Question

Suppose that the marginal benefits curve for plastic is given by: MB = 90 – 0.5Q, where quantity is measured in gallons. The private marginal cost curve is given by MC = 0.75Q. Assume that the production of plastic also leads to an additional cost to society of $5/gallon of plastic produced (Marginal External Cost = $5). Important: Please enter numbers, rounded to two decimals (e.g. 10.98, 350.01), without any symbols (do not enter $) for all of the numerical questions in this assignment.

What is the equilibrium QUANTITY of this good with NO government intervention?
What is the equilibrium PRICE of this good with NO government intervention?
What is the socially efficient quantity of this good?

What level of taxation would generate the socially efficient level of the good?

Answer 1

(1) With no government intervention, MB = MC.

90 - 0.5Q = 0.75Q

1.25Q = 90

Q = 72

P = 0.75 x 72 = 54

(2) Marginal social cost (MSC) = MC + Marginal external cost (MEC) = 0.75Q + 5

Social optimal is achieved by equating MB and MSC.

90 - 0.5Q = 0.75Q + 5

1.25Q = 85

Q = 68

(3) The optimal tax is equal to the MEC, i.e. $5 per unit.