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Consider a closed economy that lasts for two periods, t = 1,2. In period 2 there are two states of the world, s E {SLASH).
Consider a closed economy that lasts for two periods, t = 1,2. In period 2 there are two states of the world, s E {SLASH). Each state is realized with probability 1/2. The representative household has preferences log (ci) + B > >log (c2 (s)) S=SH,$L The household receives labor income y1 = 1 in period 1 and if s = SH y2 (s) = 1-24 if s = SL in period 2. The household is endowed with 100% of the shares of the two firms in the economy: firm A and firm B. Firm A and B do not pay out dividends in period 1 but they pay dividends R' (s) is period 2. In particular A ifs = SH 0 if s = SH R2 (s) = 1 = 0 ifs = $L A if s = SL Assume that A > 0 and 1 -24 > 0. There are three assets in this economy: firm A's stock (let wa be the holdings at the end of the period), firm B's stock (we), and risk free debt (b). The definition of an equilibrium is the following:An equilibrium is an allocation for the household, (c1, c2 (s) , wA, w, b), and prices (q4, qB, 1 + r) such that . given prices, the allocation solves max log c1 + B NIK (Circz(s),WA, (B,b) log C2 (SH) + - log c2 (SL) subject to ci+ qaw+ qwB+ by1+ qa+q. C2 (s)
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