Question 1. Suppose that there are many identical households who live for two periods. The population (N) is constant. Endowment profiles are given as y1 and y2. There are two assets in this economy: i) private lending (denoted by b ), associated with a gross real interest rate of R; and ii) trees (denoted by s ), which yield an uncertain crop, d, where the total amount of tree is assumed to be A. The crop behaves as follows: d=d+ where is a random variable which satisfies that = with probability 0.5 and = with probability 0.5. a. Write down the budget constraint in Period 1, denoted by (1). b. Write down the budget constraint in Period 2, denoted by (2). Suppose that a household's utility is given: U=u(c1)+u(c2). c. Find the optimality conditions for bonds and trees and interpret them. d. Write down the equilibrium conditions (for bonds and tress) in this economy. Suppose that P1=P2=P, and that A=N and y2=0. e. Assuming that u(c)=lnc, show that (3) R1=E[P+d+y1P] (4) P=(y1P) f. Using (3) and (4), show that we have the below equation and interpret it. R=PP+dP(P+d)2 g. Show that E[Re]R is increasing in 2 and decreasing in y1 and d. Interpret the results. Question 1. Suppose that there are many identical households who live for two periods. The population (N) is constant. Endowment profiles are given as y1 and y2. There are two assets in this economy: i) private lending (denoted by b ), associated with a gross real interest rate of R; and ii) trees (denoted by s ), which yield an uncertain crop, d, where the total amount of tree is assumed to be A. The crop behaves as follows: d=d+ where is a random variable which satisfies that = with probability 0.5 and = with probability 0.5. a. Write down the budget constraint in Period 1, denoted by (1). b. Write down the budget constraint in Period 2, denoted by (2). Suppose that a household's utility is given: U=u(c1)+u(c2). c. Find the optimality conditions for bonds and trees and interpret them. d. Write down the equilibrium conditions (for bonds and tress) in this economy. Suppose that P1=P2=P, and that A=N and y2=0. e. Assuming that u(c)=lnc, show that (3) R1=E[P+d+y1P] (4) P=(y1P) f. Using (3) and (4), show that we have the below equation and interpret it. R=PP+dP(P+d)2 g. Show that E[Re]R is increasing in 2 and decreasing in y1 and d. Interpret the results