Answer the following

6. (8 marks) Consider the following version of the Lucas model. The number of young individuals born on island 3' in period t, N; is random according to the following specication: NE 2 EN with probability 0.5 1 : EN with probability 0.5. Assume that the money supply grows at the constant rate 3: = z in all periods. Also assume that increases in the at money stock are implemented through lumpsum subsidies to each old person in every period t worth at = [1 (l/zt (vtMt/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 z. (1 mark)