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
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.
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