Problem 1, part | (Problem 6.2, CFH) Consider the following version of the model of this chapter. The number of young people born on island 3' in period if, NE, is random according to the following specification: i . . . NE : {i'N with probability 0.5 EN With probability 0.5 Assume that the fiat money stock grows at the fixed rate 22; = z in all periods. (a) Set up the budget constraints that a person faces when young and when old in terms of 5:. Also set up the government budget constraint and money-market clearing condition. Find the lifetime budget constraint. (b) On which island is the rate of return to labor larger? (c) Show how the rate of return to labor and the person's labor supply depend on the value of 2