Consider a competitive industry that extracts a valuable mineral from deep underground

D. $108

Reason:

Given :

Marginal Private Benefit (MPB) = P = 200 - 2Q

Marginal Private Cost (MPC) = $20

The market equilibrium is determined at the level where the MPB = MPC

Thus equating the MPB and MPC from the given data we have,

200 - 2Q = 20

2Q = 180

Q = 90 units

Putting the value of Q in the MPB equation we have,

P = 200 - (2*90)

P = 200 - 180

P = $20

Hence the market attains equilibrium at 90 units of output at a price of $20

But it is seen that, the consumption and production of this good is creating a marginal external cost : E (MEC) = 3Q

This means that the Marginal social cost > Marginal private cost

Marginal social cost (MSC) = MPC + MEC

Putting the value of MPC and MEC in the above equation we have,

MSC = 20 + 3Q

At the social optimum level, the MSC = MPB

Equating MSC and MPB we have,

200 - 2Q = 20 + 3Q

5Q = 180

Q = 36 units

Putting the value of Q in MSC we have,

MSC = 20 + 3* 36

MSC = P = $128

So the amount of pigouvian tax to be charged = $128 - $20 = $108

The additional tax of $108 per unit will internalise the negative externality generated during the consumption and production process of the good.