C* Output Labor supply demand L* 0 Given w, RC’s firm’s quantity demanded of labor is L* and output quantity supplied is C*. 24 Labor (hours) RC as a firm gets 14

Utility-Maximization Now consider RC as a consumer endowed with $ * who can work for $w per hour. n What is RC’s most preferred consumption bundle? n Budget constraint is n 15

Utility-Maximization Coconuts Budget constraint; slope = w Intercept = 0 24 Labor (hours) 16

Utility-Maximization Coconuts More preferred 0 24 Labor (hours) 17

Utility-Maximization Coconuts MRS = w Budget constraint; slope = w C* Output Labordemand supply L* 0 Given w, RC’s quantity supplied of labor is L* and output quantity demanded is C*. 24 Labor (hours) 18

Utility-Maximization & Profit-Maximization n Profit-maximization: ¨w = MPL ¨ quantity of output supplied = C* ¨ quantity of labor demanded = L* n Utility-maximization: ¨w = MRS ¨ quantity of output demanded = C* ¨ quantity of labor supplied = L* Coconut and labor markets both clear. 19

Utility-Maximization & Profit-Maximization Coconuts MRS = w = MPL Given w, RC’s quantity supplied of labor = quantity demanded of labor = L* and output quantity demanded = output quantity supplied = C*. C* 0 L* 24 Labor (hours) 20

Pareto Efficiency Coconuts …………………… 0 n 24 Labor (hours) MRS MPL, not Pareto efficient 21

Pareto Efficiency n To achieve Pareto Efficiency must have MRS = MPL. 22

Pareto Efficiency Coconuts 0 n MRS = MPL. The common slope relative wage rate w that implements the Pareto efficient plan by decentralized pricing. 24 Labor (hours) MRS = MPL, ……………. . 23

First Fundamental Theorem of Welfare Economics n A competitive market equilibrium is Pareto efficient if ¨ consumers’ preferences are ………. . ¨ there are …………. …. in consumption or production. 24

Second Fundamental Theorem of Welfare Economics n Any Pareto efficient economic state can be achieved as a competitive market equilibrium if ¨ consumers’ preferences are ………………. ¨ firms’ technologies are ………………. ¨ there are ……………. in consumption or production. 25

Non-Convex Technologies Do the Welfare Theorems hold if firms have non-convex technologies? n The 1 st Theorem does not rely upon firms’ technologies being convex. n 26

Non-Convex Technologies Coconuts 0 MRS = MPL The common slope relative wage rate w that implements the Pareto efficient plan by decentralized pricing. 24 Labor (hours) 27

Non-Convex Technologies Do the Welfare Theorems hold if firms have non-convex technologies? n The 2 nd Theorem does require that firms’ technologies be convex. n 28

Non-Convex Technologies Coconuts MRS = MPL. The Pareto optimal allocation ……… be implemented by a competitive equilibrium. 0 24 Labor (hours) 29

Production Possibilities Resource and technological limitations restrict what an economy can produce. n The set of all feasible output bundles is the economy’s …………. . . n The set’s outer boundary is the …………… n ………. . . 30

Production Possibilities Coconuts Production possibility frontier (PPF) Production possibility set Fish 31

Production Possibilities Coconuts ………………… Infeasible Feasible but inefficient Fish 32

Production Possibilities Coconuts PPF’s slope is the …………………………… Increasingly negative MRPT increasing opportunity cost to specialization. Fish 33

Production Possibilities If there are no production externalities then a PPF will be concave w. r. t. the origin. n Why? n Because efficient production requires exploitation of comparative advantages. n 34

Comparative Advantage C RC 20 C 50 MRPT = -2/3 coconuts/fish so opp. cost of one more fish is …… foregone coconuts. 30 MF F RC has the comparative opp. cost advantage in producing fish. MRPT = -2 coconuts/fish so opp. cost of one more fish is …… foregone coconuts. 25 F 35

Comparative Advantage C 20 C 50 RC MRPT = -2/3 coconuts/fish so opp. cost of one more coconut is …… foregone fish. 30 MF F MRPT = -2 coconuts/fish so opp. cost of one more coconut is …… foregone fish. MF has the comparative opp. cost advantage in producing coconuts. 25 F 36

Comparative Advantage C RC Economy C 20 70 C 50 30 MF 25 F F Use …. . to produce fish before using …… 50 Use …. . to produce coconuts before using …. . 30 55 F 37

Comparative Advantage Economy Using low opp. cost producers first results in a ppf that is concave w. r. t the origin. C More producers with different opp. costs “smooth out” the ppf. F 38

Coordinating Production & Consumption The PPF contains many technically efficient output bundles. n Which are Pareto efficient for consumers? n 39

Coordinating Production & Consumption Coconuts Output bundle is and is the aggregate endowment for distribution to consumers RC and MF. Fish 40

Coordinating Production & Consumption Coconuts OMF Allocate say efficiently; to RC and to MF. Contract Curve ORC Fish 41

Coordinating Production & Consumption Coconuts OMF However, …………………. RC’s indifferent curve MF’s indifferent curve ORC Fish 42

Coordinating Production & Consumption Coconuts OMF If instead produce and give MF same O'MF allocation as before. → MF’s utility is ………………. . ORC Fish 43

Coordinating Production & Consumption Coconuts OMF MF’s utility is unchanged, But RC’s utility is ……. . …. ; O’MF Pareto improvement ORC Fish 44

Coordinating Production & Consumption n n MRS MRPT inefficient coordination of production and consumption. Hence, MRS = MRPT is necessary for a Pareto optimal economic state. 45

Coordinating Production & Consumption Coconuts OMF ORC Fish 46

Decentralized Coordination of Production & Consumption The above Pareto optimal production and consumption can be achieved by decentralized behaviours of firms and consumers n Competitive markets, profit-maximization, and utility maximization all together can result in a Pareto optimal economic state n 47

Decentralized Coordination of Production & Consumption RC and MF jointly run a firm producing coconuts and fish. n RC and MF are also consumers who can sell labor. n Price of coconut = p. C. n Price of fish = p. F. n RC’s wage rate = w. RC. n MF’s wage rate = w. MF. n 48

Decentralized Coordination of Production & Consumption n LRC, LMF are amounts of labor purchased from RC and MF. n Firm’s profit-maximization problem is choose C, F, LRC and LMF to 49

Decentralized Coordination of Production & Consumption Equation for Isoprofit line is which rearranges to 50

Decentralized Coordination of Production & Consumption Coconuts The firm’s production possibility set. Higher profit Slopes = Fish 51

Decentralized Coordination of Production & Consumption Coconuts Profit-max. plan Competitive markets and profit-maximization Slope = Fish 52

Decentralized Coordination of Production & Consumption n So competitive markets, profitmaximization, and utility maximization all together cause the condition necessary for a Pareto optimal economic state. 53

Decentralized Coordination of Production & Consumption Coconuts Competitive markets and utility-maximization OMF ORC Fish 54

Decentralized Coordination of Production & Consumption Coconuts Competitive markets, utilitymaximization and profitmaximization OMF ORC Fish 55