Chapter 32 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. 2

Now Add Production... Add input markets, output markets, describe firms’ technologies, the distributions of firms’ outputs and profits … 3

Now Add Production... Add input markets, output markets, describe firms’ technologies, the distributions of firms’ outputs and profits … That’s not easy! 4

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

Robinson Crusoe ’ s Technology Technology: Labor produces output (coconuts) according to a concave production function. 6

Robinson Crusoe ’ s Technology Labor (hours) Coconuts Production function 24 0 Feasible production plans 7

Robinson Crusoe ’ s Preferences RC’s preferences:  coconut is a good  leisure is a good 8

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

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

Robinson Crusoe ’ s Choice Labor (hours) Coconuts Feasible production plans Production function

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

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

Robinson Crusoe ’ s Choice Labor (hours) Coconuts Production function 24 0 Leisure (hours) 240 C* L* 14

Robinson Crusoe ’ s Choice Labor (hours) Coconuts Production function 24 0 Leisure (hours) 240 C* L* Labor 15

Robinson Crusoe ’ s Choice Labor (hours) Coconuts Production function 24 0 Leisure (hours) 240 C* L* LaborLeisure 16

Robinson Crusoe ’ s Choice Labor (hours) Coconuts Production function 24 0 Leisure (hours) 240 C* L* LaborLeisure Output 17

Robinson Crusoe ’ s Choice Labor (hours) Coconuts Production function 24 0 Leisure (hours) 240 C* L* LaborLeisure MRS = MP L Output 18

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. 19

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 = . 20

Isoprofit Lines Labor (hours) Coconuts 24 Higher profit; Slopes = + w 0 21

Profit-Maximization Labor (hours) Coconuts Feasible production plans Production function

Profit-Maximization Labor (hours) Coconuts Production function

Profit-Maximization Labor (hours) Coconuts Production function 24 0

Profit-Maximization Labor (hours) Coconuts Production function 24 C* L* 0 25

Profit-Maximization Labor (hours) Coconuts Production function 24 C* L* Isoprofit slope = production function slope i.e. w = MP L 0 26

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 27

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 28

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 29

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 30

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 31

Utility-Maximization Labor (hours) Coconuts 24 0 Budget constraint; slope = w 32

Utility-Maximization Labor (hours) Coconuts More preferred

Utility-Maximization Labor (hours) Coconuts 24 0 Budget constraint; slope = w 34

Utility-Maximization Labor (hours) Coconuts Budget constraint; slope = w

Utility-Maximization Labor (hours) Coconuts 24 0 C* L* Budget constraint; slope = w 36

Utility-Maximization Labor (hours) Coconuts 24 0 C* L* MRS = w Budget constraint; slope = w 37

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* 38

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 39

Utility-Maximization & Profit- Maximization Profit-maximization:  w = MP L  quantity of output supplied = C*  quantity of labor demanded = L* 40

Utility-Maximization & Profit- Maximization Profit-maximization:  w = MP L  quantity of output supplied = C*  quantity of labor demanded = L* Utility-maximization:  w = MRS  quantity of output demanded = C*  quantity of labor supplied = L* 41

Utility-Maximization & Profit- Maximization Profit-maximization:  w = MP L  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. 42

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*. 43

Pareto Efficiency Must have MRS = MP L. 44

Pareto Efficiency Labor (hours) Coconuts 24 0 MRS  MP L 45

Pareto Efficiency Labor (hours) Coconuts 24 0 MRS  MP L Preferred consumption bundles. 46

Pareto Efficiency Labor (hours) Coconuts 24 0 MRS = MP L 47

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. 48

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. 49

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. 50

Non-Convex Technologies Do the Welfare Theorems hold if firms have non-convex technologies? 51

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. 52

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. 53

Non-Convex Technologies Do the Welfare Theorems hold if firms have non-convex technologies? The 2nd Theorem does require that firms’ technologies be convex. 54

Non-Convex Technologies Labor (hours) Coconuts 24 0 MRS = MP L. The Pareto optimal allocation cannot be implemented by a competitive equilibrium. 55

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. 56

Production Possibilities Fish Coconuts Production possibility frontier (ppf) 57

Production Possibilities Fish Coconuts Production possibility frontier (ppf) Production possibility set 58

Production Possibilities Fish Coconuts Feasible but inefficient 59

Production Possibilities Fish Coconuts Feasible but inefficient Feasible and efficient 60

Production Possibilities Fish Coconuts Feasible but inefficient Feasible and efficient Infeasible 61

Production Possibilities Fish Coconuts Ppf’s slope is the marginal rate of product transformation. 62

Production Possibilities Fish Coconuts Ppf’s slope is the marginal rate of transformation. Increasingly negative MRT  increasing opportunity cost to specialization. 63

Production Possibilities If there are no production externalities then a ppf will be concave w.r.t. the origin. Why? 64

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. 65

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. 66

Comparative Advantage F C F C RC MF

Comparative Advantage F C F C RC MF MRT = -2/3 coconuts/fish so opp. cost of one more fish is 2/3 foregone coconuts. 68

Comparative Advantage F C F C RC MF MRT = -2/3 coconuts/fish so opp. cost of one more fish is 2/3 foregone coconuts. MRT = -2 coconuts/fish so opp. cost of one more fish is 2 foregone coconuts. 69

Comparative Advantage F C F C RC MF MRT = -2/3 coconuts/fish so opp. cost of one more fish is 2/3 foregone coconuts. MRT = -2 coconuts/fish so opp. cost of one more fish is 2 foregone coconuts. RC has the comparative opp. cost advantage in producing fish. 70

Comparative Advantage F C F C RC MF MRT = -2/3 coconuts/fish so opp. cost of one more coconut is 3/2 foregone fish. 71

Comparative Advantage F C F C RC MF MRT = -2/3 coconuts/fish so opp. cost of one more coconut is 3/2 foregone fish. MRT = -2 coconuts/fish so opp. cost of one more coconut is 1/2 foregone fish. 72

Comparative Advantage F C F C RC MF MRT = -2/3 coconuts/fish so opp. cost of one more coconut is 3/2 foregone fish. MRT = -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. 73

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. 74

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. 75

Comparative Advantage F C Economy More producers with different opp. costs “smooth out” the ppf. 76

Coordinating Production & Consumption The ppf contains many technically efficient output bundles. Which are Pareto efficient for consumers? 77

Coordinating Production & Consumption Fish Coconuts Output bundle is and is the aggregate endowment for distribution to consumers RC and MF. 78

Coordinating Production & Consumption Fish Coconuts O RC O MF Output bundle is and is the aggregate endowment for distribution to consumers RC and MF. 79

Coordinating Production & Consumption Fish Coconuts O RC O MF Allocate efficiently; say to RC and to MF. 80

Coordinating Production & Consumption Fish Coconuts O RC O MF 81

Coordinating Production & Consumption Fish Coconuts O RC O MF 82

Coordinating Production & Consumption Fish Coconuts O RC O MF MRS  MRT 83

Coordinating Production & Consumption Fish Coconuts O RC O MF O’ MF Instead produce 84

Coordinating Production & Consumption Fish Coconuts O RC O MF O’ MF Instead produce Give MF same allocation as before. 85

Coordinating Production & Consumption Fish Coconuts O RC O MF O’ MF Instead produce Give MF same allocation as before. MF’s utility is unchanged. 86

Coordinating Production & Consumption Fish Coconuts O RC O MF O’ MF Instead produce Give MF same allocation as before. MF’s utility is unchanged 87

Coordinating Production & Consumption Fish Coconuts O RC O MF O’ MF Instead produce Give MF same allocation as before. MF’s utility is unchanged 88

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 89

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. 90

Coordinating Production & Consumption MRS  MRT  inefficient coordination of production and consumption. Hence, MRS = MRT is necessary for a Pareto optimal economic state. 91

Coordinating Production & Consumption Fish Coconuts O RC O MF 92

Decentralized Coordination of Production & Consumption RC and MF jointly run a firm producing coconuts and fish. RC and MF are also consumers who can sell labor. Price of coconut = p C. Price of fish = p F. RC’s wage rate = w RC. MF’s wage rate = w MF. 93

Decentralized Coordination of Production & Consumption L RC, L MF are amounts of labor purchased from RC and MF. Firm’s profit-maximization problem is choose C, F, L RC and L MF to 94

Decentralized Coordination of Production & Consumption Isoprofit line equation is 95

Decentralized Coordination of Production & Consumption Isoprofit line equation is which rearranges to 96

Decentralized Coordination of Production & Consumption Isoprofit line equation is which rearranges to 97

Decentralized Coordination of Production & Consumption Fish Coconuts Higher profit Slopes = 98

Decentralized Coordination of Production & Consumption Fish Coconuts The firm’s production possibility set. 99

Decentralized Coordination of Production & Consumption Fish Coconuts Slopes = 100

Decentralized Coordination of Production & Consumption Fish Coconuts Profit-max. plan Slopes = 101

Decentralized Coordination of Production & Consumption Fish Coconuts Profit-max. plan Slope = 102

Decentralized Coordination of Production & Consumption Fish Coconuts Profit-max. plan Slope = Competitive markets and profit-maximization  103

Decentralized Coordination of Production & Consumption So competitive markets, profit-maximization, and utility maximization all together cause the condition necessary for a Pareto optimal economic state. 104

Decentralized Coordination of Production & Consumption Fish Coconuts O RC O MF Competitive markets and utility-maximization  105

Decentralized Coordination of Production & Consumption Fish Coconuts O RC O MF Competitive markets, utility- maximization and profit- maximization  106