Copyright © 2002 by Thomson Learning, Inc. Chapter 2 Appendix Welfare Economics Copyright © 2002 Thomson Learning, Inc. Thomson Learning™ is a trademark used herein under license. ALL RIGHTS RESERVED. Instructors of classes adopting PUBLIC FINANCE: A CONTEMPORARY APPLICATION OF THEORY TO POLICY, Seventh Edition by David N. Hyman as an assigned textbook may reproduce material from this publication for classroom use or in a secure electronic network environment that prevents downloading or reproducing the copyrighted material. Otherwise, no part of this work covered by the copyright hereon may be reproduced or used in any form or by any means—graphic, electronic, or mechanical, including, but not limited to, photocopying, recording, taping, Web distribution, information networks, or information storage and retrieval systems—without the written permission of the publisher. Printed in the United States of America ISBN X

Copyright © 2002 by Thomson Learning, Inc. Efficiency Resource Use Assumptions  2 inputs (capital and labor)  2 outputs (food and clothing)

Copyright © 2002 by Thomson Learning, Inc. 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

Copyright © 2002 by Thomson Learning, Inc. Constraints L = L F + L K K = K F + L F

Copyright © 2002 by Thomson Learning, Inc. Productive Efficiency  It is not possible to reallocate inputs to alternative uses in such a manner as to increase the output of any good without reducing the output of some alternative good.

Copyright © 2002 by Thomson Learning, Inc. Figure 2A.1 Productive Efficiency F3F3 E* F6F6 F5F5 Z* F3F3 F1F1 F4F4 Z1Z1 C2C2 C3C3 C4C4 C5C5 C6C6 C1C1 D 0 K* F K L C KFKF LFLF LCLC KCKC L* F C 0'

Copyright © 2002 by Thomson Learning, Inc. Efficiency Condition MRTS F LK = MRTS C LK  The Marginal Rate of Technical substitution of Labor for Capital in each good are equal

Copyright © 2002 by Thomson Learning, Inc. Figure 2A.2 The Production-Possibility Curve A D E 1 E 2 Food per Year Clothing per Year 0 T F CT'

Copyright © 2002 by Thomson Learning, Inc. 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

Copyright © 2002 by Thomson Learning, Inc. Constraints F = F A + F B C = C A + C B

Copyright © 2002 by Thomson Learning, Inc. Food per Year Clothing per Year T T’ F C D FAFA CACA CBCB FBFB 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 UA5UA5 UA4UA4 UA2UA2 UA1UA1 UA6UA6 FA*FA* FB*FB* CB*CB* CA*CA* E* E** UA3UA3 UA7UA7 0

Copyright © 2002 by Thomson Learning, Inc. Efficiency Criterion on Consumption and Production MRS A CF = MRS B CF = MRT CF

Copyright © 2002 by Thomson Learning, Inc. 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

Copyright © 2002 by Thomson Learning, Inc. 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

Copyright © 2002 by Thomson Learning, Inc. Efficiency and Economic Institutions Given the conditions for a market rendering a Pareto Optimal outcome referred to in Chapter 2 then 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.

Copyright © 2002 by Thomson Learning, Inc. Figure 2A.4 Cost Minimization and Productive Efficiency Capital Labor F = F 1 per Year 0 K L E

Copyright © 2002 by Thomson Learning, Inc. 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

Copyright © 2002 by Thomson Learning, Inc. Pure Market Economy and Pareto Efficiency Step 1 So far we know that P F = MC F and P C = MC C from perfect competition dividing one by the other we get P C MC C P F MC F =

Copyright © 2002 by Thomson Learning, Inc. 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.

Copyright © 2002 by Thomson Learning, Inc. Pure Market Economy and Pareto Efficiency Step 3 Dividing these by each other we get : MC C  F MC F  C =

Copyright © 2002 by Thomson Learning, Inc. 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 =

Copyright © 2002 by Thomson Learning, Inc. Figure 2A.5 Consumer Choice E UA3UA3 UA2UA2 UA1UA1 Food per Year Clothing per Year 0 FAFA A BCACA

Copyright © 2002 by Thomson Learning, Inc. 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

Copyright © 2002 by Thomson Learning, Inc. Pure Market Economy and Pareto Efficiency Final MRS CF = MRS CF = MRT CF = PCPC PFPF AB

Copyright © 2002 by Thomson Learning, Inc. Market Imperfections  Monopoly P > MC  Others are affected so MB = MSB or MC = MSC