Two firms, Industrio and Capitalista, have access to five production processes, each of which has a different cost and gives off a different amount of pollution. The daily costs of the processes and the corresponding number of tons of smoke emitted are shown in the table below. Both firms currently use process A, and each emits 4 tons of smoke per day. The government is considering two plans to reduce pollution: requiring both firms to reduce pollution by 25 percent or auctioning pollution permits. Each permit would entitle the owner to emit one ton of smoke per day. Without a permit, no smoke can be emitted. $$\begin{array} { | c | c | c | c | c | c | }
\hline & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } \
\hline \text { Process } & \text { (smoke/day) } & \text { (4 tons/day) } & \text { (3 tons/day) } & \text { (2 tons/day) } & \text { (1 tons/day) } \
\hline \text { Cost to Industrio (\$/day) } & \$ 350 & \$ 400 & \$ 500 & \$ 700 & \$ 1,000 \
\hline \text { Cost to Capitalista (\$/day) } & \$ 225 & \$ 250 & \$ 290 & \$ 400 &\$600 \
\hline
\end{array}$$ Suppose a permit system has been adopted and each firm has already purchased one permit. Industrio would be willing to pay up to ______ for the right to emit a second ton of smoke, and Capitalista would be willing to pay up to ______ for the right to emit a second ton of smoke.

Question

Two firms, Industrio and Capitalista, have access to five production processes, each of which has a different cost and gives off a different amount of pollution. The daily costs of the processes and the corresponding number of tons of smoke emitted are shown in the table below. Both firms currently use process A, and each emits 4 tons of smoke per day. The government is considering two plans to reduce pollution: requiring both firms to reduce pollution by 25 percent or auctioning pollution permits. Each permit would entitle the owner to emit one ton of smoke per day. Without a permit, no smoke can be emitted. $$\begin{array} { | c | c | c | c | c | c | } 
\hline & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } \
\hline \text { Process } & \text { (smoke/day) } & \text { (4 tons/day) } & \text { (3 tons/day) } & \text { (2 tons/day) } & \text { (1 tons/day) } \
\hline \text { Cost to Industrio (\$/day) } & \$ 350 & \$ 400 & \$ 500 & \$ 700 & \$ 1,000 \
\hline \text { Cost to Capitalista (\$/day) } & \$ 225 & \$ 250 & \$ 290 & \$ 400 &\$600 \
\hline
\end{array}$$ Suppose a permit system has been adopted and each firm has already purchased one permit. Industrio would be willing to pay up to ______ for the right to emit a second ton of smoke, and Capitalista would be willing to pay up to ______ for the right to emit a second ton of smoke.

Quizplus · Accepted Answer

To reduce pollution by 25 percent, both firms need to reduce their daily emissions to 3 tons of smoke. With one permit each, they can emit a total of 4 + 4 + 2 = 10 tons of smoke per day. Thus, they need to reduce their emissions by a total of 7 tons. One way to do this is for Industrio to emit 3 tons of smoke using processes A and C, and for Capitalista to emit 3 tons of smoke using processes A, B, and D. This would cost Industrio $350 + $500 = $850 per day, and Capitalista $225 + $250 + $400 = $875 per day.

Alternatively, they can trade permits. Suppose Industrio pays x dollars to Capitalista for the second permit. Then Industrio can emit 4 tons of smoke by using processes A and B, and pay $(350 + x) per day. Capitalista can emit 4 tons of smoke by using processes A and C, and pay $(225 + 290) per day. For this trade to be profitable for both firms, they must be willing to pay the amounts that make their costs equal:

$350 + x = $225 + $290 
x = $110

Thus, Industrio is willing to pay up to $110 for the second permit, and Capitalista is willing to sell it for this price.

Therefore, the best choice is to adopt a permit system and allow firms to trade permits.

Two Firms, Industrio and Capitalista, Have Access to Five Production