1. (a) Compute an Arrow-Debreu equilibrium for an economy with two consumers, A and B, and two states, 1 and 2. Each consumer has a von Neumann-Morgenstern utility function for lotteries of money, and for each consumer the utility of x units of money is ln(x). Consumer A believes that state 1 occurs with probability 1/4 and state 2 occurs with probability 3/4. Consumer B believes that state 1 occurs with probability 3/4 and state 2 occurs with probability 1/4. Each consumer is endowed with $1 in each state.
(b) In part (a), suppose that each consumer believes that each state occurs with probability 1/2, that consumer A is endowed with $2 in state 1 and $0 in state 2, and that consumer B is endowed with $0 in state 1 and $2 in state 2. Recalculate the Arrow-Debreu equilibrium.