The production of toilet paper in a perfectly competitive market is characterized by the inverse supply curve (marginal cost curve) P = 4Q, where Q is measured in millions of 4-roll packs per month. The inverse demand for toilet paper is P = 10 - 6Q. If the production of toilet paper causes an external marginal cost of 50 cents per 4-pack, the socially optimal price of toilet paper is $____ and the socially optimal quantity of toilet paper is ____ million.
A) 4; 1
B) 4.30; 0.95
C) 4.20; 1.05
D) 3; 2

Question

Quizplus · Accepted Answer

To find the socially optimal price and quantity, we need to account for the external marginal cost. The original supply curve is P = 4Q. With an external cost of 50 cents (or $0.50), the new supply curve (social cost curve) becomes P = 4Q + 0.50. Setting this equal to the demand curve (P = 10 - 6Q) and solving for Q gives us the socially optimal quantity. 4Q + 0.50 = 10 - 6Q leads to 10Q = 9.5, so Q = 0.95 million 4-roll packs. Substituting Q back into the demand or supply equation gives us the price, P = 4(0.95) + 0.50 = 4.30. Therefore, the socially optimal price is $4.30, and the socially optimal quantity is 0.95 million.

The Production of Toilet Paper in a Perfectly Competitive Market