Question 2 Catarina is the owner of a summer hip-hop festival in Mexico City. For the Summer of 2022 she booked rapper Tino el Pinguino to headline the festival. Catarina estimates that, due to Covid-19 there is a 1/2 chance that Tino will not show up. If Tino shows up, Catarina will be making $40, 000. If Tino has to cancel, the earnings drop to $2, 500. Catarina has no other income sources and is considering taking out insurance against the risk of Tino not showing up. Catarina can buy insurance coverage C at unit price p that pays out $C when Tino doesn't show. The total insurance premium is then pc. By Xr and XNT denote total income Catarina has when Tino shows up () and when he doesn't (NT) respectively. 1. We can express XT as a function of the festival income ($40,000), the unit price of insurance p and the amount of insurance coverage chosen in the following way: XT = 40, 000 - PC. Now express XNT as a function of the festival income ($40,000), the loss $37,500, the unit price of insurance p and the amount of insurance coverage chosen. 2. Graph the contingent income space (XT, XNT) and show the no-insurance bundle (the endow- ment point). Put Xr on the horizontal axis and XNT on the vertical axis. 3. If Catarina can buy insurance coverage C at unit price p = 1/2 that pays out $C when Tino doesn't show, find an analytical expression for the budget constraint - XNT as a linear function of XT - and show this constraint on your graph in question (2.2.). Assuming Catarina cannot borrow, what is the highest income Catarina can have if Tino doesn't show? 4. Suppose Catarina's Bernoulli utility function, u(X), is given by In X. For any contingent income bundle (XT, XNT), her expected utility is then: EU(XT, XNT) = 1/2In Xr + 1/2In XNT Is Caterina risk averse (argue using a graph of her Bernoulli utility function)? 5. Find an analytical expression of the indifference curve through the endowment point: XNT as a (non-linear) function of Xr and the expected utility obtained in the endowment point. Illustrate graphically 6. Find the optimal insurance and wealth levels when p = 1/2. Does she fully insure? Illustrate graphically. 7. Find the optimal insurance and wealth levels when p' = 3/4 instead of p = 1/2. Does she fully insure? On the graph show how your answer changes from the case where p = 1/2