Ned's preferences for apples (qa) and bananas (qb) are captured by the utility function U(qa,qb)= k(qa)^1/5(qb)^4/5 , where k>0 is a parameter. The price of an apple is pa, the price of a banana is pb, and Ned's income is Y.Derive the marginal utilities of applies and bananas. Show that, for qa>0 and qb>0, Ned's preferences satisfy "more is better." State the consumer's problem of Ned. Explain why the budget constraint in the problem, (pa)(qa) + (pb)(qb) less than or equal to Y can be replaced by the budget line : (pa)(qa) + (pb)(qb) = YDerive Ned's demand functions for apples and bananasBased on the demand function for apples you derive in 3, show that apples are necessities, and sketch the Engel curve of applesSuppose k=5 for Ned. There is another consumer, Thalia, who shares the same utility function as Ernie except that for her k=10 . If we interpret utility as "satisfaction" from consumption, this suggests that, for a given consumption bundle, Thalia obtains twice the level of satisfaction as Ned. Does this imply that, for given prices and income, Thalia demands twice the amounts of apples and bananas as Ned? In light of your answer, discuss what should be the right interpretation of utility.

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Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter3: Preferences And Utility

Section: Chapter Questions

Problem 3.2P

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Ned's preferences for apples (qa) and bananas (qb) are captured by the utility function U(qa,qb)= k(qa)^1/5(qb)^4/5 , where k>0 is a parameter. The price of an apple is pa, the price of a banana is pb, and Ned's income is Y.

Derive the marginal utilities of applies and bananas. Show that, for qa>0 and qb>0, Ned's preferences satisfy "more is better."
State the consumer's problem of Ned. Explain why the budget constraint in the problem, (pa)(qa) + (pb)(qb) less than or equal to Y can be replaced by the budget line : (pa)(qa) + (pb)(qb) = Y
Derive Ned's demand functions for apples and bananas
Based on the demand function for apples you derive in 3, show that apples are necessities, and sketch the Engel curve of apples
Suppose k=5 for Ned. There is another consumer, Thalia, who shares the same utility function as Ernie except that for her k=10 . If we interpret utility as "satisfaction" from consumption, this suggests that, for a given consumption bundle, Thalia obtains twice the level of satisfaction as Ned. Does this imply that, for given prices and income, Thalia demands twice the amounts of apples and bananas as Ned? In light of your answer, discuss what should be the right interpretation of utility.

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