Adding Production. Consumer Surplus. Robinson Crusoe s Economy: Intro. Adding Production (cont)

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1 Adding Production onsumer Surplus EON 37: Microeconomic Theory Summer 24 Rice University Stanley Gilbert There will be a Production Sector Defined by some production function And onsumers with preferences and endowments Usually assume they are endowed with labor/leisure and (sometimes) apital onsumers 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 goods Econ 37 - Production 2 Adding Production (cont) onsumers 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 efficiency Robinson rusoe s Economy: Intro One agent, R, endowed w/ a fixed qty of one resource, Time = hrs an use time for labor (production) or leisure (consumption) Labor time = L Leisure time = L What will R choose? Econ 37 - Production 3 Econ 37 - Production 4 1

2 Robinson rusoe s Technology: Graph Technology: Labor produces output (coconuts) according to a concave production function Production function Robinson rusoe s Preferences To represent R 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) easible production plans Econ 37 - Production 5 Econ 37 - Production 6 Robinson rusoe s Preferences: Graph Robinson rusoe s Preferences: Graph More preferred More preferred Leisure (hours) Leisure (hours) Econ 37 - Production 7 Econ 37 - Production 8 2

3 Robinson rusoe s hoice: Graph * Schizophrenic Robinson rusoe Now suppose R 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 L* Leisure (hours) R s wage rate is w oconut output level is Econ 37 - Production 9 Econ 37 - Production 1 Robinson rusoe as a irm Isoprofit Lines: Graph R s firm s profit is π = wl Isoprofit line equation is π = wl = π + wl, in -L space Slope = + w Intercept = π π 3 π 2 π 1 Higher profit = π + wl (π 1 < π 2 < π 3 ) Slopes = + w Econ 37 - Production 11 Econ 37 - Production 12 3

4 Profit-Maximization: Graph At optimum: Isoprofit slope = production function slope That is, w = p MP L = 1 MP L = MRP L Profit-Maximization: Graph As a firm, at wage w Robinson: demands Labor L * Produces * coconuts Gets π* = * wl * in dividends from the firm π 3 π 2 π 1 Production function * π * L * Econ 37 - Production 13 Econ 37 - Production 14 Utility-Maximization: Introduction Utility-Maximization: Budget onstraint Now consider R as a consumer endowed with $π *, who can work for $w per hour What is R s most preferred consumption bundle? Budget constraint is: = π * + wl π * Budget constraint: = π* + wl Econ 37 - Production 15 Econ 37 - Production 16 4

5 Utility-Maximization: Preferences Utility-Maximization: hoice Given w, R s quantity supplied of labor is L* and output quantity demanded is * More preferred π * * π * L* Econ 37 - Production 17 Econ 37 - Production 18 Output and actor Markets lear Utility and Profit-Maximization: Graph 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 onvex production function Then such a price exists * L* Leisure (hours) Econ 37 - Production 19 Econ 37 - Production 2 5

6 Pareto Efficiency: Graph Pareto Efficiency: Must have MRS = MP MRS MP L Pareto Efficiency: Graph ommon slope relative wage rate w results in Pareto efficient outcome w=mrs = MP L Preferred consumption bundles * Leisure (hours) L* Leisure (hours) Econ 37 - Production 21 Econ 37 - Production 22 und. Theorems of Welfare Economics 1st undamental 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 undamental 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 scale Extend to Two-Good Economy onsider R economy with two goods and fish Both require labor to be produced Will now consider production possibilities of two good economy Econ 37 - Production 23 Econ 37 - Production 6

7 Production Possibilities: Introduction Production Possibilities: Graph 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 set Production possibility frontier (ppf) Production possibility set ish Econ 37 - Production 25 Econ 37 - Production 26 Production Possibilities: Graph Marginal rate of transformation (MRT) = PP s slope omparative Advantage: Introduction Two agents, R and Man riday (M) Assume linear production technologies R can produce at most 2 coconuts or 3 fish M can produce at most 5 coconuts or 25 fish R has comparative advantage in producing fish PP is concave w.r.t. origin because take advantage of comparative advantages in production ish Econ 37 - Production 27 Econ 37 - Production 28 7

8 omparative Advantage: Graph ombined Graph 2 R 5 3 Two agents, R and M R can produce at most 2 coconuts or 3 fish M can produce at most 5 coconuts or 25 fish 2 R Economy Use R to produce fish before using M Use M to produce coconuts before using R M 25 Econ 37 - Production 29 M Econ 37 - Production 3 2 R 5 omparative Advantage: Graph Economy Using low opp. cost producers first results in a ppf that is concave w.r.t the origin omparative Advantage: Graph More producers with different opp. costs smooth out the ppf Economy M Econ 37 - Production 31 Econ 37 - Production 32 8

9 Decentralized oordination R and M run the firm(s) producing coconuts and fish And receive the dividends distributing the profits R and M are also consumers who can sell labor Price of coconut = p Decentralized oordination L R and L M are amounts of labor purchased from R and M irm s profit-maximization problem is to choose,, L R and L M to maxπ = p + p w R L R w M L M Price of fish = p R s wage rate = w R M s wage rate = w M Econ 37 - Production 33 Econ 37 - Production 34 Decentralized oordination Decentralized oordination maxπ = Isoprofit line equation is constantπ = p + p p + p which rearranges to w R L R π + w L w L p R R + = M M p p { intercept w R L R w slope M L w M M L M Higher profit Slopes = p p ish Econ 37 - Production 35 Econ 37 - Production 36 9

10 Decentralized oordination Decentralized oordination Profit-max. plan Profit-max. plan The firm s production possibility set ish ompetitive markets and profit-maximization p MRT = p ish Econ 37 - Production 37 Econ 37 - Production 38 Decentralized oordination ompetitive markets, profit-maximization, and utility maximization all together cause p MRPT = p = MRS This is the condition necessary for a Pareto optimal economic state oordinating Production and onsumption The PP contains many technically efficient output bundles Which are Pareto efficient for consumers? As before, those where If both consumers and producers face the same price, Markets clear Alternatively, Given that markets clear, Both consumers and producers face the same price Econ 37 - Production 39 Econ 37 - Production 4 1

11 oordinating Production and onsumption oordinating Production and onsumption Suppose for given prices output bundle (, ) Maximized profits O M The production bundle forms an Edgeworth Box for the two consumers, with wages and dividends forming the endowment ish O R ish Econ 37 - Production 41 Econ 37 - Production 42 oordinating Production and onsumption oordinating Production and onsumption O M In this case, we do not have an equilibrium, since the price to consumers and producers is different. Efficient coordination of production and consumption requires: dx dx MRS = 2 (cons) = 2 (prod) = MRT dx dx 1 1 Or, could reallocate and make both individuals better off MRS = MRT necessary for Pareto optimality O R ish Econ 37 - Production 43 Econ 37 - Production 44 11

12 oordinating Production and onsumption O M O R ish Econ 37 - Production 45 12