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Consider the following version of the Lucas model. The number of young individuals born on island i'in period t, N: , is random according to the following specication: Ni: (1!4)N with probability 0.5 Ni: (3l4)N with probability 0.5 Assume that the at money stock grows at the xed rate 2t = z in all periods. a. Set up the budget constraints of the individuals when young and when old in toms of I. 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 by substituting for ID. b. On which island would you prefer to be born? Explain with reference to the rate of return to labor. 0. Show how the rate of tetum to labor and the individual's labor supply depend on the value of 2. For the following parts, assume that the growth rate of the at money stock zt is random according to: zt = 1 with probability 9 z, = 3 with probability 19 The realization of zt is kept secret from the young until all puchases of goods have occured (i.e. individuals do not learn M, until period t is over). Given these changes in assumption, answer the following questions: d. How many states of the world would agents be able to observe if information about every variable were perfectly available? Describe those possible states. e. How many states of the world are the agents able to distinguish when there is limited information (i.e. they do not know the value of at )