Question2 Consider an economy with two agents A and B and two states. The agents' endowment at time t= 1 is wa = (20,0), wb = (0,10) We assume that the agents have no endowment at time 0 and that the probability of each state is 1/2. We assume that agents have a VnM utility of the form d-vj u(C) j = A, B. - 7 1. Consider a market economy with an asset market for two Arrow Debreu securities with price v1 = 1 and 42 = p. Write the first order condition for the individual demand function and derive the optimal demand for the securities as a function of the Arrow Debreu price p. 2. Express the market clearing condition in the up state. Show that the market clearing condition in the down state is automatically satisfied. Solve for p numerically when 7A = 3 and 7B = 2 and the find the resulting allocation. 3. Solve for the equilibrium allocation when 7A = 2 and "B= 0.01. Interpret this result 4. Consider the same economy and assume that in addition to their endowments at time t = 1, the agent receive 5 units of the consumption good each at time 0 and that intertemporal utility function is given by 1- Co 1 - + BE j= A, B. Calculate the equilibrium risk free rate when 7A = 3, 7B = 2 and 8 = 0.98. Question2 Consider an economy with two agents A and B and two states. The agents' endowment at time t= 1 is wa = (20,0), wb = (0,10) We assume that the agents have no endowment at time 0 and that the probability of each state is 1/2. We assume that agents have a VnM utility of the form d-vj u(C) j = A, B. - 7 1. Consider a market economy with an asset market for two Arrow Debreu securities with price v1 = 1 and 42 = p. Write the first order condition for the individual demand function and derive the optimal demand for the securities as a function of the Arrow Debreu price p. 2. Express the market clearing condition in the up state. Show that the market clearing condition in the down state is automatically satisfied. Solve for p numerically when 7A = 3 and 7B = 2 and the find the resulting allocation. 3. Solve for the equilibrium allocation when 7A = 2 and "B= 0.01. Interpret this result 4. Consider the same economy and assume that in addition to their endowments at time t = 1, the agent receive 5 units of the consumption good each at time 0 and that intertemporal utility function is given by 1- Co 1 - + BE j= A, B. Calculate the equilibrium risk free rate when 7A = 3, 7B = 2 and 8 = 0.98