Suppose a hospital is planning how many patients to treat over the next two years. One key factor the hospital needs to consider in its planning is that hospitals that see many patients in one year have lower costs of care in subsequent years. Let p be the price of hospital care, let q₁ be the number of patients the hospital treats in year 1, let q₂ be the number of patients the hospital treats in year 2, and let c₁ and c₂ be the hospital’s per-patient cost in years 1 and 2. The hospital’s profits over the two-year period are

The hospital takes p₁ and p₂ as fixed and they choose q₁ and q₂ to maximize profits, ∏.

a. Suppose, as a warm-up exercise, that there is no learning by doing, and that the unit cost functions are

Is the cost of caring for patients increasing or decreasing in the number of patients seen? Derive the supply function in periods 1 and 2 for the hospital.

b. Let us introduce learning by doing into the problem. Now, the unit costs in period 2 are lower if the hospital has a higher number of patients seen in period 1. As we have seen in this chapter, there is a lot of evidence that suggests that such learning by doing by hospitals does in fact happen. The unit cost function in period 1 is still c₁ = q₁/2, but the unit cost function in period 2 now depends also on the number of patients seen in period 1: c₁ = q₁/2. Derive the supply function in periods 1 and 2 for the hospital.

c. Should the hospital see more or fewer patients in period 1 if there is learning by doing?

Transcribed Image Text:

(p₁c₁)q₁ + (P₂-C₂)9₂