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Rothschild/Stiglitz Insurance Model: Equilibrium Contracts and Market Behavior

## Equilibrium Contracts in Different Situations

Part 1. Please answer all 10 questions for a maximum of 61 points

1) Use the Rothschild/Stiglitz insurance model to determine the equilibrium contract in the following situations.

Individuals have initial wealth W.

If an individual falls ill, he always purchases one treatment. The price of the treatment is P.

There are two risk types. For high risk individuals, the probability of falling ill is ρH; for low risk individuals, the probability of falling ill is ρL. We have ρH> ρL.

The insurance market is competitive, so we only will observe contracts that break even.

Note: Please draw corresponding graphs for each situation. Each graph should include (1) the no insurance point, (2) individuals’ indifference curves for each risk group, and (3) breakeven lines for insurers when offering contracts to each risk group. In your answer, please label the optimal contract for each risk group.

a) [Experience Rating] Suppose “experience rating” is allowed, meaning that insurers know the risk type of each individual and can offer each risk group a different contract.

Show graphically that when offered policies along the corresponding breakeven line (i.e. insurers offer policies along the breakeven line for high/low risks to high/low risk individuals), which plan would be chosen by the low risk? Which plan would be chosen by the high risk?

Which risk type end up with plans with higher premium, the high-risk or the lowrisk?

Are these plans full insurance plans, i.e., plans with no out-of-pocket cost?

Suppose you are the social planner, do you think the “experience rating”equilibrium you find above should be adopted in the society? Why?

3b) Suppose “experience rating” is abandoned, meaning that insurers cannot detect, in advance, which buyers are which. Therefore, insurers have to offer the same set of contracts to both risk groups.

i. [Adverse Selection] Suppose insurers have to offer both optimal contracts you found in a) to both risk groups.

Can insurers breakeven in this situation? Why?

ii. [Cream Skimming] Now suppose insurers are allowed to offer whichever policies they find profitable.

Show graphically that insurers could offer a set of contracts to both risk groups and the two risk groups could identify themselves by choosing different insurance policies.

How does consumer welfare for the low-risk type in the equilibrium you find here compare with that in the equilibrium you find in a)?

How does consumer welfare for the high-risk type in the equilibrium you find here compare with that in the equilibrium you find in a)?

## Effects of Experience Rating

2) Use the Rothschild/Stiglitz insurance model to determine if insurance moral hazard affects the desirability of complete insurance. Specifically, suppose that as the level of insurance coverage increases, the risk of illness increases.

a) Draw the “breakeven line” for insurers under insurance moral hazard.

b) Now consider an individual who does not display this moral hazard, but must purchase as part of pool of individuals who do. Which plan will this individual prefer, when offered plans along the new breakeven line? Please show it graphically. (3 points) Is this plan a full insurance plan?

3) The issue of adverse selection exists in health insurance market because there is asymmetric information between insurers and individuals.

a) Explain what this “information asymmetry” means – i.e., which party (the insurer or the individual) has more information about what. (2 points)

b) Explain why “information asymmetry” in health insurance market could lead to “death spiral” – i.e. as more and more individuals drop out of the insurance market, the market might collapse in the end.

4) Suppose that the market demand for physical therapies is given by the equation P=100-Q. The cost of each therapy is 40.

a. What is the socially optimal number of physical therapies?

b. Suppose that the price of physical therapies is 40. Suppose further that patients have insurance that pays for 50% of the price of physical therapies. How many physical therapies will be purchased? What is the amount of deadweight loss from insurance moral hazard?

c. How would your analysis of deadweight loss change if the service in question was open heart surgery? (A qualitative response is sufficient.)

5) Suppose that all individuals have the same risk of illness, but there is a fixed cost of supplying insurance. Specifically, insurers must incur a cost of F dollars per policy, regardless of the extent of coverage or whether the individual falls ill.

a) Use the model of Rothschild and Stiglitz to show that when the fixed cost is sufficiently small, individuals will still prefer to purchase full insurance. (Hint: You must redraw the “breakeven line,” and show the optimal plan purchased by the individual.)

b) Use the model of Rothschild and Stiglitz to show that when the fixed cost is sufficiently large, individuals will prefer no insurance.

6) Suppose that demand for a surgical intervention varies across communities. In one third of communities, demand is “low.” Demand is “medium” in another third and “high” in the rest. Note that medium is halfway between low and high. Only one of these demand levels is correct, implying a deadweight loss at the other levels. Show that the deadweight loss is larger when the correct level is low versus when the correct level is medium. (Note: you can assume the supply curve to be either a horizontal line or an upward-sloping line. It doesn’t matter what shape of supply curve you are assuming.)

## Adverse Selection and Cream Skimming

7) Assume that a hospital is a profit maximizing firm and is a local monopoly. It accepts a mix of privately insured and public patients (i.e. patients who are in public insurance programs such as Medicare and Medicaid). The private sector faces a downward sloping demand curve, and the public sector faces a fixed regulated government price.

Suppose government changes its policy to reduce the reimbursement (i.e. the government price) to hospitals.

Use the economic model of price discrimination to show graphically what happens to (a) price faced by privately insured patients, (b) access for privately insured patients (i.e. the number of privately insured patients accepted by the hospital) and (c) access for public patients (i.e. the number of public patients accepted by the hospital).

8) a) What is “supplier induced demand”?

b) How can you estimate the magnitude of “supplier induced demand”? (Please describe the empirical data you propose to use, and the specification of the regression). What is the identification challenge? How would you address the identification issue?

9)You would like to test the experience curve (i.e. learning-by-doing) hypothesis: as physicians gain experience, their quality improves (where quality is measured by risk-adjusted outcomes.) You have cross-sectional data showing that physicians with higher volumes have better risk-adjusted outcomes. While the data are consistent with the experience curve hypothesis, they allow another interpretation that is quite different. Briefly offer a competing hypothesis that is consistent with the data.1

(Hint: consider the possibility of reverse causality.)

10)Offer at least two potential benefits of third party disclosure of provider quality.

1 Assume that your measures of volume and outcomes are valid.

Part 2. Please answer all 15 questions for a maximum of 15 points

1) When insurers “cream skim”, high-risk individuals will end up with plans that have substantial cost sharing. T F

2) In the real world, the extent to which health insurance leads to ex-ante moral hazard (i.e., the change of risky health behavior in response to insurance) is large. T F

3) The rationale behind the Individual Mandate of Affordable Care Act is to prevent Adverse Selection Death Spiral from happening – i.e. to make the risk pool as complete as possible. T F

4) Adverse selection is more severe in the long-term care insurance market than in the health insurance market. T F

5) Insurance moral hazard happens because there is asymmetric information between health insurers and individual enrollees of health plans. T F

6) Under insurance moral hazard, the optimal insurance should have zero deductibles and zero copayment, which eliminates patients’ financial risk. T F

7) A law stating that "No health insurer may consider any applicant's past, current or future health or age" would make both the high-risk and the low-risk individuals enroll in the same plan. T F

8) The inefficiencies in health care market stem from physician induced demand, insurance moral hazard, and physician practice variation. T F

9) The early empirical finding that “price elasticity of demand is positive (i.e. as price increases, demand increases)” reflects the fact that medical markets are not in equilibrium. T F

10) Paper clips are “experience goods” because consumers are uncertain about the quality. T F

11) The observation that “markets with more medical specialists per capita spend more on specialized medical treatments” proves that suppliers have the ability to induce demand. T F

12) Deadweight Loss from practice variation is smaller when the demand is more elastic. T F

13) Deadweight Loss from insurance moral hazard is smaller when the demand is more elastic. T F

14) The majority of healthcare providers (e.g., hospitals) in the U.S. are for-profit companies. T F

15) What distinguishes physicians from experts in other profession