Chapter Thirty - Queen's Economics Department | QED

Chapter Thirty - Queen's Economics Department | QED

Chapter Thirty-Two 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.

Now Add Production ... Add input markets, output markets, describe firms technologies, the distributions of firms outputs and profits Now Add Production ... Add input markets, output markets, describe firms technologies, the distributions of firms outputs and profits Thats not easy! Robinson Crusoes Economy

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

Technology: Labor produces output (coconuts) according to a concave production function. Robinson Crusoes Technology Coconuts Production function 0 24 Labor (hours) Robinson Crusoes Technology Coconuts

Production function Feasible production plans 0 24 Labor (hours) Robinson Crusoes Preferences RCs preferences: coconut is a good leisure is a good Robinson Crusoes Preferences

Coconuts More preferred 0 24 Leisure (hours) Robinson Crusoes Preferences Coconuts More preferred 24 0 Leisure (hours)

Robinson Crusoes Choice Coconuts Production function Feasible production plans 0 24 Labor (hours) Robinson Crusoes Choice Coconuts Production function

Feasible production plans 0 24 24 0 Labor (hours) Leisure (hours) Robinson Crusoes Choice Coconuts Production function

Feasible production plans 0 24 24 0 Labor (hours) Leisure (hours) Robinson Crusoes Choice Coconuts Production function

Feasible production plans 0 24 24 0 Labor (hours) Leisure (hours) Robinson Crusoes Choice Coconuts Production function

C* 0 24 L* 24 0 Labor (hours) Leisure (hours) Robinson Crusoes Choice Coconuts Production function

C* Labor 0 24 L* 24 0 Labor (hours) Leisure (hours) Robinson Crusoes Choice Coconuts

Production function C* Labor 0 24 Leisure L* 24 0 Labor (hours) Leisure (hours) Robinson Crusoes Choice

Coconuts Production function C* 0 24 Output Labor L* Leisure 24 0

Labor (hours) Leisure (hours) Robinson Crusoes Choice Coconuts MRS = MPL Production function C* 0 24 Output Labor

L* Leisure 24 0 Labor (hours) Leisure (hours) 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. RCs wage rate is w. Coconut output level is C. Robinson Crusoe as a Firm RCs firms profit is = C - wL. = C - wL C = + wL, the equation of an isoprofit line. Slope = + w . Intercept = .

Isoprofit Lines Coconuts Higher profit; 1 2 3 C wL Slopes = + w 3 2 1 0 24 Labor (hours)

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

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

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

Isoprofit slope = production function slope Production function C* 0 L* 24 Labor (hours) Profit-Maximization Coconuts Isoprofit slope = production function slope

i.e. w = MPL Production function C* 0 L* 24 Labor (hours) Profit-Maximization Coconuts Isoprofit slope = production function slope i.e. w = MPL = 1 MPL = MRPL.

Production function C* 0 L* 24 Labor (hours) Profit-Maximization Coconuts Isoprofit slope = production function slope i.e. w = MPL = 1 MPL = MRPL. Production function

C* * 0 RC gets L* 24 * C * wL * Labor (hours) Profit-Maximization Coconuts

Isoprofit slope = production function slope i.e. w = MPL = 1 MPL = MRPL. Production function C* * Given w, RCs firms quantity demanded of labor is L* Labor demand 0 RC gets L*

24 * C * wL * Labor (hours) Profit-Maximization Coconuts Isoprofit slope = production function slope i.e. w = MPL = 1 MPL = MRPL. Production function C* *

Given w, RCs firms quantity demanded of labor is L* and output quantity supplied is C*. Labor Output demand supply 0 RC gets L* 24 * C * wL * Labor (hours) Utility-Maximization

Now consider RC as a consumer endowed with $* who can work for $w per hour. What is RCs most preferred consumption bundle? Budget constraint is C * wL. Utility-Maximization Coconuts Budget constraint

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

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

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

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

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

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

C * wL. C* * Given w, RCs quantity supplied of labor is L* Labor supply 0 L* 24 Labor (hours)

Utility-Maximization Coconuts MRS = w Budget constraint; slope = w C * wL. C* * Labor Output supply demand 0 L* Given w, RCs quantity

supplied of labor is L* and output quantity demanded is C*. 24 Labor (hours) Utility-Maximization & ProfitMaximization Profit-maximization: w = MPL quantity of output supplied = C* quantity of labor demanded = L* Utility-Maximization & ProfitMaximization Profit-maximization:

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

quantity of labor demanded = L* Utility-maximization: w = MRS quantity of output demanded = C* quantity of labor supplied = L* Utility-Maximization & ProfitMaximization Coconuts MRS = w = MPL Given w, RCs quantity supplied of labor = quantity demanded of labor = L* and output quantity demanded = output quantity supplied = C*.

C* * 0 L* 24 Labor (hours) Pareto Efficiency Must have MRS = MPL.

Pareto Efficiency Coconuts 0 MRS MPL 24 Labor (hours) Pareto Efficiency Coconuts MRS MPL Preferred consumption bundles.

0 24 Labor (hours) Pareto Efficiency Coconuts 0 MRS = MPL 24 Labor (hours) Pareto Efficiency

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

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

Do the Welfare Theorems hold if firms have non-convex technologies? The 2nd Theorem does require that firms technologies be convex. Non-Convex Technologies Coconuts MRS = MPL. The Pareto optimal allocation cannot be implemented by a competitive equilibrium. 0 24

Labor (hours) Production Possibilities Resource and technological limitations restrict what an economy can produce. The set of all feasible output bundles is the economys production possibility set. The sets outer boundary is the production possibility frontier.

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

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

Feasible but inefficient Fish Production Possibilities Coconuts Ppfs slope is the marginal rate of product transformation. Fish Production Possibilities Coconuts Ppfs slope is the marginal rate of product transformation. Increasingly negative MRPT

increasing opportunity cost to specialization. Fish Production Possibilities If there are no production externalities then a ppf will be concave w.r.t. the origin. Why? 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. 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. C Comparative Advantage RC 20 C 50 30 MF

25 F F C 20 C 50 Comparative Advantage RC MRPT = -2/3 coconuts/fish so opp. cost of one

more fish is 2/3 foregone coconuts. 30 MF 25 F F C 20 C 50 Comparative Advantage

RC MRPT = -2/3 coconuts/fish so opp. cost of one more fish is 2/3 foregone coconuts. 30 MF F MRPT = -2 coconuts/fish so opp. cost of one more fish is 2 foregone coconuts. 25 F C 20

C 50 Comparative Advantage RC MRPT = -2/3 coconuts/fish so opp. cost of one more fish is 2/3 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 2 foregone coconuts. 25 F C 20 C 50 Comparative Advantage RC

MRPT = -2/3 coconuts/fish so opp. cost of one more coconut is 3/2 foregone fish. 30 MF 25 F F C 20 C 50 Comparative Advantage

RC MRPT = -2/3 coconuts/fish so opp. cost of one more coconut is 3/2 foregone fish. 30 MF F MRPT = -2 coconuts/fish so opp. cost of one more coconut is 1/2 foregone fish. 25 F C

20 C 50 Comparative Advantage RC MRPT = -2/3 coconuts/fish so opp. cost of one more coconut is 3/2 foregone fish. 30 MF F 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. 25 F C Comparative Advantage RC Economy C 20

70 C 50 30 MF 25 F F Use RC to produce fish before using MF. Use MF to produce coconuts before

using RC. 50 30 55 F C Comparative Advantage RC Economy C

20 70 C 50 30 MF 25 F F Using low opp. cost producers first results

in a ppf that is concave w.r.t the origin. 50 30 55 F Comparative Advantage Economy C More producers with different opp. costs smooth out the ppf.

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

Output bundle is ( F , C ) C F Fish Coordinating Production & Consumption Coconuts Output bundle is ( F , C ) and is the aggregate endowment for distribution to consumers RC and MF. C

F Fish Coordinating Production & Consumption Coconuts C ORC OMF F Output bundle is ( F , C ) and is the aggregate

endowment for distribution to consumers RC and MF. Fish Coordinating Production & Consumption Coconuts OMF C Allocate ( F , C ) efficiently; , C RC ) to RC say ( FRC C RC

ORC FRC F Fish Coordinating Production & Consumption Coconuts FMF C

OMF C RC C MF ORC FRC F Allocate ( F , C ) efficiently; , C RC

) to RC and say ( FRC ( FMF , C MF ) to MF. Fish Coordinating Production & Consumption Coconuts FMF C OMF

C RC C MF ORC FRC F Fish Coordinating Production & Consumption Coconuts

FMF C OMF C RC C MF ORC FRC

F Fish Coordinating Production & Consumption Coconuts FMF C OMF C RC C MF

ORC FRC F Fish Coordinating Production & Consumption Coconuts FMF C

OMF C RC C MF ORC FRC F MRS MRPT

Fish Coordinating Production & Consumption Coconuts FMF C OMF OMF C C RC

ORC Instead produce ( F , C ). C MF FRC F F Fish Coordinating Production &

Consumption Coconuts FMF C OMF OMF C C RC ORC

Instead produce ( F , C ). C MF FRC F F Fish Coordinating Production & Consumption Coconuts FMF

C OMF FMF C C RC Instead produce ( F , C ). Give MF same allocation OMF as before.

C MF C MF ORC FRC F F Fish Coordinating Production &

Consumption Coconuts FMF C OMF FMF C C RC C MF

Instead produce ( F , C ). Give MF same allocation OMF as before. MFs utility is unchanged. C MF ORC FRC F

F Fish Coordinating Production & Consumption Coconuts OMF C FMF Instead produce ( F , C ). Give MF same allocation OMF as before. MFs

utility is unchanged C MF ORC F Fish Coordinating Production & Consumption Coconuts OMF C

FMF C RC ORC Instead produce ( F , C ). Give MF same allocation OMF as before. MFs utility is unchanged C MF FRC

F Fish Coordinating Production & Consumption Coconuts OMF C FMF C RC

ORC Instead produce ( F , C ). Give MF same allocation OMF as before. MFs utility is unchanged, RCs utility is higher C MF FRC F

Fish Coordinating Production & Consumption Coconuts OMF C FMF C RC ORC FRC

Instead produce ( F , C ). Give MF same allocation OMF as before. MFs utility is unchanged, RCs utility is higher; C MF Pareto improvement. F Fish Coordinating Production &

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

OMF C RC ORC C MF FRC F Fish 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 = pC. Price of fish = pF. RCs wage rate = wRC. MFs wage rate = wMF.

Decentralized Coordination of Production & Consumption LRC, LMF are amounts of labor purchased from RC and MF. Firms profit-maximization problem is choose C, F, LRC and LMF to max pC C pF F w RC LRC w MF LMF . Decentralized Coordination of Production & Consumption max pC C pF F w RC LRC w MF LMF . Isoprofit line equation is

constant pC C pF F wRC LRC wMF LMF Decentralized Coordination of Production & Consumption max pC C pF F w RC LRC w MF LMF . Isoprofit line equation is constant pC C pF F wRC LRC wMF LMF which rearranges to w RC LRC w MF LMF pF C F. pC pC Decentralized Coordination of Production & Consumption max pC C pF F w RC LRC w MF LMF .

Isoprofit line equation is constant pC C pF F wRC LRC wMF LMF which rearranges to w RC LRC w MF LMF pF C F. pC pC intercept 2 slope Decentralized Coordination of Production & Consumption

Coconuts Higher profit pF Slopes = pC Fish Decentralized Coordination of Production & Consumption Coconuts The firms production possibility set. Fish

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

Slopes = pC Fish Decentralized Coordination of Production & Consumption Coconuts Profit-max. plan pF Slope = pC Fish Decentralized Coordination of

Production & Consumption Coconuts Profit-max. plan Competitive markets and profit-maximization pF MRPT pC pF Slope = pC .

Fish Decentralized Coordination of Production & Consumption So competitive markets, profitmaximization, and utility maximization all together cause pF MRPT MRS , pC the condition necessary for a Pareto optimal economic state. Decentralized Coordination of Production & Consumption

Coconuts C FMF Competitive markets and utility-maximization OMF pF MRS C RC ORC

C MF FRC F Fish pC . Decentralized Coordination of Production & Consumption Coconuts

C FMF Competitive markets, utilitymaximization and profitmaximization OMF pF MRS MRPT . pC C RC ORC C MF FRC

F Fish

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