. (6 marks) Consider the following version of the Lucas model. The number of young individualsbornonisland i inperiod t; Ni t israndomaccordingtothefollowingspecication:

6. (6 marks) Consider the following version of the Lucas model. The number of young individuals born on island i in period t, M is random according to the following specification: = with probability 0.5 = ;N with probability 0.5. Assume that the money supply grows at the constant rate at = = in all periods. Also assume that increases in the fiat money stock are effected through lump-sum subsidies to each old person in every period : worth at = [1 - (1/#)](v.M:/N) units of the consumption good. (a) Set up the budget constraints of the individuals when young and when old. Also set up the government budget constraint and money market clearing condition. Find the lifetime budget constraint (combine the budget constraints of the young and old). (1 mark) (b) Show how the rate of return to labor and the individual's labor supply depend on the value of 2. (1 mark) For the following parts, assume that the growth rate of money supply & is random according to 1 with probability # 2 with probability 1 - 8. The realization of a is kept secret from the young until all purchases of goods have occurred (i.e., individuals do not learn Me until period t is over). Given these changes in assumption, answer the following questions: (c) How many states of the world would individuals be able to observe if information about every variable were perfectly available? Describe those possible states. (1 mark) (d) How many states of the world are the individuals able to distinguish when there is limited information (i.e., they do not know the value of at)? (1 mark) e) Draw a graph of labor supply and the growth rate of money supply in each possible state of the world when there is limited information. What is the correlation observed between money creation and output? (1 mark f) Suppose the government wanted to take advantage of the relation between money creation and output. If it always inflate (0 = 0), will the graph you derived in part (e) remain the same. Explain your answer. (1 mark