Can someone please tell me the work out for does..?

Question 1 (7 Marks} Joan has a utility function given by MCI, Cg) = C? + 66'" , where Cl and Cg represent her consumption in the current period (i.e. Period 1) and future period (Le. Period 2), respectively. Her utility flnrction meets the four strict axioms of preferences (Com- pleteness, Transitivity, Strict Non-satiation, and Strict Convexity). Joan earns Y] in the current period and does not earn any income in the future period. Her savings earn an effective interest rate of r from the current period to future period, where r 2:- l}. (a) 1.5 Mark. Write down the range of value for 1.: so that Joan's utility function meets the strict axioms. Explain your answer. (1)) 2 Marks. Derive Joan 's Marginal Rate of lnterternporal Substitution and pure rate of time preference. (c) 2 Movies. Find Joan's optimal consumption bundle [Cf and CE). (d) 1.5 Marks. Explain the impact of 6, r and y on the optimal consumption in the current period. Question 2 {9 Marks} Tom retires at time ll. He has retirement savings of An and his savings grow at a constant rate of r per period. Tom has a multi-period utility function with a hyperbolic discount factor, which is U = 2:0 1n (0;), where 01 denotes his consumption at the beginning of period t. (a) 2 Marks. Derive an expression for Tom's budget constraint in terms of r, AU, and Cg for [i :1 t 5 T. (b) 2 Marks. In a multi-period model, the Marginal Rate of Intertemporal Substitution between t and t + 1 is dened as the ratio of the marginal utility with respect to C; and the marginal utility with respect to CH1, i.e. M RISt.t+1 = M ULIM U1+1. The pure rate of time preference between t and t + 1 is dened as the Marginal Rate of Intertemporal Substitution between t and t+1 when G; = CH1 subtract 1, Le. mun] = MRISLt+1 ] Cr=Cg+1 _ 1' Derive Tom's Marginal Rate of Intertemporal Substitution between period t and period t + 1 and the pure rate of time preference between t and t + 1. (c) 5' Marks. Tom wants to maximise his utility subject to his budget constraint. Derive the optimal consumption for each period. Hint: The utility is rnarirniserl when the Marginal Rate of lnterternparal Substitutian between t and t+ 1, for any t = I], 1, - -- ,T 1, is equal to the negative slope of the budget constraint. ((1) 2 Marks. Compare the results in {c} to those using the utility function with a constant discount factor (Le. 6). Explain how this utility function with a hyperbolic discount factor can help prevent the steep decrease of consumption at very old ages Question & ( 1 Marks ! Suppose Tal's utility function for wealth is given how` 1 - `` ASATune that That's risk mision parameter is * = 1.5 That starts with wealth of [a ] IS Mark What is the utility of That's starting value of wealth* Ibj `` Mark Todd is offered & gamble where she has a GUY chance of gaining ``. but A GO` chance of losing Still. What is the expertadd value of the gamble* |{ ! I Mark What is the exported utility of this gamble to That ?" Will Tal take the The And Jack bath ann A holiday house on the mouth mast And both have A utility* Function the same AS That's . Joe has A Starting wealth of { million dollars . Jack has An` A Starting wealth of tim thousand dollars . There's A TY chance of " brushfire that will destroy their houses causing Each of them to lose Sam. mmm. An insurance policy to cover brushfire damage is an offer in the market . but it has & Sell. an excess . (Only Amounts If logs ATLater than the Exces Are married b` the insurance contract , in other words . the person who buys the insurance policy has to cover the cost of the first SAIL. AND If damage And the company purrs the rest . ! The cast for insurance for the fire damage is `) I Mart . Do Joe And / or Jack buy insurance* !" lel I Mart . If the premium was not final At Sad. It . what is the maximum amount due And Jack would pay for the insurance ! "