1 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.

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, Robinson Crusoe (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 24 0

9 Robinson Crusoe’s Choice Labor (hours) Coconuts Feasible production plans Production function 24 0 Leisure (hours) 240 More preferred

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

11 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.

12 Robinson Crusoe as a Firm RC’s firm’s profit is  = C - wL.  = C - wL  …………………..…, the equation of an isoprofit line. Slope = + w. Intercept = .

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

14 Profit-Maximization Labor (hours) Coconuts Production function 24 C* L* Isoprofit slope = production function slope i.e. w = …………………………………. RC as a firm gets 0 Given w, RC’s firm’s quantity demanded of labor is L* and output quantity supplied is C*. Labor demand Output supply

15 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

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

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

18 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

19 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.

20 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*. Utility-Maximization & Profit-Maximization

21 Pareto Efficiency Labor (hours) Coconuts 24 0 …………… …………………… MRS  MP L, not Pareto efficient

22 Pareto Efficiency To achieve Pareto Efficiency must have MRS = MP L.

23 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. MRS = MP L, ………………………..

24 First Fundamental Theorem of Welfare Economics A competitive market equilibrium is Pareto efficient if  consumers’ preferences are ………..  there are …………………….…. in consumption or production.

25 Second Fundamental Theorem of Welfare Economics Any Pareto efficient economic state can be achieved as a competitive market equilibrium if  consumers’ preferences are ……………….  firms’ technologies are ……………….  there are ………………………. in consumption or production.

26 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.

27 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.

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

29 Non-Convex Technologies Labor (hours) Coconuts 24 0 MRS = MP L. The Pareto optimal allocation ……… be implemented by a competitive equilibrium.

30 Production Possibilities Resource and technological limitations restrict what an economy can produce. The set of all feasible output bundles is the economy’s ……………………... The set’s outer boundary is the …………… ………...

31 Production Possibilities Fish Coconuts Production possibility frontier (PPF) Production possibility set

32 Production Possibilities Fish Coconuts Feasible but inefficient ………………… Infeasible

33 Production Possibilities Fish Coconuts PPF’s slope is the ……………… ……………………………………… Increasingly negative MRPT  increasing opportunity cost to specialization.

34 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.

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

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

37 Comparative Advantage F C Economy F C F C RC MF Use ….. to produce fish before using …… Use ….. to produce coconuts before using …..

38 Comparative Advantage F C Economy More producers with different opp. costs “smooth out” the ppf. Using low opp. cost producers first results in a ppf that is concave w.r.t the origin.

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

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

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

42 Fish Coconuts O RC O MF However, …………………. Coordinating Production & Consumption RC’s indifferent curve MF’s indifferent curve

43 Fish Coconuts O RC O MF O' MF If instead produce and give MF same allocation as before. → MF’s utility is ……………….. Coordinating Production & Consumption

44 Fish Coconuts O RC O MF O’ MF MF’s utility is unchanged, But RC’s utility is ……..…. ; Pareto improvement Coordinating Production & Consumption

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

46 Fish Coconuts O RC O MF Coordinating Production & Consumption

47 Decentralized Coordination of Production & Consumption The above Pareto optimal production and consumption can be achieved by decentralized behaviours of firms and consumers Competitive markets, profit-maximization, and utility maximization all together can result in a Pareto optimal economic state

48 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.

49 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

50 Decentralized Coordination of Production & Consumption Equation for Isoprofit line is which rearranges to

51 Decentralized Coordination of Production & Consumption Fish Coconuts Slopes = Higher profit The firm’s production possibility set.

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

53 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.

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

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