Problem III (40 points) Consider a two-period endowment economy with two consumers i E {1,2} who wish to maximise their utility, WEI-.01) =1n(6i)+ 5111(4) subject to the budget constraints iiit c: y-t+(l+r)s.- Ci+Ss Where c,- and c'i are the current and future consumption, and s,- is the amount of savings, for i 6 {1,2} Each consumer receives exogenous income y; and y: and pays taxes t and t' in each period. The interest rate is given by r. There is a government that needs to spend G and G" respectively in the current and future period. The government can nance its expenses with tax or debt. that is, the government's budget constraint are given by G G'+(1+r)B T+B T' where T = 2t and T' = 2t' (since there are two people in this simple economy). (15 points) Explain what the variable 3 captures. Carefully dene the competitive equilibrium (c:.c', si') both for the consumer's maximisation problem as well as the credit market. Make sure to explicitly identify all the endogenous variables and the conditions they must satisfy. . (5 points) Suppose that t = t' = G = G\" = 0, y1 = yi = ya = ya, and 61 > g. Which consumer consumes more in the rst period? What about in the second period? Provide an intuition for your answer (no algebra is necessary). ' (5 pOlIltS) Suppose that t = t, = G = G, = 0| l = (32