Advanced MicroEconomics

AEB 6106: Problem Set 2

Due Sept. 12 at the start of class (9:35AM)

Instructions:

1. Please use your UF ID as the only identifying information on your problem set. Please do not include your name.

2. Please write your answers on separate paper, instead of squeezing answers into the margins of this paper.

For the following utility functions in questions 1 - 4, maximize utility subject to a budget constraint

to derive demand functions for goods x and y.

1)

𝑈 = 𝑥 4 5𝑦

1 5

2)

𝑈 = 3𝑥 + 10𝑦 3)

𝑈 = min{5𝑥, 6𝑦} 4)

𝑈 = 4𝑥 1 4 + 3𝑦

For all four utility functions in questions 5 - 8, maximize utility subject to a budget constraint

when:

𝑃𝑥 = 2, 𝑃𝑦 = 1,𝐼 = 12

5)

𝑈 = 𝑥 1 5𝑦

4 5

6)

𝑈 = 2𝑥 + 3𝑦 7)

𝑈 = min{2𝑥, 7𝑦} 8)

𝑈 = 2𝑥 1 2 + 2𝑦

For questions 9 through 12, derive the indirect utility functions for each utility function using your

answers to questions 1 through 4.

9)

𝑈 = 𝑥 4 5𝑦

1 5

10)

𝑈 = 3𝑥 + 10𝑦 11)

𝑈 = min{5𝑥, 6𝑦} 12)

𝑈 = 4𝑥 1 4 + 3𝑦