Intermediate Micro

Intermediate Micro Homework Assignment 5 Due Monday, July 28 This homework will require a calculator. I find Google’s calculator pretty handy for typing in long calculations like this. Excel is a popular option as well. 1.) Stu is about to start college. His parents have offered to pay his housing costs. The interest rate is . Plan A: Stu has found an apartment with $6000/year of rent, which he will rent for (let’s be honest here) 5 years. This means the last $6,000 is paid 4 years from now. a. What is the present value to the parents of Plan A? (Your answer should be a negative number). Plan B: Stu’s parents could buy a house, and rent some of the rooms out to other students to help cover the cost of Stu’s rent. The house costs $400,000. They could make $18,000 in rent every year, and sell it after 5 years for some price $P. This means the last rent income is 4 years from now, but the sale of the house is 5 years from now. b. What is the present value to the parents of Plan B? c. For what values of P will Stu’s parents have a positive PV from Plan B? d. For what values of P will Stu’s parents prefer Plan B to Plan A?

2.) Lucky makes $110,000 per year at his job. He has also just won $1,000,000 in the lottery. The interest rate is . a. What is the PV of Lucky’s income this year and next year? b. Lucky wants to consume all of his income over this year and next year. Write down Lucky’s budget equation for . c. His utility for consumption is . What will Lucky consume? d. Is Lucky saving or borrowing this year? How much? e. What percentage of his lottery winnings is Lucky saving/borrowing? f. Now suppose Lucky decides to give all of his income to Lucille. Lucille also plans to spend all the income within two years. What is Lucille’s budget constraint? g. Lucille wants to spend all her money at the same time, and to consume as much as possible. In other words, her utility is . She can not consume negative amounts in either period. What will Lucille consume?

3.) A consumer has utility function , and income 40 to spend on x and y. Good x has price p, and good y has price 1. a. Find the demand functions for good x and good y. b. Graph the demand curve for good x. For the rest of the question, consider a price change from p=1 to p’=3. c. Find demand for x and y, at both prices. d. Indicate on your graph the change in consumer surplus from this price change. Is the consumer better off or worse off? e. Find the equivalent variation. f. Find the compensating variation.