Question 1

Consider the 1-period Grossman’s model that we have seen in class. Denote H the
amount of health good and Z the amount of home good. Suppose in the Grossman’s
model the individual regards health and home good as perfect substitutes.

(a) Draw an indifference curve of the individual on the H-Z space.

(b) Is the following statement true or false? Explain with graphs.
Statement: “In each period the individual will demand more health than the home
good.”

Question 2

Consider the 1-period Grossman’s model that we have seen in class. Denote H the
amount of health good and Z the amount of home good. Suppose the consumer’s utility
from H and Z is U(H,Z)=HZ.

(a) Draw an indifference curve of the consumer on the H-Z space.

(b) Is the following statement true or false? Explain with graphs.
Statement: “In each period the individual will demand more health than the home
good.”

Question 3

The town Coolington has one incumbent clinic, called
Clinic A, and several physicians who recently moved to the town are considering to open
a new clinic to be called Clinic B.

There are two types of patients in Coolington, senior and junior. The size of senior
patients is n, and the size of junior patients is m. The procedure to treat a patient in
Coolington is fairly standard: each clinic only needs to follow an established practice
guideline to successfully complete the treatment. Moreover, the cost for treating a patient
has been very stable at \$ c.

The clinics are not allowed to price discriminate between the senior and junior
patients. That is, a clinic i will post one price pi, at which the two types of patients pay the
same.

A senior patient’s utility from being treated at clinic i is rh–pi, where rh measures how
much a senior patient values her recovery. Similarly, a junior patient’s utility from being
treated at clinic i is rl–pi, and it is known that rh>rl>c. If a patient does not seek treatment,
her utility is 0.

The physicians have estimated that, in order to open Clinic B, they need to incur a
fixed-cost F. In contrast, because of its long establishment in Coolington, Clinic A bears
no fixed costs.

(a) When Clinic A is the only clinic in the town, in order to maximize its profit, how
much will it charge for each patient?

(b) According to your analysis, is it wise for the physicians to open Clinic B? Please
explain.