{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# PS1key - University of Minnesota Department of Economics...

This preview shows pages 1–2. Sign up to view the full content.

University of Minnesota Department of Economics Econ 3102: Intermediate Macroeconomics Problem Set 1 Answer Key 1 Problems (65 points) Exercise 1 (10 points) Consider the utility function U ( C, ‘ ) = γlogC + (1 - γ ) log‘ . (a) Derive the marginal utility of consumption. Is it decreasing in C? Answer: The marginal utility of consumption is: U C ( C, ‘ ) = γ C (b) Derive the marginal utility of leisure. Is it decreasing in leisure? Answer: The marginal utility of leisure is: U ( C, ‘ ) = 1 - γ (c) Does this utility function satisfy the Inada Conditions? Show your answer. Answer: Yes. Given the marginal utilities, it is straightforward to verify that U C (0 , ‘ ) = + U ( C, 0) = + , Exercise 2 (15 points) Consider a representative consumer whose preferences over consumption and leisure are given by the utility function U ( C, l ) = C 1 / 3 l 2 / 3 . Assume that she has a total of h = 18 hours which she can use for leisure or she can work for the wage rate w = 6. Finally, assume that she enjoys a dividend income π = 36 and has to pay taxes T = 24. Determine the optimal consumption bundle ( C * , ‘ * ). Answer: You can do this in a variety of ways; here I’ll use the MRS = w trick. Since the MRS equals the ratio of the marginal utilities, we get that MU /MU C = w ; given that the marginal utilities are just the partial derivatives of the utility function, we rearrange and get U ( C, ‘ ) - wU C ( C, ‘ ) = 0 or 2 3 C 1 / 3 - 1 / 3 = 6 1 3 C - 2 / 3 2 / 3 . (1.1) Multiply across by - 1 / 3 C - 2 / 3 to get C = 3 ‘. (1.2) Now plug (2) in the budget constraint: 3 = 6(18 - ) + 36 - 24 . (1.3) Working this out, we get * = 13 . 33 . Since C = 3 , we get C * = (3)(13 . 33) = 40 .

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 4

PS1key - University of Minnesota Department of Economics...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online