Econ-UB 140 Health Economics (Spring 2023) Problem Set 3
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Econ-UB 140 Health Economics (Spring 2023)
Problem Set 3: Adverse Selection
Due March 6th at 11am
Instructions:
- You may type your answers or write them by hand. If you choose to write by hand, please write legibly.
- Submit your answers via the course website (Assignments Tab), by the day/time indicated above. Late submissions will not be accepted.
- Submit your answers as a unique document, in pdf format. If you are writing by hand, there are several free apps (e.g. Genius Scan, Adobe Scan, etc.) and online websites that can help you combine multiple pictures into a unique document. Please contact your TF if you encounter difficulties.
1 ANALYT1cAL PRoBLEMs
1.1 AKERLoF's MARKET FoR LEMoNs
Let’s consider the market for used cars as analyzed by Akerlof (1970).1 The quality or value of the used car to the seller, Xi, is not observable directly, but buyers know the distribution of Xi has the form: Xi ~ Uniform[q1 , q2]. For all the following questions, assume that buyers have a utility for any car that is 20% greater than its quality (or, equivalently, 1.2 times its value to a seller).
1.1.1 Let q1 = 0 and q2 = 50. Will any car be bought in this market? Explain your reasoning carefully.
1.1.2 Let q1 = 0 and q2 = 200. Will any car be bought in this market? Explain your reasoning carefully. Does raising the maximum quality of cars that sellers offer have any effect on the predictions of the model? Explain why or why not.
1.1.3 Let q1 = 50 and q2 = 100. Will any car be bought in this market? Explain your reasoning carefully. Does raising the minimum quality of cars that sellers possess have any effect on the predictions of the model? Explain why or why not.
1.2 RoTHscH1LD-ST1cL1Tz MoDEL
Imagine that policymakers in the fictional nation of Pcoria are trying to create a Pcorian National Insurance Program (PNIP) that will bring full insurance to all the citizens of Pcoria. Assume there are two types of consumers, robust and frail. There is also asymmetric information—i.e. individuals know privately whether they are robust or frail and their health state is not observable to others.
1.2.1 Figure 1 depicts the current state of the insurance market in Pcoria before the plan is implemented. The insurance market settled into a separating equilibrium such that frail types are at A, and robust types are at C. Explain why no insurance company enters with a contract at point B.
Figure 1: Rothschild-Stiglitz diagram of the Pcorian insurance market
1.2.2 Draw your own version of the Pcorian Rothschild-Stiglitz diagram which includes a robust-type indif- ference curve passing through point C. Remember that the separating equilibrium is valid, so make sure your indifference curve does not contradict the assumptions guaranteeing the existence of such equilibrium.
1.2.3 Suppose PNIP establishes a new national pooling contract at point P, and bans any private insurance company from offering any other contract. Assume both frail and robust consumers decide to join the contract at P. Draw another robust-type indifference curve through P that is consistent with this new situation.
1.2.4 Is the policy change described in point 1.2.3 a Pareto improvement with respect to the initial state described in 1.2.1? [Hint: a Pareto improvement is a new situation in which at least 1 individual is better off while the remaining individuals are at least as well off as they were before.]
1.2.5 A robust Pcorian citizen named Hercules sues PNIP because he says the new insurance rules are harming him. Due to the explosive nature of the case, it goes straight to the Pcorian Supreme Court. The chief justice asks Hercules how PNIP could possibly be harming him if he went from having barely any insurance (point C) to full insurance (point P). How should Hercules respond?
1.2.6 The Pcorian Supreme Court issues an opinion that the ban on private insurance is unconstitutional, but that the PNIP can continue to operate. Hercules decides to go into business for himself and start a health insurance company. How can he design his new contract so that it attracts the robust Pcorians, leaves the frail Pcorians in the PNIP, and makes a profit? Draw his contract (point Z) on your diagram.
1.2.7 Suppose Hercules is successful. The PNIP starts losing billions of dollars a year and is shut down by the Pcorian government. For a moment, Hercules’s contract Z is the only contract available. Is there any place in the Rothschild-Stiglitz diagram where a new insurance company can enter and earn positive profit?
2 EssAY PRoBLEMs
2.1 PooL1Nc EoU1L1BR1A AND PERFEcTLY coMPET1T1vE MARKETs
Provide a clear and concise answer to the following questions (maximum 1 page overall).
2.1.1 One major premise of the Rothschild-Stiglitz model is that there is a perfectly competitive market for health insurance. Suppose instead that the market is not perfectly competitive, and in fact competitor firms have a hard time entering the market. Could a pooling equilibrium occur in this case? What is it about competition that prevents pooling in the RS model? No formal proof is necessary, but do make your reasoning clear.
2.1.2 Given your answer above, evaluate the statement “competition in health insurance markets is harmful for consumers". [Hint: think about cases where a pooling equilibrium would be beneficial for consumer welfare and cases where it would not be beneficial.]
2.2 Sw1TcH1Nc cosTs
Provide clear answers (maximum 1 page overall) to the questions below, concerning the following abstract (from “Adverse Selection and Switching Costs in Health Insurance Markets: When Nudging Hurts" by Benjamin Handel, 2011):
“This paper investigates consumer switching costs in the context of health insurance markets, where adverse selection is a potential concern [...]. We present descriptive results to show that (i) switching costs are large and (ii) adverse selection is present. To formalize this analysis, we develop and estimate a choice model that jointly quantifies switching costs, risk preferences, and ex ante health risk. We use these estimates to study the welfare impact of an information provision policy that nudges consumers toward better decisions by reducing switching costs. This policy increases welfare in a naive setting where insurance plan prices are held fixed. However, when insurance prices change endogenously to reflect updated enrollee risk pools, the same policy substantially exacerbates adverse selection and reduces consumer welfare, doubling the existing welfare loss from adverse selection.”
2.2.1 Handel finds that providing information about health insurance plans to people can exacerbate adverse selection. Explain how barriers to switching health insurance plans can partially solve the adverse selection problem in health insurance.
2.2.2 In Handel’s model, reducing plan switching costs actually makes people worse off . In the context of the Rothschild-Stiglitz model, explain how the utility of consumers in the market might decrease if these costs are reduced. Are robust types harmed? Are frail types harmed?
2023-03-07
Adverse Selection