Consider the following version of the Lucas model. The number of young individuals born on island i'in period 1', Ni, is random according to the following specication: i: (1/4)N with probability 0.5, N= (3/4)N with probability 0.5, where N denotes the total number (i.e. across the two islands) of young people born in every period. Assume that the at money stock M, grows at the xed rate 2 in all periods. a. Set up the budget constraints of an individual when young and when old in terms of ti (where 3: denotes an individual's labour supply). Find the lifetime budget constraint of an individual. b. Set up the money market-clearing condition. c. On which island would you prefer to be born? Explain with reference to the rate of return to labour. cl. Show how the rate of return to labour and the individual's labour supply depend on the value of 2. For the remaining questions, assume now that the growth rate of the fiat money stock 2: is random according to: z, = 1 with probability 9, where 0 s 9 s 1; I: = 3with probability 1-6. The realization of 2,. is kept secret from the young until all purchases of goods have occurred (i.e. individuals do not learn M" until period tis over). Given these changes in assumption, answer the following questions: e. How many states of the world would agents be able to observe if information about every variable were perfectly available? Describe those possible states