Consider an overlapping generations model as discussed in Chapter 8. In which people live for 3 periods. People receive endowment y onlywhen they are young and zero endowments during other times. The population growth rate is nail. People can hold physical capital which yields return after two periods: each unit of capital generates Xunits of consumption goods after two periods and then capital disintegrates. Note it is impossible for an individual to observe the capital created by others. Assume no lending borrowing opportunities among individuals. a. Write down the budget constraints of an individual born in time t. when he is young. middle age and old. Explain each of your equations with clear notation. [6 marks}. b. Derive the one period and two period returns on fiat money. i2marks}. c. Derive the one period and two period returns on physical capital. (2 marks) d. What condition do you need to impose on return on physical capital [generated after 2 periods) and return on fiat money so that people will choose to hold capital when they are young? (2 marks}. e. Based on your answer for parts b and c, do you think physical capital and fiat money are perfect substitutes in this model? Explain your answer by identifying if capital is illiquid on the model. {2 marks). f. Explain the role of a possible financial intermediary in this model. {1mark}