(Ambiguity and Trade) People do not participate in the stock market to the extent that standard theory implies. In this problem, you are asked to show that this can be explained by ambiguity aversion. Suppose the state space is S = {s1, s2}. There is an asset that pays $1 in state s1 and 0 otherwise. The price of the asset is $b > 0. The agent can choose not to enter the asset market, in which case she pays 0 and gets 0. Alternatively, she can enter the market and buy the asset, in which case she pays price b and the receives the outcome of the asset depending on the state. The final possibility is that she can enter the market and sell the asset short, in which case she receives b but then must pay the outcome of the asset depending on the state. Consider an SEU with belief p and a (linear) utility function where u(x) = x for any outcome x.

(a) Compute the SEU (Subjective Expected Utility Theory) for each of the three acts defined above. Show that, whatever the price b, the agent will want to enter the market.

(b) Suppose now that the agent is a Maxmin EU agent and her set of priors admits two possible priors, p and q, where p(s1) = q(s2) < 1 2 . That is, s1 has probability 1 4 according to p and probability 3 4 according to q. Compute the MEU for each of the acts defined above. Show that there exists a range of prices for which the agent prefers not to enter the asset market.