Question

A firm in a perfectly competitive industry has patented a new process for making widgets. The new process lowers the firm’s average costs, meaning this firm alone can earn real economic profits in the long run.

(1) If the market price is $300 per widget and the firm’s marginal cost curve is given by MC=0.5q, how many widgets will the firm produce?

(2) Suppose a government study has found that the firm’s new process is polluting the air and estimates the external marginal cost of widget production by this firm to be XMC=0.1q. If the market price is still $300, what is the socially optimal level of production for the firm?

(3) What should the amount of a government – imposed excise tax be in order to bring about this optimal level of production?

Answer 1

1.The equilibrium of a profit maximising firm under perfect competition require :

Market Price = Mariginal Cost

300 = 0.5q

=> q=300/0.5

=> q=600

The firm will produce 600 units.

(2). XMC=0.1q

MP = 300

Marginal Social Cost = Marginal Cost + External Marginal Cost

= 0.5q + 0.1q = 0.6q

Socially optimal level of production is obtained when P=Total MC

300=0.6q

q=300/0.6

q=500

Hence, socially optimal level of production is 500.

(3).If goverment wants to bring about this change then goverment should impose tax upon the producers that firms marginal cost increases by negative externility.

Let the tax is denoted by T then ,

T=0.1q

Total tax imposed is 0.1*500=50.

So $50 tax is applied to bring about this optimal level of production.