Question

# I know the answer to this is 83, but I have no idea how to do...

I know the answer to this is 83, but I have no idea how to do this question. Can you help give me an explanation why? Thank you!

Refer to Table 10-5. If the government wanted to reduce pollution from 16 units to 6 units, which of the following fees per unit of pollution would achieve that goal?

Table 10-5

The following table shows the marginal costs for each of four firms (A, B, C, and D) to eliminate units of pollution from their production processes. For example, for Firm A to eliminate one unit of pollution, it would cost \$54, and for Firm A to eliminate a second unit of pollution it would cost an additional \$67.

 Firm Unit to be eliminated A B C D First unit 54 57 54 62 Second unit 67 68 66 73 Third unit 82 86 82 91 Fourth unit 107 108 107 111

Refer to Table 10-5. If the government wanted to reduce pollution from 16 units to 6 units, which of the following fees per unit of pollution would achieve that goal?

 a. \$67
 b. \$68
 c. \$81
 d. \$83

Let us do this step by step:

SInce number of units of pollution have to be reduced from 16 to 6, total reduction = 16 - 6 = 10 units

Now the table gives us the marginal cost of reducing pollution by 1 unit. A firm will reduce pollution if the marginal cost of reducing pollution is less than the fees charge per unit of pollution.

If fees is (a) 67, A reduces 2 units, B reduces 1 unit, C reduced 2 units and D reduces 1 unit. Total reduction = 6<10

If fees is (b) 68, A reduces 2 units, B reduces 2 unit, C reduced 2 units and D reduces 1 unit. Total reduction = 7<10

If fees is (c) 81, A reduces 2 units, B reduces 2 unit, C reduced 2 units and D reduces 2 unit. Total reduction = 8<10

If fees is (d) 83, A reduces 3 units, B reduces 2 unit, C reduced 3 units and D reduces 2 unit. Total reduction = 10

Thus, the required reduction is achieved at a fee of (d) \$83

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