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Ch 3 Practice - University of Toronto Department of...

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University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. 1 ECO 204 Chapter 3: Practice Problems & Solutions for Utility Maximization in ECO 204 (this version 2012-2013) Department of Economics (STG), ECO 204, Sayed Ajaz Hussain _________________________________________________________________________________________________ P RACTICE P ROBLEMS W ITH S OLUTIONS TO : C HAPTER 3 : Utility Maximization Methods in ECO 204 1 Updated: 10/26/2012 (3.1) Write down the Lagrangian objective function the first order conditions (any) Kuhn-Tucker conditions and indicate the possible “signs” of the Lagrange multipliers (i.e. positive, zero, negative) for the following revenue maximization problem (do NOT solve the problem): ( ) (3.2) Write down the Lagrangian objective function the first order conditions (any) Kuhn-Tucker conditions and indicate the possible “signs” of the Lagrange multipliers (i.e. positive, zero, negative) for the following revenue maximization problem (do NOT solve the problem): ( ) (3.3) Show if the following utility functions, defined over {( ) } , have identical indifference curves: (a) ( ) and ? Show all calculations. (b) ( ) and ? Show all calculations. (3.4) Graph an indifference curve for an arbitrary level of utility ● give expressions for the indifference curve equation, intercepts and slope and state (but do not solve) as simplified as possible UMP. Show all calculations. (a) . [ Hint: Do a positive monotonic transformation ] (b) (3.5) A consumer has the following utility function defined over {( ) } : Suppose and that and For feedback, comments and typos please e-mail [email protected]
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University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. 2 ECO 204 Chapter 3: Practice Problems & Solutions for Utility Maximization in ECO 204 (this version 2012-2013) (a) Without solving the UMP, what i s impact on the consumer’s utility due to a 1% excise tax on good 1? Show all calculations. (b) Without solving the UMP, what is impact on the consumer’s utility due to a 1% excise tax on good 2? Show all calculations. (3.6) A consumer’s preferences are representable by the following utility function over goods 1 and 2 (defined over the consumption set { } ): √( ) Does this consumer have rational preferences? Explain. (3.7) The following utility functions are given to model automobile consumers’ preferences over cubic feet of interior space (good 1) and horsepower (good 2). Which of the utility is/are not suitable? Give explanations, using graphs if necessary. In all cases, the utility function is defined over the consumption set { } . (a) where (b) ( ) where ( ) is any function of such that ( ) (c) where and Show all calculations and state all assumptions. (3.8) Consider the following utility function defined over the consumption set { } : (a) Does this consumer have monotone preferences over every bundle in the consumption set? If not, are there any bundles in the consumption set where she does have monotone preferences? Show all calculations and state all assumptions.
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