Question

Period	Clinic 1	Clinic 2	Clinic 3	Clinic 4	Total
This Year	16,640	41,600	24,960	33,280	116,480
Next Year	?	?	?	?	121,139

9.2

Your data for the clinics in Exercise 9.1 suggest that Clinic 2 is operating at capacity and is highly efficient. Its output is unlikely to increase. Furthermore, Clinic 4 has unused capacity but is unlikely to attract additional patients. How would these facts change your answer to Exercise 9.1? Continue to assume that overall volume will rise to 121,139.

9.3

You estimate that the price elasticity of demand for clinic visits is −0.25. You anticipate that a major insurer will increase the copayment from $20 to $25. This insurer covers 40,000 of your patients, and those patients average 2.5 visits per year. What is your forecast of the change in the number of visits

Answer 1

Let initial price and quantity (number of visits) be P0 and Q0, and new price and quantity (number of visits) be P1 and Q1. Then,

Using midpoint method (for individual patient visit),

- 0.25 = [(Q1 - Q0) / (Q1 + Q0)] / [(P1 - P0) / (P1 + P0)]

- 0.25 = [(Q1 - 2.5) / (Q1 + 2.5)] / [(25 - 20) / (25 + 20)]

- 0.25 = [(Q1 - 2.5) / (Q1 + 2.5)] / (5 / 45)

- 0.25 = 9 x [(Q1 - 2.5) / (Q1 + 2.5)]

- 0.25 = (9Q1 - 22.5) / (Q1 + 2.5)]

- 0.25Q1 - 0.625 = 9Q1 - 22.5

9.25Q1 = 21.875

Q1 = 2.36 (new individual patient visit)

Total patient visit = 40,000 x 2.36 = 944,000