Exercise 1 A consumer's utility function is u(x, y) = x²y³ and the budget constraint is pax +Pyy ≤ w, where the parameters pa, py and w are all strictly positive. (a) Solve the consumer's utility maximization problem. (b) Use the envelope theorem to estimate the change in the indirect utility function (i.e., the problem's value function) when the price py is changed to py + €, with € > 0.

ENGR.ECONOMIC ANALYSIS
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ISBN:9780190931919
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Chapter1: Making Economics Decisions
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Exercise 1
A consumer's utility function is u(x, y)
=
x²y³ and the budget constraint is prx +Pyy ≤ w,
where the parameters pr, Py and we are all strictly positive.
(a) Solve the consumer's utility maximization problem.
(b) Use the envelope theorem to estimate the change in the indirect utility function (i.e.,
the problem's value function) when the price py is changed to py + e, with e > 0.
Transcribed Image Text:Exercise 1 A consumer's utility function is u(x, y) = x²y³ and the budget constraint is prx +Pyy ≤ w, where the parameters pr, Py and we are all strictly positive. (a) Solve the consumer's utility maximization problem. (b) Use the envelope theorem to estimate the change in the indirect utility function (i.e., the problem's value function) when the price py is changed to py + e, with e > 0.
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