325_PracticePS1

325_PracticePS1 - Department of Economics University of...

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Department of Economics University of Maryland Economics 325 Intermediate Macroeconomic Analysis Practice Problem Set 1 Professor Sanjay Chugh Spring 2011 1. Partial Derivatives. For each of the following multi-variable functions, compute the partial derivatives with respect to both x and y . a. (, ) f xy x y b. ( ,) 2 3 x y ± c. 24 xy d. (, ) l n 2 l n x y ± e. (, ) 2 2 x y ± f. x fxy y g. y x 2. Properties of Indifference Maps. For the general model of utility functions and indifference maps developed in class, explain why no two indifference curves can ever cross each other. Your answer must explain the economic logic here, and may also include appropriate equations and/or graphs. 3. A Canonical Utility Function. Consider the utility function 1 1 () , 1 c uc V ² ² ² where c denotes consumption of some arbitrary good and (the Greek letter “sigma”) is known as the “curvature parameter” because its value governs how curved the utility function is. In the following, restrict your attention to the region 0 c ! (because “negative consumption” is an ill-defined concept). The parameter is treated as a constant.
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This document was uploaded on 11/01/2011 for the course ECON 325 at Maryland.

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325_PracticePS1 - Department of Economics University of...

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