Q.1. (SEU) You'll often hear statements in the financial news such as "the high stock market price index indicates high consumer confidence in the economy". Make sense of this in terms of SEU theory: how can the statement be recast in terms of the notions of "beliefs" and "choices reveal beliefs"? Illustrate using just two states of the world (good economy, bad economy). [5]Q.2 (SEU) Suppose that there are three states of the world S = {81, 82, 83}, corresponding to the economy being in a good, medium and bad state. In sce- nario A, an SEU agent has a preference :34 over acts (eg assets) that is rep- resented by some utility index n and prior beliefs p over S. In scenario B, she obtains information from an expert, who informs her that \"the economy is not in the bad state 83\" but cannot say anything more specic. This information does not change the agent's u, but it does lead her to update her beliefs so that it becomes a different belief q over S that recognizes that 33 is impossible and rescales her prior beliefs so that : 10(82) 10(31) +1192)- 19(81) m \"'d \"82) = 9(83) = 0: 9(31) = Her new preference :3 over acts is represented by u and q. Prove that these preference are dynamically consistent in the sense that for any outcomes 32,1),2, 81 33 31 y 81 33 81 y 32 3; 23A 32 3: i=1 32 y 83 Z 83 Z 83 Z 83 2 That is, her ranking of assets that pay a xed 2 in state 83 is unaected by the information. [The term \"dynamical consistency\" was dened differently in the topic of intertemporal choice, but the idea is similar: the prior self and the self with the information do not disagree in how they think about 31 and 82]. [5] Q.3. (Ambiguity and Trade) Empirical studies suggest that 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 = {31, 32}. There is an asset that pays $1 in state 31 and 0 otherwise. The price of the asset is $1) > 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 I) and the receives the outcome of the asset depending on the state. The nal possibility is that she can enter the market and engage in \"short-selling\". Feel free to read up on this well-known nancial strategy used by traders in the stock market, but all you really need for this problem is that short-selling entails receiving b but then paying the outcome of the asset depending on the state. Consider an SEU with belief p and a (linear) utility function where u(:1:) = :1: for any outcome 11:. (a) Compute the SEU for each of the three acts dened above. Show that, whatever the price b, the agent will want to enter the market. [2] (b) Suppose now that the agent is a Maxmin EU agent and her set of priors admits two possible priors, p and q, where 19(31) = (1(32)