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Chapter 2 Appendix

Chapter 2 Appendix. Welfare Economics. Efficiency Resource Use. Assumptions 2 inputs (capital and labor) 2 outputs (food and clothing). Production Functions. F = F ( L F ,K F ) C = C ( L C ,K C ) Where  F = food production C = clothing production

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Chapter 2 Appendix

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  1. Chapter 2Appendix Welfare Economics

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

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

  4. Constraints L = LF + LK K = KF+ LF

  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 L* LC 0' C K KC E* F6 Z* F5 C1 K* K* F C Z1 F4 C2 C3 F3 C4 D F2 C5 F1 KF C6 LF L* L 0 F

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

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

  9. 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

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

  11. Figure 2A.3 Efficient Allocation of A Given Amount of Food and Clothing per Year For Two Consumers T CB CB* D F Food per Year UA7 UB1 FB UB3 UB2 UB4 E** UA6 E* FA* FB* UB5 UB6 UA5 UB7 UA3 UA4 FA UA2 UA1 CA* CA C T’ Clothing per Year 0

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

  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 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

  14. Social Welfare Functions W = W(UA ,UB) • Where • W is social welfare • UA is A’s utility • UB 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 = PKK + PLL 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 E K F = F1per Year Labor L 0

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

  18. Pure Market Economy and Pareto Efficiency Step 1 So far we know that PF= MCFand PC= MCCin perfect competition, so dividing one by the other we get PCMCC PFMCF =

  19. Pure Market Economy and Pareto Efficiency Step 2 • 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.

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

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

  22. Figure 2A.5 Consumer Choice A Food per Year E FA UA3 UA2 UA1 CA B 0 Clothing per Year

  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 PC PC A B MRSCF = MRSCF = PF PF

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

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

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