Determine the deposit/refund amount that achieves an efficient solution.
State officials are establishing a deposit/refund system for batteries. Marginal costs and benefits have been estimated to be:
MPC = 5 + 0.5Q MPB = MSB = 20 – 0.5Q
MSC = 5 + 0.7Q,
whereQ is in millions, and the marginal cost and benefit values are in dollars per battery.
The deposit/refund amount that achieves efficiency is equal to the MEC at the efficient equilibrium. Find the efficient equilibrium by setting MSB equal to MSC, and solve for QE as follows:
MSB = MSC
20 – 0.5Q = 5 + 0.7Q
15 = 1.2Q
?QE = 12.5 million
MEC is found as the difference between MSC and MPC.
MEC = MSC – MPC = 5 + 0.7Q – (5 + 0.5Q) = 0.2Q.
Evaluating MEC at QE yields:
MEC = 0.2(12.5) = $2.50 = deposit/refund
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