In a region that must reduce emissions, three polluters currently emit 30 units of emissions. The three firms have the following marginal abatement cost functions that describe how marginal costs vary with the amount of emissions each firm reduces.

Suppose this region needs to reduce emissions by 14 units and plans to do it using a form of cap-and-trade that auctions allowances off to the highest bidder.

a. How many allowances will the control authority auction off? Why?

b. Assuming no market power, how many of the allowances would each firm be expected to buy? Why?

c. Assuming that demand equals supply, what price would be paid for those allowances? Why?

d. If the control authority decided to use an emissions tax rather than cap-and-trade, what tax rate would achieve the 14-unit reduction cost-effectively? Why?

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Firm Emissions Reduction 1 Firm 1 Marginal Firm 2 Marginal Firm 3 Marginal Cost Cost Cost $1.00 $1.00 $2.00 23 $1.50 $2.00 $3.00 $2.00 $3.00 $4.00 4 $2.50 $4.00 $5.00 5 $3.00 $5.00 $6.00 6 $3.50 $6.00 $7.00 7 $4.00 $7.00 $8.00 8 $4.50 $8.00 $9.00 6 $5.00 $9.00 $10.00 10 $5.50 $10.00 $11.00