Question

Assume the marginal cost of pollution is given by MC=Q, where Q denotes the quantity of pollution measured in % on a scale from 0 to 100. The marginal cost of reduction (MCR) is given by MCR=1. Refer to the Coase Theorem and calculate the optimal quantity of pollution AND the welfare gain that results from trade (compared to a pollution of zero or of 100, resp.) when

1. there is an exclusive property right to clean air and

2. there is an exclusive property right to polluting the air.

(note that Q ranges from zero to 100)

Answer 1

Consider the given problem here “MC” of pollution and the “MCR” of reducing pollution are given, => at the optimum “MC” must be equal to “MCR”.

=> MCR = MC, => Q=1, => the optimum pollution is given by, “Q*=1”. Consider the following fig.

So, if the pollution reduced from “Qm=100” to “Q*=1”, => the welfare increase is given by, “A1A2E1”, because total cost decreases by “QmA1E1Q*” and “total cost to firm” increases by “E1A2QmQ*”, => the difference will be the welfare gain that is “A1A2E1”.

So, the area under the “A1A2E1” is given by, “0.5*(100-1)*(100-1) = 4,900.5.

Now, if there is a property right to clean air, => firm have to reduce pollution from “100” to “1”. Similarly, if there is a property right to polluting air, => either firm will pollute “100 units” or it will reduce its pollution to “1 unit”, where society will make some compensation payment to reduce the pollution have to reduce pollution from “100” to “1”, where the maximum amount that the society pay must be less than or equal to “A1A2E1”.