2. Consider a two-period ecornomy. Households preferences are described by the utility function In C1n C2 , where C1 denotes consumption in period 1 and C2 denotes consumption in period 2. In period 1, households receive an endowment Y households receive profits from firms that they own. Households pay lump- = 10. In period 2, sum taxes Ti and T2 in periods 1 and 2, respectively, and can save at the interest rate r. Firms borrow funds in period 1 to invest I1 units of goods in physical capital. In period 2, firms produce output, denoted Y2, using the technology f(I1) 10I and back their loans. The government levies lump-sum taxes to house- рay holds in the amounts Ti and T2 in periods 1 and 2, respectively, and consumes G 2 units of goods in period 1. Government consumption in period 2 is zero. T1 equals 1. (a) State the household's budget constraints in period 1 and period 2 and derive the intertemporal budget constraint of the household. (b) Find the optimal consumption, Ci, and private saving, S, as a function of r,Y1 Ti, and Y2 T2. (c) State the government's budget constraint in period 1 and in period 2 and derive the intertemporal budget constraint of the government. Find Si and T2

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