Question

An individual's demand for hospital visits per year is Q=15 – 0.1P, where P is the price of a hospital visit. The marginal cost of producing a hospital visit is $75. a. If individuals pay full price of obtaining medical services, how many hospital visits will they make per year? b. If individuals must pay only a $40 copayment for each hospital visit, how many visits will they make per year? c. What is the deadweight loss to society associated with not charging individuals for the full cost of their health care? Show the deadweight loss on a graph.

Answer 1

P = (15 - Q) / 0.1 = 150 - 10Q

(a)

TR = PQ = 150Q - 10Q²

MR = dTR/dQ = 150 - 20Q

Setting MR = MC,

150 - 20Q = 75

20Q = 75

Q = 3.75

P = 150 - 10 x 3.75 = 150 - 37.5 = 112.5

(b)

When P = 40,

Q = 15 - 0.1 x 40 = 15 - 4 = 11

(c)

Deadweight loss = (1/2) x Change in P x Change in Q

= (1/2) x (112.5 - 40) x (11 - 3.75) = (1/2) x 72.5 x 7.25 = 262.8125

In following graph, initial position (case a) is at point A where MR intersects MC with price P0 and output Q0. Case (b) is at point B with price P1 and output Q1. Deadweight loss is area BCD.