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Unformatted text preview: 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 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. 4.2 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). 4.3 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. 4.4 This problem shows that with concave indifference curves first order conditions do not ensure a local maximum. 4.5 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 . 4.6 This problem introduces a third good for which optimal consumption is zero until income reaches a certain level. 4.7 This problem provides more practice with the Cobb-Douglas function by asking students to compute the indirect utility function and expenditure function in this case. The manipulations here are often quite difficult for students, primarily because they do not keep an eye on what the final goal is....
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- Spring '09