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_ i sno individual, who lives Tob wey © Consider a rational forward-looking individual, WE seuime* cam ot mm, smited lifetime reg ce e fe ti ili r is ited litetl 2. His objective is to maximize his life tirne utility from his im oe . | 1s respectively BAS sadind soaps s. jahor i ., the two perio individual has initial endowment, Ao and his labor income in th keg the fallow- Mby function, assumed to b s a shrietly concave, £8 wy. and yp. The instantaneous ut i=l, as ae period 9. The ing form, u = u(C,) = InC;, where C, is the lovel af consumption in peow’, ‘ et 3 fen sete ssumed to be individual discounts future utility at the rate p and the market interest rate 18 7) all as constant over the individual’s lifetime. a Write down the individuals two-period lifetime utility function and intertemporal budget constraint. Carefully interpret each of these equations. Also explain why the lifetime budget constraint must be satisfied as a strict equality. b Graph the two-period budget constraint, and clearly label the intercepts and slope. Superim- pose the lifetime utility and determine the optimal consumption in both périods. c Suppose that the individuals initial endowment is 100 cedis and his labor incomes for period 1 and period 2 respectively are 1000 cedis and 2000 cedis. Determine the optimal consumption for period 1 and period 2, denoted C] and Cy respectively, if the market mterest rate is 10% (0.1) and the subjective rate of time preference, p, is 5% (or 0.05). d What is the optimal consumption in. each period, if both the utility discount rate and market interest rate are zero? How does this compare with your solution in (c) above? Explain the observed differences intuitively. V3 Scanned with CamScanner 
