Chapter 2 Appendix Welfare Economics 1 Efficiency Resource

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Chapter 2 Appendix Welfare Economics 1

Chapter 2 Appendix Welfare Economics 1

Efficiency Resource Use Assumptions n 2 inputs (capital and labor) n 2 outputs (food

Efficiency Resource Use Assumptions n 2 inputs (capital and labor) n 2 outputs (food and clothing) 2

Production Functions F = F(LF, KF) C = C(LC, KC) Where n F =

Production Functions F = F(LF, KF) C = C(LC, KC) Where n F = food production n C = clothing production n Li = labor devoted to the production of good i n Ki = capital devoted to the production of good i 3

Constraints L = LF + LK K = K F + LF 4

Constraints L = LF + LK K = K F + LF 4

Productive Efficiency It is not possible to reallocate inputs to alternative uses so that

Productive Efficiency It is not possible to reallocate inputs to alternative uses so that we can increase the output of any good without reducing the output of some alternative good. 5

Figure 2 A. 1 Productive Efficiency L*C K LC 0' KC Z* K*F E*

Figure 2 A. 1 Productive Efficiency L*C K LC 0' KC Z* K*F E* C 3 KF 0 D C 6 F 1 LF C 5 F 2 C 4 F 5 F 6 C 1 K* C Z 1 F C 2 4 F 3 L*F L 6

Efficiency Condition MRTSFLK = MRTSCLK n The Marginal Rate of Technical substitution of Labor

Efficiency Condition MRTSFLK = MRTSCLK n The Marginal Rate of Technical substitution of Labor for Capital for each good are equal 7

Figure 2 A. 2 The Production-Possibility Curve Food per Year T E 1 A

Figure 2 A. 2 The Production-Possibility Curve Food per Year T E 1 A E 2 D F 0 C T' Clothing per Year 8

Pareto Efficiency Preferences on Consumption UA = U(FA, CA) UB = U(FB, CB) Where

Pareto Efficiency Preferences on Consumption UA = U(FA, CA) UB = U(FB, CB) Where Ui = the utility of person i Fi = food consumed by person i Ci = clothing consumed by person i 9

Constraints F = FA + FB C = CA + CB 10

Constraints F = FA + FB C = CA + CB 10

Figure 2 A. 3 Efficient Allocation of A Given Amount of Food and Clothing

Figure 2 A. 3 Efficient Allocation of A Given Amount of Food and Clothing per Year For Two Consumers Food per Year T CB CB* F UB 1 UB 3 UB 4 FA* UB 7 UB 5 UA 1 CA UA 7 FB UA 6 UA 5 UA 3 FA 0 UB 6 E* UB 2 E** D FB* UA 4 UA 2 CA* C Clothing per Year T’ 11

Efficiency Criterion on Consumption and Production MRSACF = MRSBCF = MRTCF 12

Efficiency Criterion on Consumption and Production MRSACF = MRSBCF = MRTCF 12

Interpretation of Efficiency Criterion Suppose we say that the “price of a unit of

Interpretation of Efficiency Criterion Suppose we say that the “price of a unit of clothing is $1. ” Then clothing is the same as “money. ” We can then say that MRSACF is A’s willingness to substitute clothing for money, which is their marginal benefit of clothing, MBAC. The same is true for B. If these are equal to the MRTCF, , then this represents the capability of turning money into clothing as well. Thus it reflects the costs of production. Lastly, if there are no other people who gain from either A or B consuming clothing or food then: MSB = MBAC = MBBC = MSCC 13

Social Welfare Functions W = W(UA , UB) n Where n n n W

Social Welfare Functions W = W(UA , UB) n Where n n n W is social welfare UA is A’s utility UB is B’s utility 14

Efficiency and Economic Institutions Given the conditions for a market rendering a Pareto Optimal

Efficiency and Economic Institutions Given the conditions for a market rendering a Pareto Optimal outcome referred to in Chapter 2, if costs are: C = P K K + P LL then production of a particular amount of a good is efficient if the slope of the production function for each good is equal to the slope of the isocost line. 15

Capital Figure 2 A. 4 Cost Minimization and Productive Efficiency E K F =

Capital Figure 2 A. 4 Cost Minimization and Productive Efficiency E K F = F 1 per Year 0 L Labor 16

Implications of Figure 2 A. 4 n n n MRTSFLK = PL/PK MRTSCLK =

Implications of Figure 2 A. 4 n n n MRTSFLK = PL/PK MRTSCLK = PL/PK MRTSFLK = MRTSCLK = PL/PK 17

Pure Market Economy and Pareto Efficiency Step 1 So far we know that PF

Pure Market Economy and Pareto Efficiency Step 1 So far we know that PF = MCF and PC = MCC in perfect competition, so dividing one by the other we get = PC PF MCC MCF 18

Pure Market Economy and Pareto Efficiency Step 2 n n n MCF is the

Pure Market Economy and Pareto Efficiency Step 2 n n n MCF is the amount of other resources that must be given up to produce more food. We will denote this fact by saying: MCF = DC. It is the forgone clothing to produce more food. The same applies the other way around: MCC = DF. 19

Pure Market Economy and Pareto Efficiency Step 3 Dividing these by each other we

Pure Market Economy and Pareto Efficiency Step 3 Dividing these by each other we get: MCC DF = MCF DC 20

Pure Market Economy and Pareto Efficiency Step 4 Since DF DC And Then =

Pure Market Economy and Pareto Efficiency Step 4 Since DF DC And Then = MRTCF = MCC MCF = PC PF DF DC = MRTCF = PC PF 21

Figure 2 A. 5 Consumer Choice Food per Year A E FA UA 3

Figure 2 A. 5 Consumer Choice Food per Year A E FA UA 3 UA 2 UA 1 0 CA B Clothing per Year 22

Pure Market Economy and Pareto Efficiency Step 5 As just seen, the slopes of

Pure Market Economy and Pareto Efficiency Step 5 As just seen, the slopes of the individual’s indifference curves are equal to the ratio of the prices. So A MRSCF B MRSCF = = PC PF 23

Pure Market Economy and Pareto Efficiency Final A B MRSCF = MRTCF = PC

Pure Market Economy and Pareto Efficiency Final A B MRSCF = MRTCF = PC PF 24

Market Imperfections n n Monopoly P > MC Others are affected so MB =

Market Imperfections n n Monopoly P > MC Others are affected so MB = MSB or MC = MSC 25