Problem Set 2
Eco5, Instructor: Marco Del Negro

1) Assume that in 1998 the price of 1 ounce of gold in Mexico is 10 Pesos and the price of an haircut is 1 Peso. Assume the exchange rate is 1 US Dollar for 10 Pesos. Assume that in the US the relative price of an haircut with respect to gold is 5 (with one ounce of gold you buy 5 haircuts). Use the model discussed in class with $\gamma=.3$ to answer the following questions: (remeber: gold is a tradable good!)
a) let us say you give 100 Pesos to a Mexican, and 10 10 US Dollar to a US citizen: who is happier?
b) let us say that in 1999 the exchange rate drops to 1 US Dollar for 20 Pesos. The price of gold in the US is unchanged, and so are relative prices in both countries. b1) Calculate inflation in Mexico. b2) if you give 200 Pesos to a Mexican, and 10 US Dollar to a US citizen, who is happier in 1999?
2) A consumer has initial real wealth of 20, current real income of 90, and future real income of 110. The real interest rate r is .1 (10 percent) per period.
a) what is the present value of the consumer's resources?
b) write the equation for the counsumer's budget constraint (using the numerical values) ad graph the budget line.
Use the model taught in class to answer the following questions (assume that $\beta =1$) :
c) how much will he save and consume in the current period?
d) how will current savings and consumption be affected by an increase of 11 in: d1) current income? d2) in future income? d3) initial wealth?
3) (Abel Bernanke question 1 pg.281) If you are a utility-maximizing consumer with no borrowing constraints, how would each of the following affect your current consumption and saving? a) You are informed that a long-lost relative has left you a large bequest. However, the bequest is to be kept in a trust, and you will not be able to withdraw any of the money for ten years. b) Your doctor tells you that you have an amazingly healthy constitution and that you shold easily live to age ninety. This prediction doesn't change your plan to retire at age sixty-five in order to perfect your fishing skills. c) You are a taxpayer, an you read in the paper tha your state government's deficit is much worse than thought. A tax increase next year now seems inevitable. d) You work in the auto industry and read in the newspaper that a serious recession and tough foreign competition are predicted to drive down car sales.