PID 1: PID 2: HEALTH ECONOMICS ECON 450 UNIVERSITY OF NORTH CAROLINA AT CHAPEL HILL SPRING 2024 HOMEWORK 5 LOGISTICS 。 You must submit your answers on the problem set document. Answers submitted in other formats (e.g. your own notebook pages) will not be graded. 。 Students are allowed to work in groups of at most two people and they can turn in either a single (joint) solution or two separate solutions, one for each member of the team. 。 Write very clearly and keep your answers inside of the allocated space. Do not use extra pages. 。 BHT below stands for: Bhattacharya, Jay, Timothy Hyde, and Peter Tu. Health Economics. Palgrave Macmillan, 2014. 。 Grading will be based on a single question randomly selected per each section. The probability that a question is drawn will be proportional to the points it has. Your over- all grade homework grade will be computed as the average across all the homeworks;. The answer key will contain answers to all questions. In exams, all questions will be graded. 。 When solving numerical problems write your answers as though you were explaining things to someone. Avoid writing just the numbers, briefly explain what the numbers mean and how you got there. 。 To guarantee the originality of your or your team's work, please state whether you adhere to the honor code (make sure you understand what adherence to the honor code entails) by providing your initials below: "I hereby adhere to UNC's honor code" 1 Initials: Question 1 (100 pts) Consider a world in which each individual i will be unhealthy with probability på and healthy with probability 1 – pi. The probability p; can take on four different values {0, .25, .50, 1}. If unhealthy they must spend $100 in health-related expenditures, if healthy they do not need to spend any dollars in health-related expenditures. Individuals know their health probability. The only insurance company in town offers a unique contract: full insurance at premium P. The company does not know the health probability of any single individual but it knows that there are 100 people with p¿ = 0, 200 people with pi 0.25, 100 people with Pi = .50, and 20 people with pi and that their utility is given by: = = - 1. Suppose all individuals have gross income M > 100 - U(M, Xi, Ii) = M − Xi + I¿((1+8)X; − P) (1) where Є (0, 1), X¿ are the individual's health expenses and I¿ is a variable that takes the value of 1 if the individual is insured and zero otherwise. Firms make choices based solely on expected profits. a. (25 pts) Derive the condition for a consumer with probability på to buy insurance. b. (25 pts) If ♂ = = insurance market? .4 and the premium is P = 60, how many consumers remain in the Explain. Who are these consumers? consumers 2 c. (20 pts) Would the insurer be willing to offer this insurance contract? Explain. Willing Unwilling = d. (30 pts) The government now regulates the market, mandating that all individuals with at least mild risk (pi .2) must buy insurance and that companies in the market must charge the median expenses among the people they insure. Will any insurer enter the market? Are consumers better off, worse off, or the same than they were without insurance? Explain. Insurers enter do not enter Consumers are better off same 3 worse off