Question

Unit of Pollution Marginal Cost of damage Consider a scenario where there are 15 total units of pollution occurring within a given area. The per unit cost of damage increases by $3 each time pollution increases as the pollution gets ever closer to the absorptive capacity of the environment (see the table to the left). There are three sectors in this economy each contributing 5 units of pollution. Each firm could conceivably clean up this pollution; however due to differences in their production processes and technological capacities each sector has its own cost of control (see the table below). Use this information to assess different policies for achieving pollution control. Unit of Marginal cost Marginal cost Marginal cost of tement of control in of control in control in /Control Agriculture Tranport Manufacturing 0 SO $0 $5 $4 21 $10 S8 $15 $12 $20 $16 $25 $20 $48 15 $45 1) (5 points) Graphically illustrate the marginal cost of damage and the marginal costs of control on the same graph where pollution goes from left to right on the horizontal axis, abatement goes from right to left on the horizontal axis and costs are displayed from $0 to $50 on the vertical axis. Based on this information, what would the socially optimal level of pollution (and abatement) be? What would the optimal tax rate be under this scenario?

Answer 1

Profit = Total marginal control cost- Total cost of pollution=B-C....., x= units of pollution, y= unit of control

First order condition or FOC= B'-C'=0 or B'=C' and second order condition or SOC= B'' $\leqslant$ C''

B= 12 for 1 unit, 24 for 2unit, 39 for 3rd unit, 60 for 4 unit, 93 for 5 unit.

FOC is equal at x= 4, 8, 13. B'= 12 for y=1, B'=15 for y=2, B'=21 for y=3.The SOC is satisfied for x= 8, y=2 where B''=C''=3

So, optimal solution= y=2 and B= 24, MC=24, x=8.... so, socially optimal level of control=2 and socially optimal level of pollution=0.

social marginal cost= private marginal cost + tax rate

or s=p+t

or s= 24*8= 192, here p= unknown

so, optimal tax = 192-p.

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