Assume that the preferences of a consumer can be expressed by the utility function utw,4 2 x* + x, (i) Show that based on this utility function, the demand functions are for the benefits provided by 81 p x = 81 p P m and x; : P2 der i p is the price per unit i x, 2 p is the price per unit 2 x and m are the income of the consumer. (ii) Explain what is meant by the cross-price elasticity of a good. Calculate the cross-price elasticity of the gook igiven in question (i), and give an interpretation of the result.

Microeconomic Theory
12th Edition
ISBN:9781337517942
Author:NICHOLSON
Publisher:NICHOLSON
Chapter4: Utility Maximization And Choice
Section: Chapter Questions
Problem 4.11P
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Assume that the preferences of a consumer can be expressed by the utility function
0.75
utx), 4
+ x
(i) Show that based on this utility function, the demand functions are for
the benefits provided by
81 p
x =
4
3
81 р;
т
and x
P2
P
der 1 p is the price per unit 1 x, 2 p is the price per unit 2 x and m are the income of
the consumer.
(ii) Explain what is meant by the cross-price elasticity of a good. Calculate
the cross-price elasticity of the goodigiven in question (i), and give an interpretation of
the result.
Transcribed Image Text:Assume that the preferences of a consumer can be expressed by the utility function 0.75 utx), 4 + x (i) Show that based on this utility function, the demand functions are for the benefits provided by 81 p x = 4 3 81 р; т and x P2 P der 1 p is the price per unit 1 x, 2 p is the price per unit 2 x and m are the income of the consumer. (ii) Explain what is meant by the cross-price elasticity of a good. Calculate the cross-price elasticity of the goodigiven in question (i), and give an interpretation of the result.
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