Econ question, please figure out it step by step.

Problems 1. Assume that everybody earns $100 which is spent on consumption c. Individuals face a prob- ability s of becoming sick. If they are sick, they cannot work and earn $0. Individuals can purchase insurance from private firms. The insurance pays $100 if they get sick. The price of insurance is p. Assume that there are three types of people that differ in the probability of getting sick s and their utility function over consumption c: . Type 1: $1 = 60% and U1(c) = cl/2 . Type II: $2 = 20% and U2(c) = cl/2 . Type III: $3 = 10% and Us(c) = c There are 50 people of each type. (a) Explain why only type I and type II would benefit from insurance. [1 mark] Assume that the market for insurance is perfectly competitive and firms know the type of each consumer and charge each type of consumer a different price (P1, P2, P3) (b) Calculate the prices (P1, P2, P3) that firms will charge each type. [1 mark] Assume for the remaining questions that firms cannot observe types (the market for insurance is still perfectly competitive). (c) Calculate how much each type is willing to pay for insurance w. [1 mark] (d) What is the equilibrium price of insurance? Who gets insured in equilibrium? [2 marks] (e) In light of your answer to question (d), should the government intervene in this market and why? [2 marks] (f) Assume instead that the probability of getting sick for type I individuals drops to $1 = 40%. What is the equilibrium price of insurance? Who gets insured in equlibrium. [2 marks]