Determine the retail disposal charge that will produce an efficient allocation of antifreeze.

Question

Suppose you are a public official responsible for setting a retail disposal charge on antifreeze. Estimated marginal benefit and cost functions for antifreeze are as follows:
MPB = 10.0 – 0.5Q MPC = MSC = 1.0 + 0.4Q
MSB = 10.0 –1.1Q,
whereMPB, MSB, and MPC are measured in dollars per gallon, and Q is in millions of gallons.

Answer 1

To calculate the retail disposal charge that achieves efficiency, first solve for the efficient output level (QE), where MSB = MSC, as follows:
MSB = MSC
10.0 –1.1Q = 1.0 + 0.4Q
9.0 = 1.5Q
QE = 6 million gallons

Notice how the efficient amount of antifreeze is less than the competitive level. This is to be expected for a good that generates a negative external benefit.

To achieve efficiency, the retail disposal charge should be set equal to –MEBat QE.
From part (a), MEB = –0.6Q
Evaluating –MEB at QE = 6 yields:–MEB = 0.6(6) = $3.60 per gallon
Adding this $3.60 to the value of MSB at QE, which is 10.0 – 1.1(6) = $3.40, yields an effective price to the consumer, including the retail disposal charge, of $7.00 per gallon.