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Suppose there are two traders, two commodities x = (1, x2) and two potential states at time 1 s E {1, 2}. At time -1, both traders believe each state is equally likely at time 1; at time 0, however, trader 1 receives a private signal that fully informs him about the state at time 1. That is, at time 0, agent 1 either receives a the signal of = (1, 0) that state 1 is occurring with probability 1 or he receives the signal of = (0, 1) that state 2 is occurring with 100 percent probability. The second trader, however, receives the signal o2, that has no special information. Assume state-independent endowments are W1 = W2 = (3, 3) and define utilities as v1 (X) = (3 - s) log x1 + s log(x2) and V2 (X) = s log(x1) + (3 - s) log(x2). (a) (15 points) Intuitively explain what a rational expectations equilibrium is. Compare and con- trast the role of prices in a rational expectations equilibrium and Walrasian and Arrow-Debreu equilibria. (b) (15 points) Is there a rational expectations equilibrium for this economy? If so, what is it? If not, fully explain why not. (c) (20 points) Read F. Hayek (1945). "The use of knowledge in society". In: American Eco- nomic Review 35.4, pp. 519-530 and discuss the view that the existence of a fully revealing rational expectations equilibrium is the appropriate formalisation of Hayek's idea that the market mechanism is informationally efficient