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

General equilibrium & welfareslide 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 & welfareslide 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 & welfareslide 4 T* = Total tacos available B* = Total beer available T M = Mike’s taco consumption B M = Mike’s beer consumption T S = Sally’s taco consumption B S = Sally’s beer consumption

General equilibrium & welfareslide 5 So the following are assumed to be true: T* = T M + T S, and B* = B M + B S So Mike and Sally consume all the Beer and Tacos. Nothing goes to waste.

General equilibrium & welfareslide 6 A Starting Allocation (B M )' (T M )' T B*OMOM T* B M1M1 M2M2 M0M0

General equilibrium & welfareslide 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 M 1.

General equilibrium & welfareslide 8 So here's Sally's allocation. T B*OSOS T* B S1S1 S2S2 S0S0 BSBS TSTS

General equilibrium & welfareslide 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 & welfareslide 10 Rotate Sally's indifference curves 180 degrees. T B*OSOS T* B S1S1 S2S2 S0S0 BSBS TSTS

General equilibrium & welfareslide 11 And place the graph on top of Mike's indifference curve graph. BSBS TSTS (B M )' (T M )' B T OSOS B S1S1 S2S2 S0S0 T OMOM M1M1 M2M2 M0M0

General equilibrium & welfareslide 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 & welfareslide 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 & welfareslide 14 "Better" allocations lie in the shaded area. T OSOS B S1S1 S2S2 S0S0 BSBS TSTS (B M )' (T M )' T OMOM B M1M1 M2M2 M0M0

General equilibrium & welfareslide 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 & welfareslide 16 T OSOS B S* T OMOM M1M1 Z

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

General equilibrium & welfareslide 20 T OSOS B S* T OMOM M0M0 Z Y X

General equilibrium & welfareslide 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 & welfareslide 22 T OSOS B S* T OMOM M0M0 Z Y X Contract curve B

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

General equilibrium & welfareslide 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 & welfareslide 25 L* = Total labor available K* = Total capital available L T = Labor used in taco production L B = Labor used in beer production K T = Capital used in taco production K B = Capital used in beer production

General equilibrium & welfareslide 26 So the following are assumed to be true: L* = L T + L B, and K* = K T + K B So all the labor and capital are used in production. No resources are unemployed.

General equilibrium & welfareslide 27 A Starting Allocation (L T )' (K T )' K L*OTOT K* L T1T1 T2T2 T0T0

General equilibrium & welfareslide 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 T 1.

General equilibrium & welfareslide 29 So here's the allocation to beer. K L*OBOB K* L B1B1 B2B2 B0B0 LBLB KBKB

General equilibrium & welfareslide 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 & welfareslide 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 & welfareslide 32 Rotate the Beer isoquants 180 degrees. K L*OBOB K* L B1B1 B2B2 B0B0 LBLB KBKB

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

General equilibrium & welfareslide 34 "Better" allocations lie in the shaded area. K OBOB L B1B1 B2B2 B0B0 LBLB KBKB (L T )' (K T )' K OTOT L T1T1 T2T2 T0T0

General equilibrium & welfareslide 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 & welfareslide 36 K OBOB L B* K OTOT T1T1 Q L

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

General equilibrium & welfareslide 40 K OBOB L B* K OTOT T0T0 Q R P

General equilibrium & welfareslide 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 & welfareslide 42 K OBOB L B* K OTOT T0T0 Q R P Production Contract curve L

General equilibrium & welfareslide 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 & welfareslide 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 & welfareslide 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 & welfareslide 46 K OBOB L B* K OTOT T0T0 Q R P L B2B2 B0B0 T2T2 T* For example, when T 2 tacos are produced, maximum beer is B 0. T 2 and B 0 are one point the PPC.

General equilibrium & welfareslide 47 B2B2 T0T0 T T2T2 T* BB*B0B0 r q p Each point on the Production Contract Curve "maps" to a point on the Production Possibilities Curve.

General equilibrium & welfareslide 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 & welfareslide 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 & welfareslide 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 & welfareslide 51 Question 3 Where on the Production Possibilities Curve should we produce? In other words, what should be the output mix? Are some points on the PPC better (in the sense of the Pareto Criterion) than others?

General equilibrium & welfareslide 52 If there were only one consumer (Robinson Crusoe?) the problem would be simple.

General equilibrium & welfareslide 53 T T2T2 T* BB*B0B0 B 0, T 2 is not a best point for a consumer with indifference curves shown. T*, B* is optimal. U0U0 U1U1

General equilibrium & welfareslide 54 Rule 3 Produce amounts of goods so that the Marginal Rate of Transformation equals the Marginal Rate of Substitution in consumption. [MRT = MRS]

General equilibrium & welfareslide 55 Application of Rule 3 If goods are not priced at marginal cost, then production will not be optimal. Why?

General equilibrium & welfareslide 56 If Rules 1 and 2 are satisfied, then Rule 3 implies that MC should equal P. 1) Suppose MRT = MRS [Rule 3]. 2) If consumers maximize utility, and all face the same prices, then MRS(Beer for Tacos) = P B /P T. So MRT = (P B /P T ) 3)MRT equals the marginal cost of beer in terms of tacos. So MC B = (P B /P T ) 4) But since Tacos are the "unit of account", P T  1, so MC B = P B.

General equilibrium & welfareslide 57 Implications for markets Free trade. Competitive markets efficient. Monopoly inefficient. Price discrimination inefficient.