eco question

Econ 5860: Health Economics Professor Kurt Lavetti Ohio State University

Spring 2019 Problem Set 4

Due Date: Apr 10, 2019 by the beginning of class

Please submit assignments on Carmen.osu.edu or on paper in class

A. True/False Explain. Indicate whether each of the following statements is true or false and then explain why you think this. Include in your explanation any pertinent institutional details

and economic reasoning (including appropriate graphs and equations). Please provide concise, clear answers with minimal irrelevant detail. Explanation is required.

1. Policymakers in at least 14 states in the US have in recent history passed laws called “community-rating” laws. The idea of these laws is that, since individual private health

insurance markets don’t seem to function very well, leaving many older and sickly

people unable to purchase affordable insurance, community rating laws impose

restrictions on prices that insurance companies are allowed to charge. Consider a

community rating law that forces insurance companies to charge the same price to all

individuals (and forces insurance companies to sell insurance to anyone who is willing to

pay the chosen price).

True or false: the Rothschild-Stiglitz model suggests that this law will help old and sickly

people gain access to insurance.

B. Analytical Problems

2. Consider the market for used cars discussed by Akerlof. Car sellers have the utility function

U! = M+ !x! where M is the amount of money they have, xj is the quality level of the jth car, and 'a' is the

coefficient on car quality in the utility function.

Buyers have utility function

U! = M+ !x! There is a uniform distribution of quality of the cars held by sellers, x!~U[0,2]. Sellers know the quality of the cars, but buyers only know the average quality of the cars on the market.

Buyers also know the utility function of sellers.

a. [5 points] Let P be the price of used cars put up for sale. What is the average quality of cars put up for sale as a function of P and a?

b. [5 points] For what values of b will buyers be willing to buy the cars?

3. [10 points] Consider a version of the Akerlof model in which neither buyers nor sellers observe car quality (though somehow – please suspend your disbelief – both buyers and sellers enjoy higher utility from higher quality cars). For this question, please assume

that both buyers and sellers recognize that neither can observe car quality.

Sellers’ utility function is given by U! = M+ x! and buyers’ utility is given by U! = M+ 3x! where M is the level of consumption of non-car goods and x! is the quality level of car, and there is a uniform distribution of quality of the cars held by

sellers, x!~U[0,100].

In this market, is there is a price, p, at which all cars will sell? If not, prove there is no

such price. If so, calculate what prices will work.

4. Consider the figure below

a. [2 points] Explain why UH is not a valid indifference curve.

b. [3 points] Draw a new version of the diagram with the same indifference curve. On the new diagram, label two insurance contracts, A and B, such that A

provides more income in both states of the world but the individual with the

indifference curve in the diagram nonetheless prefers contract B over contract A.

c. [2 points] Draw a new diagram with a version of the indifference curve that represents valid preferences

d. [3 points] Is the set of contracts (F, H) a valid separating equilibrium if the high risk individuals have preferences as you have drawn them in part c?

5. Consider the basic Rothschild-Stiglitz model with asymmetric information and two types on consumers. A policymaker who has taken this class suggests that is might be

beneficial to impose a flat tax on healthy people and distribute the tax revenue to sick

people, providing partial insurance to people.

a. [3 points] Since the tax will only offer partial insurance, there will still be a private competitive market for additional insurance. Will a separating

equilibrium be possible in the insurance market if this tax is implemented? Draw

a diagram to justify you answer.

b. [3 points] After the tax is implemented a recession hits and a new policymaker decides to make up for a tax revenue shortfall by expanding the tax to include

sick people as well as healthy people. Will a separating equilibrium be possible

in the insurance market under this policy?