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

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 iii—t
c: — yfi-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 finance 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 define 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 > fig. Which consumer consumes more in the first period? about in the second period? Provide an intuition for your answer (no algebra is necessary). ‘ (5 pOlIltS) Suppose that t = t, = G = G, = 0| fil = (32 < 1! (ylvyi) = (10:5)9 and (“21 ya) = (5! 10)’ WhiCh consumer consumes more in the first period? about in the second period? Provide an intuition for
your answer (no algebra is necessary). . (5 points) Suppose that t = t’ = G = G’ = 0,61: 52 =1, 1;; = y’i, and y: = ya. do you expect will be the consumers savings? about government debt? Provide an intuition for your answer (no
algebra is necessary). . (10 points) Consider again the parameters described in part (3.4), but with a new timing for taxes. now denoted by f and t". Suppose t = —1. Compute government debt in this case. Compute t’ that balances
the government’s present value budget constraint. do you expect will be the consumers savings?
Would consumers’ welfare change as a result of this change in taxation timing. Explain the economic intuitions.

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