(a) Consider a household seeking to allocate disposable income over two periods: current period and a future period. The household derives utility from its consumption as follows: U(c,c')=c+ac', implying a constant marginal rate of substitution between consumption today and in the future: no matter the bundle in (c,c')-space, this household is willing to give up one unit of c for (1/a) unites of c'. i. Graphically represent these preference in (c,c')-space. ii. Consider(y-t,y'-t',r): the household's disposable income in the current period, in the future period, and the market interest rate, repectively. Write down the household's lifetime budget constraint. What is the household's wealth(we)? iii. Solve for the household's optimal c in terms of we. (there are 3 cases.) (b) Now consider a household identical to the one in (a), only this household's preferences are given by U(c,c')=c+bc', where b1+r>(1/a). How does the equilibrium r vary with an exogenous increase in y'? Is this intuitive? iii. From your answer to (ii.) you should be able to make an argument as to whether Ricardian Equivalence holds in this economy.