Chapter Thirty. Production
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1 Chapter Thirty Production
2 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.
3 Now Add Production... Add input markets, output markets, describe firms technologies, the distributions of firms outputs and profits
4 Now Add Production... Add input markets, output markets, describe firms technologies, the distributions of firms outputs and profits That s not easy!
5 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?
6 Robinson Crusoe s Technology Technology: Labor produces output (coconuts) according to a concave production function.
7 Robinson Crusoe s Technology Production function 0 24 Labor (hours)
8 Robinson Crusoe s Technology Production function Feasible production plans 0 24 Labor (hours)
9 Robinson Crusoe s Preferences RC s preferences: coconut is a good leisure is a good
10 Robinson Crusoe s Preferences More preferred 0 24 Leisure (hours)
11 Robinson Crusoe s Preferences More preferred 24 0 Leisure (hours)
12 Robinson Crusoe s Choice Production function Feasible production plans 0 24 Labor (hours)
13 Robinson Crusoe s Choice Production function Feasible production plans Labor (hours) Leisure (hours)
14 Robinson Crusoe s Choice Production function Feasible production plans Labor (hours) Leisure (hours)
15 Robinson Crusoe s Choice Production function Feasible production plans Labor (hours) Leisure (hours)
16 Robinson Crusoe s Choice C* Production function 0 L* Labor (hours) Leisure (hours)
17 Robinson Crusoe s Choice C* Production function Labor 0 L* Labor (hours) Leisure (hours)
18 Robinson Crusoe s Choice C* Production function Labor Leisure 0 L* Labor (hours) Leisure (hours)
19 Robinson Crusoe s Choice C* Labor Output Leisure 0 L* Production function Labor (hours) Leisure (hours)
20 Robinson Crusoe s Choice MRS = MP L C* Labor Output Leisure 0 L* Production function Labor (hours) Leisure (hours)
21 Robinson Crusoe as a Firm Now suppose RC is both a utilitymaximizing consumer and a profitmaximizing 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.
22 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 =.
23 Isoprofit Lines Higher profit; C wl Slopes = + w 0 24 Labor (hours)
24 Profit-Maximization Production function 0 Feasible production plans 24 Labor (hours)
25 Profit-Maximization Production function 0 24 Labor (hours)
26 Profit-Maximization Production function 0 24 Labor (hours)
27 Profit-Maximization C* Production function 0 L* 24 Labor (hours)
28 Profit-Maximization Isoprofit slope = production function slope C* Production function 0 L* 24 Labor (hours)
29 Profit-Maximization Isoprofit slope = production function slope i.e. w = MP L C* Production function 0 L* 24 Labor (hours)
30 Profit-Maximization Isoprofit slope = production function slope i.e. w = MP L = 1 MP L = MRP L. C* Production function 0 L* 24 Labor (hours)
31 Profit-Maximization Isoprofit slope = production function slope i.e. w = MP L = 1 MP L = MRP L. C* * Production function 0 RC gets L* 24 * C * wl * Labor (hours)
32 Profit-Maximization Isoprofit slope = production function slope i.e. w = MP L = 1 MP L = MRP L. C* * Labor demand Production function Given w, RC s firm s quantity demanded of labor is L* 0 RC gets L* 24 * C * wl * Labor (hours)
33 Profit-Maximization Isoprofit slope = production function slope i.e. w = MP L = 1 MP L = MRP L. C* * Labor demand Output supply Production function Given w, RC s firm s quantity demanded of labor is L* and output quantity supplied is C*. 0 RC gets L* 24 * C * wl * Labor (hours)
34 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.
35 Utility-Maximization * Budget constraint C * wl Labor (hours)
36 Utility-Maximization * Budget constraint; slope = w C * wl Labor (hours)
37 Utility-Maximization More preferred 0 24 Labor (hours)
38 Utility-Maximization * Budget constraint; slope = w C * wl Labor (hours)
39 Utility-Maximization * Budget constraint; slope = w C * wl Labor (hours)
40 Utility-Maximization C* * Budget constraint; slope = w C * wl. 0 L* 24 Labor (hours)
41 Utility-Maximization C* * MRS = w Budget constraint; slope = w C * wl. 0 L* 24 Labor (hours)
42 Utility-Maximization C* * MRS = w Labor supply Budget constraint; slope = w C * wl. Given w, RC s quantity supplied of labor is L* 0 L* 24 Labor (hours)
43 Utility-Maximization C* * MRS = w Labor supply Output demand Budget constraint; slope = w C * wl. Given w, RC s quantity supplied of labor is L* and output quantity demanded is C*. 0 L* 24 Labor (hours)
44 Utility-Maximization & Profit- Maximization Profit-maximization: w = MP L quantity of output supplied = C* quantity of labor demanded = L*
45 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*
46 Utility-Maximization & Profit- Maximization Profit-maximization: Coconut and labor w = MP L markets both clear. quantity of output supplied = C* quantity of labor demanded = L* Utility-maximization: w = MRS quantity of output demanded = C* quantity of labor supplied = L*
47 Utility-Maximization & Profit- C* * Maximization 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*. 0 L* 24 Labor (hours)
48 Pareto Efficiency Must have MRS = MP L.
49 Pareto Efficiency MRS MP L 0 24 Labor (hours)
50 Pareto Efficiency MRS MP L Preferred consumption bundles Labor (hours)
51 Pareto Efficiency MRS = MP L 0 24 Labor (hours)
52 Pareto Efficiency MRS = MP L. The common slope relative wage rate w that implements the Pareto efficient plan by decentralized pricing Labor (hours)
53 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.
54 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.
55 Non-Convex Technologies Do the Welfare Theorems hold if firms have non-convex technologies?
56 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.
57 Non-Convex Technologies MRS = MP L The common slope relative wage rate w that implements the Pareto efficient plan by decentralized pricing Labor (hours)
58 Non-Convex Technologies Do the Welfare Theorems hold if firms have non-convex technologies? The 2nd Theorem does require that firms technologies be convex.
59 Non-Convex Technologies MRS = MP L. The Pareto optimal allocation cannot be implemented by a competitive equilibrium Labor (hours)
60 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.
61 Production Possibilities Production possibility frontier (ppf) Fish
62 Production Possibilities Production possibility frontier (ppf) Production possibility set Fish
63 Production Possibilities Feasible but inefficient Fish
64 Production Possibilities Feasible and efficient Feasible but inefficient Fish
65 Production Possibilities Feasible and efficient Feasible but inefficient Infeasible Fish
66 Production Possibilities Ppf s slope is the marginal rate of product transformation. Fish
67 Production Possibilities Ppf s slope is the marginal rate of product transformation. Increasingly negative MRPT increasing opportunity cost to specialization. Fish
68 Production Possibilities If there are no production externalities then a ppf will be concave w.r.t. the origin. Why?
69 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.
70 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.
71 C Comparative Advantage RC 20 C MF F 25 F
72 20 C Comparative Advantage RC MRPT = -2/3 coconuts/fish so opp. cost of one more fish is 2/3 foregone coconuts. C MF F 25 F
73 20 C Comparative Advantage RC MRPT = -2/3 coconuts/fish so opp. cost of one more fish is 2/3 foregone coconuts. C MF F MRPT = -2 coconuts/fish so opp. cost of one more fish is 2 foregone coconuts. 25 F
74 20 C Comparative Advantage RC MRPT = -2/3 coconuts/fish so opp. cost of one more fish is 2/3 foregone coconuts. C MF F RC has the comparative opp. cost advantage in producing fish. MRPT = -2 coconuts/fish so opp. cost of one more fish is 2 foregone coconuts. 25 F
75 20 C Comparative Advantage RC MRPT = -2/3 coconuts/fish so opp. cost of one more coconut is 3/2 foregone fish. C MF F 25 F
76 20 C Comparative Advantage RC MRPT = -2/3 coconuts/fish so opp. cost of one more coconut is 3/2 foregone fish. C MF F MRPT = -2 coconuts/fish so opp. cost of one more coconut is 1/2 foregone fish. 25 F
77 20 C Comparative Advantage RC MRPT = -2/3 coconuts/fish so opp. cost of one more coconut is 3/2 foregone fish. C MF F MRPT = -2 coconuts/fish so opp. cost of one more coconut is 1/2 foregone fish. 25 F MF has the comparative opp. cost advantage in producing coconuts.
78 C 20 C 50 Comparative Advantage RC 30 MF F C Economy Use RC to produce fish before using MF. Use MF to produce coconuts before using RC. 25 F F
79 C 20 C 50 Comparative Advantage RC 30 MF F C Economy Using low opp. cost producers first results in a ppf that is concave w.r.t the origin. 25 F F
80 Comparative Advantage More producers with different opp. costs smooth out the ppf. C Economy F
81 Coordinating Production & Consumption The ppf contains many technically efficient output bundles. Which are Pareto efficient for consumers?
82 Coordinating Production & C Consumption Output bundle is ( F, C ) F Fish
83 Coordinating Production & C Consumption ( F, C ) Output bundle is and is the aggregate endowment for distribution to consumers RC and MF. F Fish
84 Coordinating Production & C Consumption O MF ( F, C ) Output bundle is and is the aggregate endowment for distribution to consumers RC and MF. O RC F Fish
85 Coordinating Production & C Consumption O MF ( F, C ) ( F, C ) Allocate efficiently; say to RC RC RC C RC O RC F RC F Fish
86 Coordinating Production & C F MF Consumption O MF ( F, C ) Allocate efficiently; say ( FRC, CRC ) to RC and to MF. ( F, C ) MF MF C RC C MF O RC F RC F Fish
87 Coordinating Production & C F MF Consumption O MF C RC C MF O RC F RC F Fish
88 Coordinating Production & C F MF Consumption O MF C RC C MF O RC F RC F Fish
89 Coordinating Production & C F MF Consumption O MF C RC C MF O RC F RC F Fish
90 Coordinating Production & C F MF Consumption O MF MRS MRPT C RC C MF O RC F RC F Fish
91 Coordinating Production & C C F MF Consumption O MF Instead produce O MF ( F, C ). C RC C MF O RC F RC F F Fish
92 Coordinating Production & C C F MF Consumption O MF Instead produce O MF ( F, C ). C RC C MF O RC F RC F F Fish
93 Coordinating Production & C C F MF Consumption O MF F MF Instead produce ( F, C ). Give MF same allocation O MF as before. C RC C MF C MF O RC F RC F F Fish
94 Coordinating Production & C C C RC F MF Consumption O MF F MF C MF Instead produce ( F, C ). Give MF same allocation O MF as before. MF s utility is unchanged. C MF O RC F RC F F Fish
95 Coordinating Production & C Consumption O MF F MF Instead produce ( F, C ). Give MF same allocation O MF as before. MF s utility is unchanged C MF O RC F Fish
96 Coordinating Production & C C RC Consumption O MF F MF Instead produce ( F, C ). Give MF same allocation O MF as before. MF s utility is unchanged C MF O RC F RC F Fish
97 Coordinating Production & C C RC Consumption O MF F MF Instead produce ( F, C ). Give MF same allocation O MF as before. MF s utility is unchanged, RC s utility is higher C MF O RC F RC F Fish
98 Coordinating Production & C C RC Consumption O MF F MF Instead produce ( F, C ). Give MF same allocation O MF as before. MF s utility is unchanged, RC s utility is higher; C MF Pareto improvement. O RC F RC F Fish
99 Coordinating Production & Consumption MRS MRPT inefficient coordination of production and consumption. Hence, MRS = MRPT is necessary for a Pareto optimal economic state.
100 Coordinating Production & Consumption C F MF O MF C RC C MF O RC F RC F Fish
101 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.
102 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 max p C p F w L w L. C F RC RC MF MF
103 Decentralized Coordination of Production & Consumption max pc C pf F wrc LRC wmf LMF. Isoprofit line equation is constant p C p F w L w L C F RC RC MF MF
104 Decentralized Coordination of Production & Consumption max pc C pf F wrc LRC wmf LMF. Isoprofit line equation is constant p C p F w L w L which rearranges to C C F RC RC MF MF w L w L p RC RC MF MF C p p F C F.
105 Decentralized Coordination of Production & Consumption max pc C pf F wrc LRC wmf LMF. Isoprofit line equation is constant p C p F w L w L which rearranges to C C F RC RC MF MF wrc LRC wmf LMF p F p 2 p F. C C intercept slope
106 Decentralized Coordination of Production & Consumption Higher profit Slopes = p p F C Fish
107 Decentralized Coordination of Production & Consumption The firm s production possibility set. Fish
108 Decentralized Coordination of Production & Consumption Slopes = p p F C Fish
109 Decentralized Coordination of Production & Consumption Profit-max. plan Slopes = p p F C Fish
110 Decentralized Coordination of Production & Consumption Profit-max. plan Slope = p p F C Fish
111 Decentralized Coordination of Production & Consumption Competitive markets and profit-maximization p MRPT F. p C Profit-max. plan Slope = p F pc Fish
112 Decentralized Coordination of Production & Consumption So competitive markets, profitmaximization, and utility maximization all together cause MRPT p F MRS, p C the condition necessary for a Pareto optimal economic state.
113 Decentralized Coordination of C Production & Consumption F MF O MF Competitive markets and utility-maximization MRS p F. p C C RC C MF O RC F RC F Fish
114 Decentralized Coordination of C Production & Consumption F MF Competitive markets, utilitymaximization and profitmaximization O MF p MRS F MRPT. p C C RC C MF O RC F RC F Fish
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