Question 2 Consider a two-period economy where consumers have the following lifetime utility: U = Ing + #Inc2 (3) Where c and c, are consumption in the first and second period respectively and # is the discount factor. They receive exogenous income Yi, profits *1 and pay lump sum taxes 7, in the first period and Y2, #2 and 72 respectively in the second period. They buy or sell any amount of bonds at the same interest rate r. (i) Derive the expressions for the optimal level of consumption ci and cz, and savings s. Illustrate the solution with a graph. (10 marks) Answer: (ii) Assume that there are two consumers in this economy, Maria and Paul. They receive the same lifetime income with Y1 = 70, Yz = 100, earn the same profits #1 = 20, #2 = 20 and pay the same lump-sum taxes 71 = 10, 72 = 10. Maria is patient and trustworthy and has 3 = 0.8 and can lend and borrow at an interest rate ~ = 10%. On the other hand Paul is inpatient and untrustworthy and has # = 0.7565 and can borrow and lend at an interest rate r = 15%. Find Maria's and Paul's consumption ci, c2, and savings s assuming that can buy and sell bonds freely. Illustrate the solution with a graph and explain. (15 marks) Total: 25 marks