Two firms, Kegareta Inc. and Sucio Enterprises, have access to five production processes, each one of which has a different cost and gives off a different amount of pollution. The daily costs of the processes and the corresponding number of tons of smoke emitted are shown in the accompanying table.
Suppose the government wants to reduce pollution by 50 percent by imposing a tax of $T per day on each ton of smoke emitted. Of the options listed, what's the smallest tax, $T, that will achieve this goal?
A)$51
B)$56
C)$61
D)$54

Question

Two firms, Kegareta Inc. and Sucio Enterprises, have access to five production processes, each one of which has a different cost and gives off a different amount of pollution. The daily costs of the processes and the corresponding number of tons of smoke emitted are shown in the accompanying table.   
Suppose the government wants to reduce pollution by 50 percent by imposing a tax of $T per day on each ton of smoke emitted. Of the options listed, what's the smallest tax, $T, that will achieve this goal?
A)$51 
B)$56 
C)$61 
D)$54

Quizplus · Accepted Answer

Initially both firms will choose production process A, and together they will emit 8 tons of smoke per day. To reduce pollution by 50 percent, total emissions will need to fall to 4 tons per day. For each firm, the marginal benefit of reducing pollution by 1 ton is the amount of the tax, $T. The marginal cost to Kegareta Inc. of reducing pollution by 1 ton (moving from A to B, from B to C, from C to D, and from D to E)is $45, $50, $55, and $60, respectively; for Sucio Enterprises, the corresponding marginal costs are $55, $75, $95, and $115. When the tax is $56, Kegareta will move to production process D (and emit 3 tons per day), and Sucio Enterprises will move to production process B (and emit 1 ton per day), which will meet the 4 ton per day goal. Any tax less than $56 will not achieve the desired reduction in pollution.

Two Firms, Kegareta Inc