Question

Suppose you are charged with determining the optimal amount of pollution for a community. You are told that the marginal social cost (MSC) of pollution for the community can be expressed as a linear relationship over the relevant quantities of pollution. You are also told that the marginal social benefit (MSB) of pollution for the community can be expressed as a linear relationship over the relevant quantities of pollution. data available:

- When there are 10 tons of pollution per day, the marginal costal cost of this level of pollution is $2000 per day

- When there are 20 tons of pollution per day the marginal social cost of this level of pollution is $3000 per day

- When all pollution per day is eliminated, the marginal social benefit of this level of pollution is $10,000 per day

- When there are 100 tons of pollution per day, the marginal social benefit of this level of pollution is $0 per day

A) Given this information write an equation for the MSC for this community. For your equation use MSC as your Y variable and the quantity of pollution (Q) as your X variable. Express your equation in slope-intercept form.

B) Given this information write an equation for the MSB for this community. For your equation use MSB as your Y variable and the quantity of pollution (Q) as your X variable. Express equation in slope intercept form.

C) Given the Equations you found in A and B, determine the optimal amount of pollution for this community. Explain why the optimal amount of pollution is not likely to be zero tons of pollution

Answer 1

Optimal level of pollution is given by condition where MSB is equal to MSC. If MSB>MSC (at lower level of Q), community will continue production since social profit is positive. this increases MSC and decreases MSB until both become equal. Similarly, if MSC>MSB (for higher level of Q), production will decrease as Social profit (MSB-MSC) is negative to a point where MSB=MSC.