1Consumer SurplusECON 370: Microeconomic TheorySummer 2004 – Rice UniversityStanley GilbertEcon 370 - Production 2Adding Production• There will be a Production Sector– Defined by some production function• And Consumers with preferences and endowments– Usually assume they are endowed with labor/leisure and (sometimes) Capital• Consumers own the production firms– So all profits are distributed back to the consumers in some way• Markets and prices– We assume there are factor markets for labor and capital– And consumer markets for the produced good(s)– And market prices for all factors and produced goodsEcon 370 - Production 3Adding Production (cont)• Consumers and firms decide how much to demand/supply of inputs/outputs based on– Profit maximization for firms– Utility maximization for consumers– Market prices• We are interested in:– Efficiency in production– Overall economic efficiencyEcon 370 - Production 4Robinson Crusoe’s Economy: Intro• One agent, RC, endowed w/ a fixed qty of one resource, Time = 24 hrs• Can use time for – labor (production) or – leisure (consumption)• Labor time = L• Leisure time = 24 – L• What will RC choose?2Econ 370 - Production 5Robinson Crusoe’s Technology: GraphLabor (hours)CoconutsProduction function240Feasible productionplansTechnology: Labor produces output (coconuts) according to a concave production functionEcon 370 - Production 6Robinson Crusoe’s Preferences• To represent RC’s preferences:– coconut is a good– leisure is a good• Yields standard indifference map with leisure• Yields indifference curves with positive slopes if plot labor (bad)Econ 370 - Production 7Robinson Crusoe’s Preferences: GraphLeisure (hours)CoconutsMore preferred240Econ 370 - Production 8Robinson Crusoe’s Preferences: GraphLeisure (hours)CoconutsMore preferred24 0Labor (hours)3Econ 370 - Production 9Robinson Crusoe’s Choice: GraphLeisure (hours)Coconuts024Labor (hours)C*L*Econ 370 - Production 10Schizophrenic Robinson Crusoe• Now suppose RC is both – a utility-maximizing consumer and – a profit-maximizing firm– And decides separately how much to produce or consume • Use coconuts as the numeraire good– So, price of a coconut = $1• RC’s wage rate is w• Coconut output level is CEcon 370 - Production 11Robinson Crusoe as a Firm• RC’s firm’s profit is π= C – wL• Isoprofit line equation is •π= C – wL ⇔ C = π+ wL, in C-L space• Slope = + w• Intercept = πEcon 370 - Production 12Isoprofit Lines: GraphHigher profit Slopes = + wC = π + wL(π1< π2< π3)Labor (hours)Coconuts240π1π2π34Econ 370 - Production 13Profit-Maximization: Graph• At optimum:– Isoprofit slope = production function slope– That is, w = p × MPL= 1 × MPL= MRPLProduction functionLabor (hours)Coconuts240π1π2π3Econ 370 - Production 14Profit-Maximization: Graph• As a firm, at wage w Robinson:– demands Labor L*– Produces C*coconuts–Gets π* = C*– wL*in dividends from the firmLabor (hours)Coconuts240C*L*π*Econ 370 - Production 15Utility-Maximization: Introduction• Now consider RC as a consumer endowed with $π*, who can work for $w per hour• What is RC’s most preferred consumption bundle?• Budget constraint is:wL*C +π=Econ 370 - Production 16Utility-Maximization: Budget ConstraintBudget constraint:Labor (hours)Coconuts240π*C = π* + wL5Econ 370 - Production 17Utility-Maximization: PreferencesMore preferredLabor (hours)Coconuts240π*Econ 370 - Production 18C*L*Utility-Maximization: Choice•Given w, – RC’s quantity supplied of labor is L* and– output quantity demanded is C*Labor (hours)Coconuts240π*Econ 370 - Production 19Output and Factor Markets Clear• Price is determined based on the requirement that all markets clear• That is:– quantity output supplied = quantity output demanded – quantity labor demanded = quantity labor supplied • If we have:– well-behaved preferences, and– Convex production function• Then such a price existsEcon 370 - Production 20Utility and Profit-Maximization: GraphLeisure (hours)Coconuts024Labor (hours)C*L*6Econ 370 - Production 21Pareto Efficiency: GraphMRS ≠ MPLPareto Efficiency:Must have MRS = MPLeisure (hours)Coconuts024Labor (hours)Preferred consumptionbundlesEcon 370 - Production 22Pareto Efficiency: GraphCommon slope ⇒ relative wage rate w results in Pareto efficient outcomeLeisure (hours)Coconuts024Labor (hours)C*L*w=MRS = MPLEcon 370 - Production 23Fund. Theorems of Welfare Economics• 1st 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• 2nd Fundamental Theorem of Welfare Economics– Any Pareto efficient outcome can be achieved as a competitive market equilibrium if:– the appropriate redistribution of endowments occurs – consumers’ preferences are convex– there are no externalities in consumption or production– firms’ technologies are convex• Note convex firm technology rules out increasing returns to scaleEcon 370 - Production 24Extend to Two-Good Economy• Consider RC economy with two goods– Coconuts and fish– Both require labor to be produced– Will now consider production possibilities of two good economy7Econ 370 - Production 25Production Possibilities: Introduction• Resource and technological limitations restrict what an economy can produce• Production possibility set - set of all feasible output bundles• Production possibility frontier - the outer boundary of the production possibility setEcon 370 - Production 26Production Possibilities: GraphFishCoconutsProduction possibility frontier (ppf)Production possibility setEcon 370 - Production 27Production Possibilities: GraphMarginal rate of transformation (MRT) = PPF’s slopeFishCoconutsEcon 370 - Production 28Comparative Advantage: Introduction• Two agents, RC and Man Friday (MF)• Assume linear production technologies• RC can produce at most 20 coconuts or 30 fish• MF can produce at most 50 coconuts or 25 fish• RC has comparative advantage in producing fish • PPF is concave w.r.t. origin because take advantage of comparative advantages in production8Econ 370 - Production 29Comparative Advantage: Graph• Two agents, RC and MF • RC can produce at most 20 coconuts or 30 fishFCRC2030FCMF5025• MF can produce at most 50 coconuts or 25 fishEcon 370 - Production