Brandon lives for two periods (period 0 and 1). In what follows, a subscript denotes period.

Suppose that Brandon's preferences are represented by u(c0, c1) = log(c0) + 1/3 log(c1), and his income is (y0, y1) = (16, 20), of which the government takes away (t0, t1) = (6, 0). Due to his reckless eating habit, no one wants to lend to him. As a result, in addition to his usual intertemporal budget constraint, he also faces credit constraint s0 0. The interest rate is given by r = 1.

1. Explain why s1, his savings in period 1, is not positive.

2. Write his utility maximization problem.