Question

A firm produces a good q and receives a price p = 10 for the good. The marginal private cost of producing the good is MC = 2q. The production of each unit causes marginal external damage of 2 monetary units.

a) Without regulation, how many units does the firm produce?

b) How many units does the firm produce if it is liable for its damage?

c) What are the efficiency gains from implementing liability laws if the implementation has no cost?

d) How high should a Pigouvian tax per unit of production be to incentivize socially efficient production?

e) Instead of a tax, the government subsidizes production with 2 monetary units per unit of production. How high is the efficiency loss of production with subsidies compared to the socially efficient production level?

(No explanation needed)

Answer 1

a) P = MC gives 10 = 2q and so q (market quantity) is 10/2 = 5 units in an unregulated market

b) Then we have MSB = MSC and so we use 10 = 2q + 2. This gives q = 4 units at socially efficient level

c) It will be the increase in welfare = 0.5*(10 - 8)*(5 - 4) = $1

d) Tax should be the marginal external cost at efficient quantity. It is $2.

e) Now MC is 2q - 2. This causes quantity to rise to 6 units

Efficiency loss = 0.5*(10 - 6)*(6 - 4) = $4