2. Consider a representative household in the two-period consumption-savings model whose preferences are given by: \"(c-1:32} = 'yl- ISV'E In the rst period the household receives exogenous real lahor income yl and real interest income reg. on their wealth endowment of on. which they split between real consumption expenditures c1 and saving 31. In the second period they again receive exogenous real lahor income pg and real interest income rel on their wealth my spending any remaining lifetime income on consumption 63 while leaving behind no assets so that egg = I]. You may assume that the subjective discount factor and real interest rate are equal to B = 1f1.1 and r = {11, and the initial wealth endowment is equal to on = U: {a} Write down the period-1 and period-2 budget constraints in real terms. {h} Set up the sequential Lagrangian1 derive the consumption-savings optimality con- dition1 and solve for the optimal levels of period-1 and -2 consumption, {che}. in terms of the exogenous variables? yl and y2. {c} Compute the numerical values of {c}, cg} and 31\"\" for: i. in = 61, y; = 11 i-i' '91 = 1|]: y2 = 66': Interpret your answers above in terms of the 'permanent income hypothesis'. {The computations are messy and the nal answers do not neclllarily work out 'nicely'.} {d} Suppose that lenders impose a borrowing constraint on households such that they are not allowed to he in debt at the end of period 1. Determine whether this constraint affects the household's desired consumption levels in part {cjfi} or in {c){ii]