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General Equilibrium & Welfare

General Equilibrium & Welfare. How should society organize the production and distribution of goods if the objective is to maximize social welfare?. The Pedagogy. The questions are answered by taking a hypothetical economy in which there are only two consumers, two goods, and two inputs.

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General Equilibrium & Welfare

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  1. General Equilibrium &Welfare • How should society organize the production and distribution of goods if the objective is to maximize social welfare? General equilibrium & welfare

  2. The Pedagogy • The questions are answered by taking a hypothetical economy in which there are only two consumers, two goods, and two inputs. • Once the answers to the questions are found in this special case, it will be apparent that these answers are generalizable. General equilibrium & welfare

  3. Question 1 • Suppose there are two consumers, Sally and Mike. Suppose also that there are two goods, Beer and Tacos, that are available in fixed quantities. • What’s the best way to divide the Beer and Tacos between Sally and Mike? General equilibrium & welfare

  4. T* = Total tacos available • B* = Total beer available • TM = Mike’s taco consumption • BM = Mike’s beer consumption • TS = Sally’s taco consumption • BS = Sally’s beer consumption General equilibrium & welfare

  5. So the following are assumed to be true: • T* = TM + TS, and • B* = BM + BS • So Mike and Sally consume all the Beer and Tacos. Nothing goes to waste. General equilibrium & welfare

  6. A Starting Allocation T T* M2 (TM)' M1 M0 OM B* B (BM)' General equilibrium & welfare

  7. The preceding diagram shows Mike’s starting amounts of consumption for Beer and Tacos, as well as the total amounts available. • Three of Mike’s indifference curves are also shown. He starts off with utility level M1. General equilibrium & welfare

  8. So here's Sally's allocation. T T* TS S2 S1 S0 OS B* B BS General equilibrium & welfare

  9. Edgeworth Box • Use the graphs showing the initial allocation to construct an Edgeworth Box diagram. • The box diagram shows simultaneously the allocations of goods and the utility levels of Mike and Sally. General equilibrium & welfare

  10. Rotate Sally's indifference curves 180 degrees. BS B B* OS S0 S1 S2 TS T* T General equilibrium & welfare

  11. And place the graph on top of Mike's indifference curve graph. T BS OS B S0 S1 S2 M2 TS (TM)' M1 M0 B OM (BM)' T General equilibrium & welfare

  12. So in the box diagram each point shows: • Mike's consumption of both goods, • Sally's consumption of both goods, • Sally's utility level, and • Mike's utility level. General equilibrium & welfare

  13. Is it possible to move away from the starting allocation and make at least one of the people better off without making the other one worse off? • Yes, in this case. We can see all of the "better" allocations. General equilibrium & welfare

  14. "Better" allocations lie in the shaded area. T BS OS B S0 S1 S2 M2 TS (TM)' M1 M0 OM B (BM)' T General equilibrium & welfare

  15. So what must a "best" allocation of the goods look like? • In the following diagram, the point Z is one best way to allocate the goods. • [Any change from Z must make one of the two people worse off.] General equilibrium & welfare

  16. T OS B S* Z  M1 OM T General equilibrium & welfare

  17. The distinguishing characteristic of Z is the indifference curves for the two people are tangent (have the same slope). • At any optimal allocation the people will have equal Marginal Rates of Substitution (MRS) between the goods. General equilibrium & welfare

  18. Rule 1 • Allocate goods to consumers so that the consumers have equal marginal rates of substitution. • MRS(B for T)Mike = MRS(B for T)Sally General equilibrium & welfare

  19. But many allocations are optimal! • There are infinitely many optimal ways to allocate the goods between the two people. General equilibrium & welfare

  20. T OS B S* Y  Z  X  M0 OM T General equilibrium & welfare

  21. Contract Curve • Points like X, Y, and Z fall on the "Contract Curve" in the box diagram. • The Contract curve shows all of the Pareto Optimal ways to distribute the goods to Mike and Sally. General equilibrium & welfare

  22. Contract curve T OS B S* Y  Z  X  M0 B OM T General equilibrium & welfare

  23. Application of Rule 1 • Price discrimination will result in an inefficient (not Pareto Optimal) allocation of goods among consumers. • Why? General equilibrium & welfare

  24. Question 2 • Suppose Tacos and Beer can be produced using two inputs, Labor (L) and Capital (K). • What's the best way to allocate the labor and capital to the production of beer and tacos? General equilibrium & welfare

  25. L* = Total labor available • K* = Total capital available • LT = Labor used in taco production • LB = Labor used in beer production • KT = Capital used in taco production • KB = Capital used in beer production General equilibrium & welfare

  26. So the following are assumed to be true: • L* = LT + LB, and • K* = KT + KB • So all the labor and capital are used in production. No resources are unemployed. General equilibrium & welfare

  27. A Starting Allocation K K* T2 (KT)' T1 T0 OT L* L (LT)' General equilibrium & welfare

  28. The preceding diagram shows an allocation of labor and capital to taco production, and the total amounts of L and K available. • Three isoquants are also shown. We start off with production level T1. General equilibrium & welfare

  29. So here's the allocation to beer. K K* KB B2 B1 B0 OB L* L LB General equilibrium & welfare

  30. Is it possible to move away from the starting allocation and increase the production of one good without reducing the production of the other? • Yes, in this case. We can see all of the "better" allocations. General equilibrium & welfare

  31. Edgeworth Box • Use the graphs showing the initial allocation to construct another Edgeworth Box diagram. • The box diagram shows simultaneously the allocations of inputs and the output levels of Tacos and Beer. General equilibrium & welfare

  32. Rotate the Beer isoquants 180 degrees. LB L L* OB B0 B1 B2 KB K* K General equilibrium & welfare

  33. And place it on top of the Taco isoquants. • Each point in the box shows an allocation of the inputs to the outputs and the resulting levels of output of the two goods. General equilibrium & welfare

  34. "Better" allocations lie in the shaded area. K LB OB L B0 B1 B2 T2 KB (KT)' T1 T0 OT L (LT)' K General equilibrium & welfare

  35. So what must a "best" allocation of the inputs look like? • In the following diagram, the point Q is one best way to allocate the inputs. • [Any change from Q must reduce output of at least one of the goods.] General equilibrium & welfare

  36. K OB L B* Q  T1 L OT K General equilibrium & welfare

  37. The distinguishing characteristic of Q is the isoquants for the two goods are tangent (have the same slope). • At any optimal allocation the people will have equal Marginal Rates of Technical Substitution (MRTS) between the goods. General equilibrium & welfare

  38. Rule 2 • Allocate inputs to goods so that the goods have equal marginal rates of substitution. • MRTS(L for K)Tacos = MRTS(L for K)Beer General equilibrium & welfare

  39. But many allocations are optimal! • There are infinitely many optimal ways to allocate the inputs between the goods. General equilibrium & welfare

  40. K OB L B* R  Q  P  T0 OT K General equilibrium & welfare

  41. Production Contract Curve • Points like P, Q, and R fall on the "Production Contract Curve" in the box diagram. • The contract curve shows all of the Pareto Optimal ways to distribute the inputs between the outputs. General equilibrium & welfare

  42. Production Contract curve K OB L B* R  Q  P  T0 L OT K General equilibrium & welfare

  43. Application of Rule 2 • Price discrimination in inputs will result in an inefficient (not Pareto Optimal) allocation of inputs across goods. • Why? General equilibrium & welfare

  44. From PCC to PPC • The next step in the exercise is to show how the analysis of productive efficiency can be used to derive the Production Possibilities Curve for our 2 by 2 economy. General equilibrium & welfare

  45. Notice that each point on the Production Contract Curve shows the maximum amount of one output that can be produced, given some amount of the other good to be produced. General equilibrium & welfare

  46. For example, when T2 tacos are produced, maximum beer is B0. T2 and B0 are one point the PPC. K OB L B0 B* R  B2 Q T2  P  T* T0 L OT K General equilibrium & welfare

  47. Each point on the Production Contract Curve "maps" to a point on the Production Possibilities Curve. T r T2 T* q T0 p B0 B* B2 B General equilibrium & welfare

  48. Alternative interpretation of Rule 2 • Efficiency requires that we be on the PPC. Point "inside" the PPC correspond to points off the Production Contract Curve. • So Rule 2 says: "Get on the Production Possibilities Curve." General equilibrium & welfare

  49. Marginal Rate of Transformation • The Marginal Rate of Transformation of Beer for Tacos is the amount of Tacos you must give up in order to get 1 more unit of Beer. • It is the same as: • Minus the slope of the PPC. • The marginal (opportunity) cost of beer in terms of tacos. General equilibrium & welfare

  50. Notice that for the PPC we constructed, the MRT of Beer for Tacos rises as more Beer is produced. • That is, marginal (opportunity) cost of beer rises as more beer is produced. General equilibrium & welfare

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