Consider the choice of insurance model from the class: Income $y$; loss $L$ occurring with probability $\pi_2$, insurance premium rate $p$. The consumer chooses the cover $q$, the amount that he receives if the loss occurs. The optimal choice implicitly defines a demand for insurance $q^* = D(y; L; p; \pi_2)$. In the class, we showed that if the insurance is not actuarially fair ($p > \pi_2$), she buys less-than-full insurance ($q^* < L$) or may not buy insurance at all.\
a) For a given $p > \pi_2$, how does the decision whether to buy insurance at all depend on the size of the loss? That is, if for some $L$ the consumer is just indifferent between buying no insurance and a small positive insurance, will she strictly prefer positive insurance or no insurance if the loss increases? Derive formally and show on a graph.\
b) Since provision of insurance has real costs for the insurance providers, $p > \pi_2$ for all real-world insurance products. When you buy travel insurance, it typically includes coverage against medical expenditures, plus optional add-ons such as insurance against damaged luggage or trip cancellation (you get the price of your ticket back if you cannot travel). In the light of your answer to a), would a rational expected utility maximizer buy such add-ons?
