Money, Banking and Financial Markets Semester 1, 2020 End-of-Semester Written Report Part A (20 marks) Typed answers are preferred. Neat hand writing is acceptable. Consider the following version of the Lucas model. The number of young individuals born on island iin period t, , is random according to the following specification: = (1/4)N with probability 0.5, = (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 fiat money stock grows at the fixed rate in all periods. a. Set up the budget constraints of an individual when young and when old in terms of (where 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. d. Show how the rate of return to labour and the individual's labour supply depend on the value of .