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Homework answers / question archive / Consider a competitive industry that extracts a valuable mineral from deep underground
Consider a competitive industry that extracts a valuable mineral from deep underground. The industry faces market demand for the mineral given by P=200−2QP=200−2Q and extraction incurs a constant marginal private cost and an average cost of 20. Suppose that the government realizes that by extracting minerals, the industry is seriously harming and contaminating underground aquifers. The marginal external cost imposed by the activity is equal to E=3QE=3Q. What is the Pigouvian tax imposed on firms that pushes the industry to produce at the socially efficient level of output?
A. 20
B. 36
C. 90
D. 108
E. 540
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.
