Please answer part 2,3,4

ECON 303 Question 1 Consumers live for two poriods and hnve the following lifetime utility: U = Ing+Bino (1) Where cand o are consumption in the first and second period respectively anul 3 is the discount factor. Everyone has full-time contracts and cannot change their hours of work. They receive exogenous income Yi, profits ? and pay lump tim taxes T, in the first period and Y. and Trespectively in the second period. Consumers can buy or sell any amount of bonds at the same interest rater. (1) Derive the expressions for the optimal level of consumption and on and savings in terms of the exogenous variables Y, Y., 27.7 Sandr. Slow the optimal allocation in a graph. (10 mardos) (1) Assume that there are two consumers in this economy, Ina and Paul They live the same stream of exogotions income Y; -90, Y; -78. carn the same profits = 20.12 =20, pay the same dump-sum taxes T-10, T: - 10 and face the same market interest rater - 10% However, they have a single difference as Ina is more patient than Paul Inau 3-0.8 and Paullus a 3-04 Find Ina's and Paul consumption G., and savings # assuming that consumers cannot sell bonds (1.c. cannot borrow) but can buy bonds (1.6. can save) caining interest rate r = 10%. Explain why or why not they choose the same consumption and savings, and draw the corte spomuling graph (10 marks) Cil) Assume that the government wants to give a tax break of 5 units in the first period without clunging the overall government spending. Given that the government needs to balance the lifetime budget over the two periods, find the new Ti and T. (5 marlo) (iv) Find the optimal cotistimption and savings for both consumers taking into account the new taxes. Discuss the results and draw the corresponding graphs. (15 mark) Total: 40 marks 2