Answers to Odd-Numbered Problems 19optimal result in part (b). The competitive market price, including
tax, becomes: 60 10 $70.
d. At an added cost of $12, low-impact studded tires are not cost
effective. At a market price of $70 as in part (b) or (c), they cannot
compete profitably and should not be produced.- a. The firms’ costs are C 1 2Q 1 .1Q 12 and C 2 .15Q 22. It follows
that MC 1 2 .2Q 1 ; MC 2 .3Q 2. In turn, MB 9 .4Q 9
.4(Q 1 Q 2 ).
b. Setting MB MC 1 MC 2 , we find Q 1 5 and Q 2 10, and the
common marginal value is $3. It is economically efficient for firm 2 to
clean up more pollution than firm 1 since its marginal cost of cleanup
is lower.
c. Each firm cleans up to the point where MC $4; Using the MC
expressions in part (a), we find Q 1 10 and Q 2 13.33.
d. The optimal tax is $3.00 (equal to the common value of MB MC 1
MC 2 ). Facing this tax, the firms choose Q 1 5 and Q 2 10, as in
part (b). - a. To maximize net benefit (i.e. benefit minus cost), RWE should
compare MB and MC, where MC $150,000 per facility. The optimal
number of facilities is: N 4. Adopting the program at the fourth
facility implies MB $225,000 (greater than MC) but adopting at the
fifth facility has MB $100,000 (less than MC). RWE’s maximum net
benefit at N 4 is: 1,600,000 (4)(150,000) $1,000,000.
b. The additional benefit to society means that MB increases by $75,000.
Now the optimal number of facilities is N 6. Adopting the program
at the sixth facility has MB $100,000 $75,000 (greater than MC)
but adopting at the seventh facility has MB $50,000 $75,000 (less
than MC).
c. Requiring N 8 reduces total net benefit relative to N 6 in part
(b). The marginal benefits of adopting the program at the seventh
and eighth facilities are not worth the marginal costs.
d. Without any regulatory intervention, RWE would enroll only 4
facilities in the health and safety program (as in part a). An OSHA
subsidy per facility would encourage RWE to expand the safety
program. The optimal subsidy is exactly equal to the marginal social
benefit generated by the program. Thus, the appropriate subsidy is
exactly $75,000 per facility. In response, RWE will extend the program
to 6 facilities as recommended in part (b). - a. Sketching the demand curve, we find the price intercept to be $3.00
and the quantity intercept to be 900 cars. At a rate of $1.50, 450 cars
will park each hour, implying revenue of $675 per hour. In turn,
BMAns.qxd 9/26/11 11:18 AM Page 19