Chapter4: Utility Maximization And Choice
Section: Chapter Questions
Problem 4.3P
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![we consider an agent Ann who consumes goods x and y and has a utility
U(x, y) = r²y. In these problems, Good r costs P and good y costs Py.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1b2e65f2-c472-45bf-885c-00dffce84016%2F8875882b-a8d9-48a7-bf1b-f1c59e44660b%2Fsksslje_processed.png&w=3840&q=75)
Transcribed Image Text:we consider an agent Ann who consumes goods x and y and has a utility
U(x, y) = r²y. In these problems, Good r costs P and good y costs Py.
![(2)
(a) Write out Ann's expenditure minimization problem for U(x, y) > Ū.
(b) Write out the tangency condition for expenditure minimization. (You do not need to show your
work.) How does it compare to the tangency condition in Part (1c) above. Explain (50 words or
fewer.)
(c) Now set, P₂ = 4 and Py = 2. Use the tangency condition and U(x, y) = Ū to solve for Ann's
compensated demands as a function of U. (Normally, compensated demands are functions of Ū, PE,
and Py. Here we have explicit values for the prices, and compensated demands will be a function
of only Ū. It is worth noting that if a = 6³, then b = a)
(d) Use your answer to Part c to write out Ann's expenditure function.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1b2e65f2-c472-45bf-885c-00dffce84016%2F8875882b-a8d9-48a7-bf1b-f1c59e44660b%2Fx4q9jqk_processed.png&w=3840&q=75)
Transcribed Image Text:(2)
(a) Write out Ann's expenditure minimization problem for U(x, y) > Ū.
(b) Write out the tangency condition for expenditure minimization. (You do not need to show your
work.) How does it compare to the tangency condition in Part (1c) above. Explain (50 words or
fewer.)
(c) Now set, P₂ = 4 and Py = 2. Use the tangency condition and U(x, y) = Ū to solve for Ann's
compensated demands as a function of U. (Normally, compensated demands are functions of Ū, PE,
and Py. Here we have explicit values for the prices, and compensated demands will be a function
of only Ū. It is worth noting that if a = 6³, then b = a)
(d) Use your answer to Part c to write out Ann's expenditure function.
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