4. Consider a two-period economy. The consumer maximizes ln(c1) + E1 ln(c2). They have an initial endowment of w1. At time 1, they can invest in a risk-free bond with gross return Rf and in a risky asset with a price p1 and payoff v at time 2.

a) Write down the first order conditions for the price of the risky asset, p1, and the gross return of the risk free-asset, Rf .

b) Suppose that the supply of the risky asset is a1 = 1 and the risk-free bond is b1 = 0. What happens to p1 and Rf when w1 increases? Explain