Consider an economy with two periods (0 and 1) in which the individuals are expected utility maximizers and only consume in period 1. The Bernoulli utility function is u(Wh s ) = ln Wh s ; for h = 1; 2; and s = 1; 2; 3 where Wh s is the wealth (or amount of numeraire/money) of investor h in state s. Assume that there are only two investors, h = 1; 2, and that each of them is the owner of a rm. Investor h owns rm h, h = 1; 2. The cash-ows of rms are the only source of income in this economy. The cash-ows generated by each rm vary across the states of the nature in period 1. There are three states in period 1, s = 1; 2; 3. The cash ow of rm h in state s is denoted by csh and is measured in millions of dollars. We assume that c1 = (c11; c21; c31) = (6; 2; 0) and c2 = (c12; c22; c32) = (1; 1; 1): The three states are equally likely. These two investors can exchange shares to the two rms at time 0 in a competitive nancial market before observing s. Firm 1 also issues titles of debt (bonds) on which it defaults in state 3. In states 1 and 2, rm 1s debt is worth $2 million. This debt is also exchanged in a competitive market. The payo of asset i in state s is denoted xsi. We obviously see that the payo (or value) of rm 1s stock of equity is x1 = (x11; x21; x31) = (4; 0; 0); the value of rm 2s stock is x2 = (x12; x22; x32) = (1; 1; 1); and the value of the debt issued by rm 1 is x3 = (x13; x23; x33) = (2; 2; 0): Assume that p2, the stock price of rm 2, is normalized so that p2 = 1. Let p1 be the stock price of rm 1, and p3 is the price of the debt issued by rm 1. (a) Compute the equilibrium state prices (qs; s = 1; 2; 3). (b) Compute the value of both the stock and the debt of rm 1. What of the two rms has a higher market value at time 0? (c) Compute the equilibrium portfolios held by each investor (z h i ; h = 1; 2; i = 1; 2; 3). Compute also the investors wealth in each state (Wh i ; h = 1; 2; i = 1; 2; 3). (d) Compute the prices of both a put (qp) and a call (qc) on the total stock of rm 1 with a common strike price equal to $2 million. (e) Compute the equilibrium interest rate in this economy. (f) Compute the forward (or futures) price of rm 1s stock of equity. (g) Characterize the equivalent martingale probability measure of this economy. Now suppose that rm 1 is nancially restructured. In particular, rm 1 still issues both shares of stock and bonds. However, the total value of the debt becomes x3 = (x13; x23; x33) = (1; 1; 0): (h) Compute the price of both the stock and the debt of rm 1 after this nancial restructuring. Has the market value of rm 1 changed after the restructuring? Why