Question

Two firms, Washburn (W) and Pillsbury (P), emit effluent into the Mississippi River as part of their flour-making operations. This effluent causes problems with the biochemical balance in the river and so the government wants to cut the amount of emissions by 10,000 gallons per day. W has an older factory and so has a higher cost of reducing its effluent emissions.The two total abatement cost functions (with abatement measured in thousands of gallons per day) are:

TCw = 6 + 4Aw + 3Aw²

TCp = 4 + 2Ap + Ap²

a. Find each firm’s marginal abatement cost function.

b. The government decides to fix the effluent problem using tradable permits. What is the market price of a permit? How much abatement does each firm do?

c. How much money does the tradable permits plan save relative requiring W to do all the abatement itself?

Answer 1

a.Abatement Cost Function

TCw= 6+4Aw+3Aw²

TCp= 4+2Ap+Ap^{​​​​​2}

Here

6,4 quantum of emission(in measure of 1000Gallons) by Washburn (W) and Pillsburry (P)

4Aw, 2Ap are the abatement cost of the emission

3Aw², Ap​​​^​2​​​​ are the abatement permit cost of the emission

b. Market Price of the Permit

W = 3× 1000 = 3000

P= 1× 1000 = 1000

Abatement done by each firm

W = 6×1000=6000

P= 4×1000= 4000

c.If W did all abatement itself without considering permit

It will save upto 3000

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