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Production

Production. Exchange Economies (revisited). No production, only endowments, so no description of how resources are converted to consumables. General equilibrium: all markets clear simultaneously. Now Add Production.

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Production

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  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 -- 24 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 Coconuts Production function Feasible productionplans 24 0 Labor (hours)

  7. Robinson Crusoe’s Preferences • RC’s preferences: • coconut is a good • leisure is a good

  8. Robinson Crusoe’s Preferences Coconuts More preferred 24 0 Leisure (hours)

  9. Robinson Crusoe’s Choice Coconuts More preferred Production function Feasible productionplans 24 0 Labor (hours) Leisure (hours) 24 0

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

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

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

  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 Coconuts Budget constraint; slope = w Intercept = 24 0 Labor (hours)

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

  18. MRS = w Output demand Given w, RC’s quantity supplied of labor is L* and output quantity demanded is C*. Labor supply Utility-Maximization Coconuts Budget constraint; slope = w C* L* 24 0 Labor (hours)

  19. Utility-Maximization & Profit-Maximization • 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* Coconut and labor markets both clear.

  20. Utility-Maximization & Profit-Maximization Coconuts MRS = w= MPL Given w, RC’s quantity supplied of labor = quantity demanded of labor = L* and output quantity demanded = output quantity supplied = C*. C* L* 24 0 Labor (hours)

  21. Pareto Efficiency Coconuts …………… …………………… 24 0 Labor (hours) • MRS  MPL, not Pareto efficient

  22. Pareto Efficiency • To achieve Pareto Efficiency must have MRS = MPL.

  23. Pareto Efficiency Coconuts MRS = MPL. The common slope  relative wage rate w that implements the Pareto efficient plan by decentralized pricing. 24 0 Labor (hours) • MRS = MPL, ………………………..

  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 Coconuts MRS = MPLThe common slope  relative wage rate w that implements the Pareto efficient plan by decentralized pricing. 24 0 Labor (hours)

  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 Coconuts MRS = MPL. The Pareto optimal allocation……… be implemented by a competitive equilibrium. 24 0 Labor (hours)

  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 Coconuts Production possibility frontier (PPF) Production possibility set Fish

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

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

  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 C RC MRPT = -2/3 coconuts/fish so opp. cost of one more fish is …… foregone coconuts. 20 RC has the comparative opp. cost advantage in producing fish. 30 F C MF 50 MRPT = -2 coconuts/fish so opp. cost of one more fish is …… foregone coconuts. 25 F

  36. Comparative Advantage C RC MRPT = -2/3 coconuts/fish so opp. cost of one more coconut is …… foregone fish. 20 30 F C MF 50 MRPT = -2 coconuts/fish so opp. cost of one more coconut is …… foregone fish. MF has the comparative opp. cost advantage in producing coconuts. 25 F

  37. Comparative Advantage C RC Economy C 20 Use ….. to produce fish before using …… 70 30 F C MF 50 Use ….. to produce coconuts before using ….. 50 30 55 F 25 F

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

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

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

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

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

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

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

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

  46. Coordinating Production & Consumption Coconuts OMF ORC Fish

  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 = pC. • Price of fish = pF. • RC’s wage rate = wRC. • MF’s wage rate = wMF.

  49. Decentralized Coordination of Production & Consumption • LRC, LMF are amounts of labor purchased from RC and MF. • Firm’s profit-maximization problem is choose C, F, LRC and LMF to

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

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