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CHAPTER 4 UTILITY MAXIMIZATION AND CHOICE The problems in this chapter focus mainly on the utility maximization assumption. Relatively simple computational problems (mainly based on Cobb-Douglas and CES utility functions) are included. Comparative statics exercises are included in a few problems, but for the most part, introduction of this material is delayed until Chapters 5 and 6. Comments on Problems 4.1 This is an example of a "fixed proportion" utility function. The problem might be used to illustrate the notion of perfect complements and the absence of relative price effects for them. Students may need some help with the min ( ) functional notation by using illustrative numerical values for v and g and showing what it means to have "excess" v or g . 4.2 This problem introduces a third good to the Cobb-Douglas case for which optimal consumption is zero until income reaches a certain level. 4.3 This problem shows that with concave indifference curves first order conditions do not ensure a local maximum. 4.4 Asks students to construct the expenditure function for a linear utility function. Notice that this problem cannot be solved with calculus – rather students must work through the various possibilities logically. 4.5 This starts as an unconstrained maximization problem -- there is no income constraint in part (a) on the assumption that this constraint is not limiting. In part (b) there is a total quantity constraint. Students should be asked to interpret what Lagrangian Multiplier means in this case. 4.6 This problem shows how various considerations can be grafted onto a simple utility-maximization problem. 4.7 This uses the Cobb-Douglas utility function to solve for quantity demanded at two different prices. Instructors may wish to introduce the expenditure shares interpretation of the function's exponents (these are covered extensively in the Extensions to Chapter 4 and in a variety of numerical examples in Chapter 5). 4.8 This problem repeats the lessons of the lump sum principle for the case of a subsidy. Numerical examples are based on the Cobb-Douglas expenditure function. 4.9 This is a simple Cobb-Douglas example. Part (b) asks students to compute income compensation for a price rise and may prove difficult for them. As a hint they might be told to find the correct bundle on the original indifference curve first, then compute its cost. This edition is intended for use outside of the U.S. only, with content that may be different from the U.S. Edition. This may not be resold, copied, or distributed without the prior consent of the publisher. 16
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17 Chapter 4: Utility Maximization and Choice Analytical Problems 4.10 Stone-Geary utility: Introduces a simple two-good Stone-Geary function in which a certain amount must be devoted to x consumption before any y consumption occurs. More detail on this functional form is provided in the Extensions to the chapter.
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This note was uploaded on 06/09/2010 for the course AP 4010 taught by Professor Anam,mahmudul during the Fall '10 term at York University.

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