1. Mansour consumes only peanut butter (X) and jelly (Y) and has the following utility function: U = u( x, y) = 100*x0.75-y0.25 Let his income be 120. Hint: His Marginal Rate of Substitution is given by MRS = -(0.75 * Y/0.25 * X ). He faces prices of px = $8 and py $4 and consumes 10 units of each good. %3D A. Show clearly how Mansour's utility function meets all of the criteria required for preferences. B. Write an alternative utility function that would represent the same preferences for Mansour. C. Is Mansour maximizing his utility? Why or why not? D. What is his utility-maximizing bundle? E. How does your answer change if the price of peanut butter falls to $6? Is Mansour better off than before? How much better? F. Show the analysis graphically.
1. Mansour consumes only peanut butter (X) and jelly (Y) and has the following utility function: U = u( x, y) = 100*x0.75-y0.25 Let his income be 120. Hint: His Marginal Rate of Substitution is given by MRS = -(0.75 * Y/0.25 * X ). He faces prices of px = $8 and py $4 and consumes 10 units of each good. %3D A. Show clearly how Mansour's utility function meets all of the criteria required for preferences. B. Write an alternative utility function that would represent the same preferences for Mansour. C. Is Mansour maximizing his utility? Why or why not? D. What is his utility-maximizing bundle? E. How does your answer change if the price of peanut butter falls to $6? Is Mansour better off than before? How much better? F. Show the analysis graphically.
Economics: Private and Public Choice (MindTap Course List)
16th Edition
ISBN:9781305506725
Author:James D. Gwartney, Richard L. Stroup, Russell S. Sobel, David A. Macpherson
Publisher:James D. Gwartney, Richard L. Stroup, Russell S. Sobel, David A. Macpherson
Chapter20: Consumer Choice And Elasticity
Section: Chapter Questions
Problem 4CQ
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Transcribed Image Text:1. Mansour consumes only peanut butter (X) and jelly (Y) and has the following utility
function:
U = u( x, y) = 100*xº.75»y0.25
Let his income be 120. Hint: His Marginal Rate of Substitution is given by
MRS = -(0.75 * Y/0.25 * X).
He faces prices of pPx = $8 and py = $4 and consumes 10 units of each good.
A. Show clearly how Mansour's utility function meets all of the criteria required for
preferences.
B. Write an alternative utility function that would represent the same preferences for
Mansour.
C. Is Mansour maximizing his utility? Why or why not?
D. What is his utility-maximizing bundle?
E. How does your answer change if the price of peanut butter falls to $6? Is Mansour
better off than before? How much better?
F. Show the analysis graphically.
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