Question

Consider a market where the demand curve is given by P = 200 – 0.2Q and the supply curve is given by P = 50 + 0.1Q. Production of this good generates an external cost as measured by the marginal external cost function MEC = 0.1Q.

If the government wants to encourage firms to produce at the socially efficient level of output then how large should the per unit tax be?

Answer 1

The private benefit function is the demand curve.

P = 200 - 0.2Q

The private cost function is the supply curve.

P = 50 + 0.1Q

The social cost curve = Private cost + MEC = 50 + 0.1Q + 0.1Q = 50 + 0.2Q

The social optimal output is where,

Private benefit = Social cost

200 - 0.2Q = 50 + 0.2Q

0.4Q = 200 - 50 = 150

Q = 150 / 0.4 = 375

MEC = 0.1Q = 0.1(375) = $37.50

The per unit tax is equal to the MEC.

Thus, if the government wants to encourage firms to produce at the socially efficient level of output, then the per unit tax should be $37.50.