2. This problem is based on the Einev and Finkelstein JEP 2013 model of adverse selection. Assume that there are 10,000 people in a market to be insured. The number of people wanting to buy insurance (the demand for insurance) is N = 10000 a where a is the premium. a) What is the highest premium that anyone is willing to pay to buy insurance? At a zero premium, how many people in the market buy health insurance? b) Solve for the inverse demand function that expresses Premium a as a function of number of enrollees N. c) Assume that the marginal cost of people as they start to buy insurance is as follows MC = 3000 - N/2 Draw the marginal cost function on the same axes as the demand function. Do the two cross? What is the significance of this crossing point? d) Calculate the average cost function for people in this plan as a function of N and add it to the diagram. At what quantity N does it cross the demand curve? What is the premium at this quantity? e) If there is no government regulation or interference in this market, and premiums are based on the average cost of enrollees, then how many people will buy insurance and what will be the preumium? f) At what subsidy will the socially optimal number of people buy health insurance in this market? g) At what fixed dollar tax will everyone want to buy insurance in this market? That is, people choose to either pay the tax or pay the premium. How much revenue will the government raise through this tax at this rate? h) How does this problem relate to US Health insurance problems? 2. This problem is based on the Einev and Finkelstein JEP 2013 model of adverse selection. Assume that there are 10,000 people in a market to be insured. The number of people wanting to buy insurance (the demand for insurance) is N = 10000 a where a is the premium. a) What is the highest premium that anyone is willing to pay to buy insurance? At a zero premium, how many people in the market buy health insurance? b) Solve for the inverse demand function that expresses Premium a as a function of number of enrollees N. c) Assume that the marginal cost of people as they start to buy insurance is as follows MC = 3000 - N/2 Draw the marginal cost function on the same axes as the demand function. Do the two cross? What is the significance of this crossing point? d) Calculate the average cost function for people in this plan as a function of N and add it to the diagram. At what quantity N does it cross the demand curve? What is the premium at this quantity? e) If there is no government regulation or interference in this market, and premiums are based on the average cost of enrollees, then how many people will buy insurance and what will be the preumium? f) At what subsidy will the socially optimal number of people buy health insurance in this market? g) At what fixed dollar tax will everyone want to buy insurance in this market? That is, people choose to either pay the tax or pay the premium. How much revenue will the government raise through this tax at this rate? h) How does this problem relate to US Health insurance problems
