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Chapter 32 Production

Chapter 32 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.

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Chapter 32 Production

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  1. Chapter 32Production

  2. 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.

  3. Now Add Production ... • Add input markets, output markets, describe firms’ technologies, the distributions of firms’ outputs and profits …

  4. Now Add Production ... • Add input markets, output markets, describe firms’ technologies, the distributions of firms’ outputs and profits … That’s not easy!

  5. Robinson Crusoe’s 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?

  6. Robinson Crusoe’s Technology • Technology: Labor produces output (coconuts) according to a concave production function.

  7. Robinson Crusoe’s Technology Coconuts Production function Feasible productionplans 24 0 Labor (hours)

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

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

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

  11. Robinson Crusoe’s Choice Coconuts Production function Feasible productionplans 24 0 Labor (hours)

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

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

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

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

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

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

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

  19. 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.

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

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

  22. Profit-Maximization Coconuts Production function Feasible productionplans 24 0 Labor (hours)

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

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

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

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

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

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

  29. Profit-Maximization Isoprofit slope = production function slope i.e. w = MPL = 1 MPL = MRPL. Coconuts Production function C* Given w, RC’s firm’s quantity demanded of labor is L* Labor demand L* 24 0 Labor (hours) RC gets

  30. Profit-Maximization Isoprofit slope = production function slope i.e. w = MPL = 1 MPL = MRPL. Coconuts Production function C* Output supply Given w, RC’s firm’s quantity demanded of labor is L* and output quantity supplied is C*. Labor demand L* 24 0 Labor (hours) RC gets

  31. 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

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

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

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

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

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

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

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

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

  40. Utility-Maximization & Profit-Maximization • Profit-maximization: • w = MPL • quantity of output supplied = C* • quantity of labor demanded = L*

  41. 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*

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

  43. 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)

  44. Pareto Efficiency • Must have MRS = MPL.

  45. Pareto Efficiency Coconuts MRS  MPL 24 0 Labor (hours)

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

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

  48. 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)

  49. 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.

  50. 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.

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