1. Consider an innitely lived household whose preferences are given by Z 'um; it) 20 with u(ct, it) = 2\\/c_t alog It where ct is the household's consumption in period t, It is the household's labor supply in period t, 0 0. If the household supplies 1; units of labor in period t, the household gets wtlt units of income, where {wt}:0 is a sequence of real wage rates which the household takes as given (exogenous). The income of the household in period t is taxed at rate 7}. The household has access to a perfect credit market, on which it can save and borrow at a constant interest rate r. We also assume that u + r) = 1. (A) Denoting the amount of savings in period t by hi, state the household's period-t budget constraint. (B) Using the period-t budget constraint from above, derive the household's lifetime budget constraint and specify the transversality condition that you used to derive it. Assume that b_1 = 0