Question

1. A patient with arthritis of the knee is planning to have a knee replacement. He has applied for a loan for this surgery, the loan has an annual interest rate of 6%. The artificial knee can function for 10 years before it needs to be replaced. Fees for knee replacement surgery are expected to grow at 5% annually. (a) Why is an artificial knee a form of health capital? (b) Assume the artificial knee depreciates at a constant rate every year until the time of replacement, which is 10 years hence, what is the exact cost of this capital (COC)? (Hint: 5% is the appreciation rate of a unit of capita (c) Suppose that instead of a loan the patient plans to pay for the surgery from his or her own savings Assume that the bank's interest rate on savings deposits equals its rate on loans. Does this change your answer to (b)? Why or why not? (d) Draw the COC line on a graph, with health capital on the x-axis and the COC rate on the y-axis. What is the slope of the COC? Explain why the slope has that value.

Answer 1

a. Why is an artificial knee a form of health capital?
An artificial knee could serve as a part of body function for
several years, which is similar to capital stock that could yield
the flow of return annually in the sense that artificial knee could
help a person to work normally every day.
b. Assume the artificial knee depreciates at a constant rate
every year until the time of replacement, which is 10 years
hence. What is the cost of this capital?
As noted in this chapter, cost of capital (COC) = i+?+a, where i
indicates the cost of obtaining a dollar of capital for a period, ?
is the depreciation rate on the capital stock, and a is the
appreciate rate of a unit capital. In this case, i = 0.06, ? = 0.1, a =
0.05. Thus, COC = 0.06+0.1+0.05 = 0.21. 5
c. Suppose that instead of a loan, the patient plans to pay the
surgery from his or her own savings. Assume that the bank