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Home Tools Assignment 3 and... x o A Sign In Q O 2/3 75% 14 Learning by doing. 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 qi be the number of patients the hospital treats in year I, let be the number of patients the hospital treats in year 2, and let and c2 be the hospital's per-patient cost in years 1 and 2. The hospital's profits over the two-year period are n Cl)ql + (P2 C2)q2 The hospital takes and P2 as fixed and they choose and to maximize profits, 11. a Suppose, as a warm-up exercise, that there is no learning by doing, and that the unit cost functions are = and c2 = n. 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. [Hint: Substitute the unit cost func- tions into the profit functions and take the derivative of II with respect to qi and q2] 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 I. 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 = L, but the unit cost function in period 2 now depends also on the number of patients seen in period I: c2 = -Q. Derive the supply function in periods I and 2 for 2.11 the hospital. [Hint: Solve first for the optimal taking qi as given. Then use your question for (12* in your expression for q{.] c Should the hospital see more or fewer patients in period I if there is learning by doing?