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 capital).

(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.

5. Explain: bounded rationality. How would your utility function in Question 1 changed under bounded rationality?

6. Why would marginal cost of capital shift upward? What would happen to the optimal health stock?

i already know the question one, but i dont know how to handel with question 5 and 6

Answer 1

Since you asked for solutions to questions 5 and 6, let us go through what these terms mean before we answer the problem.

Q5. Bounded rationality is a phenomena observed in behavioral economics. The concept implies that rationality in our decisions is bounded because there are limits to our thinking capacity, available information, and time. Another important term you need to know is "satisficing". This means that in any given situation, a decision-maker will attempt alternatives until a satisfactory outcome is reached, instead of the optimal outcome.

In Question 1, the patient has the following knowledge:
- Fees for knee replacement surgery are expected to grow at 5% annually.
- The loan has an annual interest rate of 6%.
- The knee can function for the next 10 years before requiring replacement.
Given the following information, the patient will most likely get the surgery done immediately, to avoid the 5% growth of cost of surgery. However, the patient is constrained by knowledge and has no idea of future interest rates which might lead to an optimal outcome in the near future. Marginal cost of the surgery might decrease before sloping upwards reducing the opportunity cost. Bounded rationality limits utility. It is also important to note that perfectly rational decision-makers maximize expected utility, but crucially ignore the resource costs incurred when determining optimal actions.

Q6. Why would marginal cost of capital shift upward? What would happen to the optimal health stock?

Here, the artificial knee is considered as capital. An increase in real wage shifts the marginal cost upward. The marginal cost of knee surgery depends on the real wage: an increase in the real wage will lead to increase in real marginal costs. As the real wage increases, the marginal cost of one more knee surgery increase, so less knee surgeries will occur. The cost of knee surgery will increase because the demand will increase. The optimal health stock will increase with the increase in demand. (as the profit maximizing value will shift to the right).

Hope this helped!