Qualitative Questions Let a consumer’s choice of games be between “Nintendo” (N) and “PlayStation” (P ), and the quantities she chooses are qN and qP respectively. The price of the two goods are pN and pP respectively. The consumer has an income of w. Answer the following questions. (a) Let the consumer’s utility be of the Cobb-Douglas variety, that is U = xa x1−a, where 0 <= a <= 1. Depict on a well labeled diagram the consumer’s choice, and explain the equilibrium choice, making sure you write down the equation that describes it. (b) Depict on a new well labeled diagram the effect of a price decrease in “PlaySta- tion” games, assuming that “PlayStation” games are Normal goods, making sure you decompose the change into its components, in other words its (i) substitution, and (ii) income effects. Explain your diagram carefully. (c) Explain how such a Cobb-Douglas utility function and their associated in- difference curves depicts this consumer as Risk Averse. (d) How would your answer to part (b) change, if instead the consumer’s prefer- ences is characterized by a Leontieff utility function. In other words, N and P are perfect complements to the consumer. Depict your answer on a well labeled diagram.

Economics (MindTap Course List)

13th Edition

ISBN:9781337617383

Author:Roger A. Arnold

Publisher:Roger A. Arnold

Chapter20: Consumer Choice: Maximizing Utility And Behavioral Economics

Section: Chapter Questions

Problem 5WNG

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Qualitative Questions

Let a consumer’s choice of games be between “Nintendo” (N) and “PlayStation” (P ), and the quantities she chooses are qN and qP respectively. The price of the two goods are pN and pP respectively. The consumer has an income of w. Answer the following questions.

(a) Let the consumer’s utility be of the Cobb-Douglas variety, that is U = xa x1−a, where 0 <= a <= 1. Depict on a well labeled diagram the consumer’s

choice, and explain the equilibrium choice, making sure you write down the equation that describes it.

(b) Depict on a new well labeled diagram the effect of a price decrease in “PlaySta- tion” games, assuming that “PlayStation” games are Normal goods, making sure you decompose the change into its components, in other words its (i) substitution, and (ii) income effects. Explain your diagram carefully.

(c) Explain how such a Cobb-Douglas utility function and their associated in- difference curves depicts this consumer as Risk Averse.

(d) How would your answer to part (b) change, if instead the consumer’s prefer- ences is characterized by a Leontieff utility function. In other words, N and P are perfect complements to the consumer. Depict your answer on a well labeled diagram.

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