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Problem 5. Consider an economy in which there are two dates t = 0 and t = 1, and two possible states, 0 = 1 and 0 = 2, at t = 1, which occur with equal probability, so that 71 = 72 = ?. In this economy, two "complex" assets are traded. The first sells for price PO = 2 at t = 0 and makes payoffs of Z, = 2 in state 0 = 1 at t = 1 and Z? = 4 in state 0 = 2 at t = 1. The second sells for Po = 1.25 at t = 0 and makes payoffs Z? = 1 in state 0 = 1 at t = 1 and Z? = 3 in state 0 = 2 at t = 1. (a) Use this information to compute the price q at t = 0 of a contingent claim that pays off one in state 0 = 1 at t = 1 and zero in state 0 = 2 at t = 1 and the price q2 = 0 at t = 0 of a contingent claim that pays off zero in state 0 = 1 at t= 1 and one in state 0 = 2 at t = 1. (b) Use your answers from part (a), above, to compute the price PI at t = 0 of a bond that pays off Zy = 1 in state 0 = 1 at t = 1 and Z? = 1 in state 0 = 2 at t = 1. (c) Use your answers from part (a), above, to compute the price Po at t = 0 of a share of stock that makes no dividend payments, but can be sold for P. = 2 in state 0 = 1 at t = 1 and P2 = 3 in state 0 = 2 at t = 1