Assume the representative consumer lives in two periods and his preferences can be described by U(c0, c1) = c0^(4/9) + 0.95 c1^(4/9), where c is the current consumption, c1 is next period consumption. Let's assume that the consumer can borrow or lend at the interest rate r = 10%. The consumer receives an income y0 = 100 in the current period and y1 = 150 in the next period. The government wants to spend G0 = 40 in the current period and G1 = 60 in the future period.

1. Solve the consumer's problem by finding the optimal allocation (c*0, c*1).

2. What is the equilibrium interest rate r? in this economy?