Question

Ralph has a demand curve for office visits (Qd) to the doctor in a year given by Qd = 20 – (P/10) where P is the price of an office visit for Ralph.

If the marginal cost to the doctor for providing each visit is $50, what is the value of the moral hazard cost (hint: area of a triangle) resulting from Ralph buying this insurance?

Answer 1

Qd = 20 - (P/10)

10Qd = 200 - P

P = 200 - 10Qd

In efficient outcome, P = MC.

200 - 10Qd = 50

10Qd = 150

Qd = 15

P = MC = $50

A monopolist will equate marginal revenue (MR) with MC.

Total revenue (TR) = P x Qd = 200Qd - 10Qd²

MR = dTR/dQd = 200 - 20Qd

Equating with MC,

200 - 20Qd = 50

20Qd = 150

Qd = 7.5

P = 200 - (10 x 7.5) = 200 - 75 = $125

Moral hazard cost ($) = (1/2) x Change in price x Change in Qd =(1/2) x (125 - 50) x (15 - 7.5) = (1/2) x 75 x 7.5 = $281.25