Arrow-Debreu

1. Suppose that there are three states of the world, a, b, and c. The probabilities of the three states are m = 0.25, 712 = 0.5, and 7:3 = 0.25. Let A, B, and C denote the Arrow-Debrcu securities that pay $1 in states a, b, and c, respectively. That is, A = (1,0,0), B = (0,1,0) and C = (0,0,1). Let pA = 0.4, p3 = 0.5 and pa = 0.2 denote the prices of A, B, and C. Consider a security X which is worth $2 in state a, $3 in state b, and $1 in state c. If there are liquid markets for A, B, C and X, what is the price of X