2) Suppose a consumer has the budget constraint y = p1x1 + P2¤2, where y is income, x1 and x2 are the demands for goods 1 and 2, respectively, and p1 and p2 are their respective prices. Below are the marginal utility of goods 1 and 2 under different preferences. x2 U(x1, x2) = 2/¤102, MUE MU2 (1) X2 2/3 1/3 (2), ()". U(x1, x2) = 3x;^x, MU1 MU2 = 2 x2 (2) a) Using the information above, define what the Marginal rate of substitution is (Not the definition but the technical form) b) In order to solve for your demand functions using a) you need to equate the the marginal rate of substitution to something. What is that? Show it formally and then solve for your demand functions. c) Given your answers to b), for each case plot the income offer curve, Engel curve, price offer curve and demand curve (for both pi and p2) for x2 making sure to label the graph in each case correctly ( If you look at the utility func- tions in 1 and 2 they are actually very similar except for a small difference. What does that difference imply about how these consumers would like to

2) Suppose a consumer has the budget constraint y = p1x1 + P2¤2, where y is income, x1 and x2 are the demands for goods 1 and 2, respectively, and p1 and p2 are their respective prices. Below are the marginal utility of goods 1 and 2 under different preferences. x2 U(x1, x2) = 2/¤102, MUE MU2 (1) X2 2/3 1/3 (2), ()". U(x1, x2) = 3x;^x, MU1 MU2 = 2 x2 (2) a) Using the information above, define what the Marginal rate of substitution is (Not the definition but the technical form) b) In order to solve for your demand functions using a) you need to equate the the marginal rate of substitution to something. What is that? Show it formally and then solve for your demand functions. c) Given your answers to b), for each case plot the income offer curve, Engel curve, price offer curve and demand curve (for both pi and p2) for x2 making sure to label the graph in each case correctly ( If you look at the utility func- tions in 1 and 2 they are actually very similar except for a small difference. What does that difference imply about how these consumers would like to

Exploring Economics

8th Edition

ISBN:9781544336329

Author:Robert L. Sexton

Publisher:Robert L. Sexton

Chapter10: Consumer Choice Theory

Section: Chapter Questions

Problem 8P

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Given a consumer has a money budget M = 90 and utility function ? ( ? , ?) = ? 1/4? 1 / 2 If she consumes two goods x and y with prices given by ? = 2 and ? = 4 state the ? ? budget constraint equation. Determine the utility maximizing quantities X and Y for the consumer
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