Find an analytical expression of the indifference curve through the endowment point: XNT as a(non-linear) function of XT and the expected utility obtained in the endowment point. Illustrate it graphically.

Background information: 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 XT and XNT denote total income Catarina has when Tino shows up (T) and when he doesn't(N T) respectively.