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There are two states, 1 and 2, two consumers, A and B, and one good in each state. The two states occur with equal probability. The endowment of consumer A is 2 in state 1 and 0 in state 2. The endowment of consumer B is 0 in state 1 and 1 in state 2. Both consumers have von Neumann-Morgenstern utility functions. Let uA and uB be the utility functions of consumers A and B, respectively, for the one good in either state. Suppose that uA(x) = ln(x).
(a) Compute an Arrow-Debreu equilibrium if uB(x) = ln(x).
(b) Compute an Arrow-Debreu equilibrium if uB(x) = x.
(c) Is there an equilibrium if uB(x) = ex ? If so, calculate it. If not, show why there is no equilibrium. A good drawing would suf?ce in this case.
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