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 2 EN with probability 0.5. Assume that the money supply grows at the constant rate st : :3 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 (1/:t)](vtMt/N) units of the consumption good. For the following parts. assume that the growth rate of money supply st is random according to St = 1 with probability 6 : 2 with probability 1 9. The realization of st is kept secret from the young until all purchases of goods have occurred (i.e., individuals do not learn Mt 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. (2 marks) (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 st)? (2 marks) (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. 1What 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 inates (6 = 0), will the graph you derived in part (e) remain the same. Explain your answer. (1 mark)