Econ 323
Comprehensive Problem Set (CPS) [Optional]
This problem set will be made up of three blocks. Block 1 is published, and 3 will be filled in later in the semester. This block corresponds to material between MT1 and MT2.
The CPS is optional. If a student elects to do it, it may replace one of the three midterm exams. That is, the CPS can replace a low midterm score, or if a student has not taken one of the exams for some reason, it can fill in for the missing test.
As described in the syllabus and in class, the CPS is intended to be incrementally more challenging than the “standard” practice problems or exam problems we do routinely. You can think of it as a “stretch” assignment. All questions will have a small novelty or two that the student needs to work out on their own. The problems should then seem harder than our “standard” work.
Answer 2 of the following 3 problems.
1) Congestion Pricing
This problem models market inefficiencies related to a congestible public good: a road. We did this model one day in class. You should refer to that work for guidance. I’ve made one adjustment in the effect of traffic on speed.
The ingredients of the problem are:
N- the number of cars on the road.
n=2000 the threshold number of cars. Below this threshold, cars do not lead to traffic slowdowns. N above n will lead to a slowdown in traffic speeed, as described in the formula below.
a=55 the speed of traffic, in MPH, withen N
S(N)-the speed, in MPH of a car as function of N.
b= 50, opportunity cost of an hour spent in car.
a) Write down the function T(N), which is the time to travel one mile.
b) The ATC is the average opportunity cost of driving one mile. Write the the ATC as a function of N.
The ATC is each driver’s perception of their marginal cost of driving one mile. So we can also think of it as the MPC.
c) Calculate the Total Cost function (TC(N)) to society of having N drivers on the road. [Hint: you’ll know you’re at least on track if you have N3 in your formula.]
d) You can use Calculus and take the derivative of TC(N) wrt N to get the MSC function. Doing the equivalent algebraically is pretty annoying (I assume it is, at least, as I haven’t done it). But since Calculus is not required in this class, here’s the general result: MSC(N)= n2a/3b N2.
The MSB of driving is 10-.002N.
e) What is the market equilibrium level of traffic, N*?
f) What is the optimal level of traffic, N+?
g) What is the toll on drivers that will deliver N+?
h) Estimate the deadweight loss resulting from the inefficient level vs the optimal level. [Because the change in speed is non-linear, this will not be triangle with straight sides (one side will be a curve). But it will look triangle-ish. Your estimate can assume that all the edges are straight.]
2) Suppose a society contains two individuals. Joe, who smokes, and Tanya, who does not. They each have the same utility function U(C)=ln(C). If they are healthy, they will each get to consume their income of $15,000. If they need medical attention, they will have to spend $10,000, leaving them $5,000 for conumption. Smokers have a 12% chance of needing medical attention, and nonsmokers have a 2% chance.
An insurance company is willing to insure Joe and Tanya. The twist here is that the insurance company offers two different kinds of policies. One policy is called the “low deductible,” (L) for which the insurance company will pay any medical costs over $3,000. The other is a “high deductible,” (H) for which the insurance company will pay any medical costs over $8000.
a. What is the actuarially fair premium for each type of policy for Joe and Tanya?
b. If the insurance company can determine who smokes and who does not, and they charge the actuarially fair prices to each, what policy will Joe select? Tanya?
c. Now, suppose that the insurer cannot determine who smokes and who doesn’t. The insurer sets prices for each product. The price of L is $840 and the price of H is $40. (Why did I choose these numbers?) What will Joe and Tanya choose to do? Will adverse selection push Tanya out of the market? [Hint: No.] Calculate the total expected utility for our society under this outcome.
d. What has happened here? What does the second policy option accomplish?
e. How does this outcome compare to the scenario we’ve done several times in class, where the government mandates both to get a full insurance plan (F), and the insurer charges the actuarially fair premium.
3) In the 1983, Medicare (health insurance for the elderly) switched from Retrospective Billing to Prospective Billing. After this transition, health care researchers noted two facts: 1) for any given diagnosis, patients received less care than they had before before the transition; 2) despite the decrease in the quantity of care, health care outcomes were largely unchanged from before.
Compose a 2-3 page essay in which you develop your own argument as to what might be producing this pair of outcomes. You will probably want to describe the differences between billing systems, how incentives changed health providers, moral hazard, and any other relevant ideas.