- a. OPEC maximizes its profit by setting MR MC. We have 115 4Q
15. Therefore, Q 25 million barrels per day. In turn, P $65 per
barrel.
b. If it sets P $50, then Q 57.5 (.5)(50) 32.5 million barrels
per day. Profit (per day) is: (50 15)(32.5) $1.1375 billion.
If it sets P $65, its initial profit is: 1 (65 15)(25) $1.25
billion per day. In the second 5-year period, its optimal quantity and
price are: Q 2 18 million barrels per day and P 2 $60. (Check this
by using the long-run demand curve and setting MR MC.) Thus,
its profit is: 2 (60 15)(18) $.81 billion per day. OPEC’s
average profit over the decade (ignoring discounting) is $1.03
billion per day—lower than $1.1375 billion from holding its price to
$50 per barrel. - a. At P $10, 2 million trips are demanded. In the text, we saw that
each fully utilized taxi had an average cost per trip of $8 and,
therefore, earned an excess profit of (10 8)(140) $280 per week.
The commission should set the license fee at L $280 to tax away all
this excess profit. Assuming that 14,286 taxis operate (just enough to
meet the 2 million trips demanded), the commission collects a total of
$4 million in license fees.
b. The rearranged demand curve is P 14 2Q. We saw that the extra
cost of adding a fully occupied taxi is $1,120 per week, or $8 per trip.
The relevant MC per trip is $8. Setting MR MC, we have 14 4Q 8.
Thus, QM1.5 million trips and PM$11. The maximum total
profit for the industry is (11 8)(1.5) $4.5 million. The
number of taxis 1,500,000/140 10,714.
c. If the market could be transformed into a perfectly competitive one,
the result would be PCmin AC $8, QC 7 (.5)(8) 3 million
trips, and the number of taxis is 21,428.
d. Taxi trips are not perfect substitutes. If a taxi charges a fare slightly
higher than the industry norm, it will not lose all its sales. (Customers
in need of a taxi will take the one in hand, rather than wait for a slightly
cheaper fare.) Since there is room for product differentiation and price
differences, the taxi market probably is best described as monopolistic
competition. In this setting, all cabs make zero profit (due to free
entry). If price settles at P $9, then AC $9 for each cab. This AC
occurs at about 121 trips per week; each taxi is 86 percent utilized. Trip
demand is 2.5 million supplied by 2,500,000/121 20,661 taxis.
*11. a.Each supplier maximizes profit by setting P MC. Since MC 4 2Q,
this implies QF(P 4)/2. With 10 firms, QS5P 20.
b. The buyer’s profit is (10 P)QS(10 P)(5P 20). To
maximize profit, set d/dP 0. The result is 70 10P 0, implying
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