Assume the household has preferences given by lnc + lnc0 and (0, 1]. The household is given income y in period 1 and net income y 0 in period 2. Assume there is no government in this problem and taxes are therefore equal to zero in every period.

2 Consumption and Borrowing Constraints Assume the household has preferences given by lnc+ lnc' and 6 (0,1]. The household is given income y in period 1 and net income 31' in period 2. Assume there is no government in this problem and taxes are therefore equal to zero in every period. 1. Solve for optimal C 2. Suppose the household wins a lottery in the rst period. Show how consumption changes with respect to a change in temporary income y 3. Now suppose that y = y' [assume no lottery win for part (c)). Suppose instead that households can only borrow against a fraction of their discounted income in the second period, i.e. let the borrowing constraint be given as: I y >_ 3_ 71+?\" where 7 E (U, 1) and 'y