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CHAPTER 3 PREFERENCES AND UTILITY These problems provide some practice in examining utility functions by looking at indifference curve maps and at a few functional forms. The primary focus is on illustrating the notion of quasi-concavity (a diminishing MRS) in various contexts. The concepts of the budget constraint and utility maximization are not used until the next chapter. Comments on Problems 3.1 This problem offers some practice in deriving utility functions from indifference curve specifications. 3.2 This problem focuses on whether some simple utility functions exhibit convex indifference curves. 3.3 This problem shows how utility functions can be inferred from MRS segments. It is a very simple example of “integrability”. 3.4 This problem shows that diminishing marginal utility is not required to obtain a diminishing MRS . All of the functions are monotonic transformations of one another, so this problem illustrates that diminishing MRS is preserved by monotonic transformations, but diminishing marginal utility is not. 3.5 In this problem students are asked to provide a formal, utility-based explanation for a variety of advertising slogans. The purpose is to get students to think mathematically about everyday expressions. 3.6 Introduces the formal definition of quasi-concavity (from Chapter 2) to be applied to the functions studied graphically in Problem 3.8. 3.7 This problem is an exploration of the fixed-proportions utility function. The problem also shows how the goods in such problems can be treated as a composite commodity. 3.8 This problem requires students to graph indifference curves for a variety of functions, some of which are not quasi-concave. Analytical Problems 3.9 Independent marginal utilities. Shows how analysis can be simplified if the cross partials of the utility function are zero. 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. 9
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10 Chapter 3: Preferences and Utility 3.10 Utility functions and preferences. The problem asks students to think about how a common phenomenon might be reflected in a mathematical functional form. 3.11 Cobb-Douglas utility. Provides some exercises with the Cobb-Douglas function including how to integrate subsistence levels of consumption into the functional form.
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