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Unformatted text preview: Department of Economics W3211 Columbia University Fall 2011 SO LUTIO NS T O Probl e m S e t 1 Int e rm e diat e Mi c ro ec onomi c s Prof . S e yhan E Arkona c S ec tion 3 1. Suppose a consumer’s utili ty derived from consuming bananas is described by the function U 10 X 3 X 2 (1/3) X 3 . Compute marginal utility. a. Make a table showing total and marginal utility for X from 0 to 7 units. b. Would this individual ever choose to consume more than 7 units? Explain. Solution: MU 10 6 X – X 2 a. Units of X 1 2 3 4 5 6 7 MU (10) 15 18 19 18 15 10 3 b. No. Marginal utility of the 8th unit would be negative. 2. For each of the utility functions below, draw a set of indifference curves showing utility levels U 12, U 16, and U 24. Find MRS for each. a. U XY b. U X Y c. U X Y d. U ln X ln Y e. U min{2 X, Y } f. What is true about the commodities in (b)? g. What is true about commodities in (e)? h. What about the commodities in (c)? i. What can you say about the utility function in (a) and (d)? Solution: a. Figure 1 MRS=Y/X 2. For each of the utility functions below, draw a set of indifference curves showing utility levels U 12, U 16, and U 24. Find MRS for each. a. U XY b. U X Y c. U X Y d. U ln X ln Y e. U min{2 X, Y } f. What is true about the commodities in (b)? g. What is true about commodities in (e)? h. What about the commodities in (c)? i. What can you say about the utility function in (a) and (d)?...
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This note was uploaded on 10/25/2011 for the course ECON W3211 taught by Professor Elmes during the Fall '09 term at Columbia.
 Fall '09
 Elmes
 Microeconomics, Utility

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