# Draw the points from the 2-2 matrix in a diagram that has two time periods (pre and post) on the horizontal axis and emergency room utilization on the vertical axis. Add the hypothetical

Health Economics 445: Problem Set 3

Professor Martin Hackmann

Due: Tuesday the 26th of April 2016 in Class

Total 100 points

1) Difference-in-Differences (30 points)

Suppose we are interested in quantifying the effects of Massachusetts health reform on emergency

room utilization. Hypothetically, suppose that 208,000 out of the 4 million nonelderly adults living in

Massachusetts were using the emergency room in a representative pre-reform year. This compares,

hypothetically, to 12 million nonelderly emergency room users adults out of the 200 million nonelderly

adults living in other states in a representative pre-reform year. Suppose that in a representative postreform year, about 192,000 out of the 4 million people in Massachusetts use the emergency room.

Suppose also that we see about 12.5 million (out of the 200 million people living in other states) using

the emergency room in a representative post-reform year.

a) Draw a 2 by 2 matrix which describes the fraction of people using the emergency room in the

treatment group and the control group before and after the reform ( 5points)

b) Quantify the difference-in-differences effect of Massachusetts health reform on emergency

room utilization. Interpret the finding. (10 points)

c) Provide an intuition for the difference-in differences strategy (5 points)

d) Draw the points from the 2-2 matrix in a diagram that has two time periods (pre and post) on

the horizontal axis and emergency room utilization on the vertical axis. Add the hypothetical

emergency room utilization in Massachusetts had Massachusetts not had the health reform

(Hint: we are using the difference-in-differences strategy that assumes that Massachusetts

would see the same national trend in emergency room utilization in the absence of a reform).

Show the difference-in-differences effect graphically in the diagram (10 points)

2) Pharma Pricing (40 points)

Imagine you are the CEO of Bayer and your R&D team has just developed a blockbuster drug to treat

high blood pressure. You successfully went through clinical trials and you have FDA approval so you are

ready sell it on the market. The regulator has given you a patent length of 20 years and now you are

trying to figure out the optimal price for the drug. Your marketing department has crunched a few

numbers and figured the following demand curve per year:

Q=1,800,000- 2,000*P

Where P is the price per drug in dollars and Q is the quantity demanded in the year at that price. The

research group also tells you that they spent $2 billion on research and development. However they can

now produce the drug for $400 per piece.

a) Derive the inverse demand curve (5 points)

b) Derive the annual revue curve in terms of the quantity of drugs being sold, and quantify the

marginal revenue curve which indicates the marginal increase in revenues from a marginal

increase in quantity (hint:

Δa∗Q∗Q

ΔQ

= 2 ∗ ∗ ) (5 points)

c) Derive the profit-maximizing price and quantity. What is the variable profit per year? (5 points)

d) In a diagram with quantity on the horizontal axis and price and mc on the vertical axis, draw the

inverse demand curve, the marginal revenue curve, and the marginal cost curve. Derive the

optimal price graphically. (5 points)

e) Is the marginal revenue steeper or flatter than the inverse demand curve? If so why? (5 points)

f)

Quantify the average cost curve (5 points)

g) Suppose that generic companies enter the market once the patent elapses, which leads to

perfect competition. Suppose the generic companies have the same marginal costs. What will

be the equilibrium price under perfect competition? (5 points)

h) Is Bayer able to recover the fixed costs of R&D through variable profits? Assume that there is no

profit discounting in future years, so profits next year count equally as profits this year. (5

points)

3) Supplier Induced Demand (30 points)

Greedy John has his own outpatient imaging center on Beaver Avenue and specializes in CT scans. For

each scan, he receives a reimbursement of $0.5 from the insurer. He knows his patients very well and

considers that 8 scans per month are clinically adequate. However, Greedy John also knows that he can

boost his income by inducing additional CT scan images, I. On the other hand, Greedy John knows that

the insurer might come after him if he conducts too many scans. Therefore, his utility increasing in

income, Y, but decreasing in the number of induced additional CT scan images, I, and given as follows:

= 200 ∗ − 10 ∗ 2 − (100 ∗ − 5 ∗ 2 )

With the following marginal utilities = 200 − 20 ∗ and

= −100 + 10 ∗ .

a) Suppose that John’s income is solely generated from CT scans. Describe John’s budget constraint

(5 points)

b) Calculate the optimal number of induced CT scans ≥ 0. (10 points)

c) Now suppose that the insurer reduces the reimbursement rate to $0.25, how does that affect

the number of CT scans? Is this measure effective in reducing wasteful procedures? (5 points)

d) Let’s abstract from the specific numeric example. Does a reduction in the reimbursement rate

necessarily lead to a reduction or increase in the number of CT scans? If not, on which effects

does it depend on? Discuss your answer graphically using a diagram with CT scans on the

horizontal axis and income on the vertical axis. (10 points)

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