There are four steel mills in town, A, B, C, and D. The following table reports

Question

There are four steel mills in town, A, B, C, and D. The following table reports
their current pollution and their respective marginal reduction cost (MCR). For
each plant, MCR is assumed to be constant (i.e., it doesn’t change with quantity).

Plant A: Pollution = 100; MCR per ton = $4

Plant B: Pollution = 80; MCR per ton = $3

Plant C: Pollution = 60; MCR per ton = $2

Plant D: Pollution = 40; MCR per ton = $2

Suppose the government wants to cut pollution in half and grants each plant permits
worth half of its current pollution.

(a) If the permits cannot be traded, what is the overall reduction cost?

(b) Calculate the overall reduction cost if the permits can be traded. Also, say who
buys and who sells?

Explanation / Answer

If the government gives each plant permits for half their current pollution amounts then the amount of permits, and thus amount of pollution each plant can produce, will be as follows...
Plant A: 50
Plant B: 40
Plant C: 30
Plant D: 20

a. Each firm must reduce their pollution by the above-mentioned amount at their current MCR.
Overall Reduction Cost = 50*$4 + 40*$3 + 30*$2 + 20*$2
Overall Reduction Cost = $420

b. Before the reduction, 280 units of pollution are produced. To cut that in half, 140 permits for polluting a unit are distributed, meaning 140 units must be eliminated. If permits are tradeable, the plants who are the most efficient at reducing pollution, the ones with the lowest MCR, will sell their permits to the plants who are least efficient. So, Plant C and D together are willing to sell 50 permits for anything above $2. Plant B is willing to buy 40 permits for anything below $3, and Plant A will buy 50 permits for anything below $4. The competitive bidding will cause Plant C and D to sell 50 permits to Plant A for $3. This leaves Plant A making no reductions, Plant B reducing by 40, Plant C reducing by 60, and Plant D reducing by 40 units.

Total Cost of Reduction = 50*$3 + 60*$2 + 40*$2
Total Cost of Reduction = $350

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.