1 Chapter 2 Appendix Welfare Economics

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

3 Production Functions F = F(L F,K F ) C = C(L C,K C ) Where F = food production C = clothing production L i = labor devoted to the production of good i K i = capital devoted to the production of good i

4 Constraints L = L F + L K K = K F + L F

5 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.

6 Figure 2A.1 Productive Efficiency F3F3 F6F6 F5F5 F2F2 F1F1 F4F4 C2C2 C3C3 C4C4 C5C5 C6C6 C1C1 E* Z* D F C F K* L* C 0 K L 0' LFLF LCLC KCKC KFKF Z1Z1

7 Efficiency Condition MRTS F LK = MRTS C LK The Marginal Rate of Technical substitution of Labor for Capital for each good are equal

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

9 Pareto Efficiency Preferences on Consumption U A = U(F A,C A ) U B = U(F B,C B ) Where U i = the utility of person i F i = food consumed by person i C i = clothing consumed by person i

10 Constraints F = F A + F B C = C A + C B

11 Figure 2A.3 Efficient Allocation of A Given Amount of Food and Clothing per Year For Two Consumers UB1UB1 UB2UB2 UB3UB3 UB4UB4 UB5UB5 UB6UB6 UB7UB7 FA*FA* FB*FB* CB*CB* CA*CA* E* E** CACA FAFA CBCB FBFB F C D UA5UA5 UA4UA4 UA2UA2 UA1UA1 UA6UA6 UA3UA3 UA7UA7 Food per Year Clothing per Year T T’ 0

12 Efficiency Criterion on Consumption and Production MRS A CF = MRS B CF = MRT CF

13 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 MRS A CF is A’s willingness to substitute clothing for money, which is their marginal benefit of clothing, MB A C. The same is true for B. If these are equal to the MRT CF,,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 = MB A C = MB B C = MSC C

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

15 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 L L 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.

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

17 Implications of Figure 2A.4 MRTS F LK = P L /P K MRTS C LK = P L /P K MRTS F LK = MRTS C LK = P L /P K

18 Pure Market Economy and Pareto Efficiency Step 1 So far we know that P F = MC F and P C = MC C in perfect competition, so dividing one by the other we get P C MC C P F MC F =

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

20 Pure Market Economy and Pareto Efficiency Step 3 Dividing these by each other we get : MC C  F MC F  C =

21 Pure Market Economy and Pareto Efficiency Step 4 = MRT CF FF CC Since And MRT CF = PCPC PFPF Then = MRT CF = PCPC PFPF FF CC MC C MC F =

22 Figure 2A.5 Consumer Choice A B E FAFA CACA Food per Year Clothing per Year 0 UA3UA3 UA2UA2 UA1UA1

23 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 MRS CF = PCPC PFPF A PCPC PFPF B

24 Pure Market Economy and Pareto Efficiency Final MRS CF = MRS CF = MRT CF = PCPC PFPF AB

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