A = a constant, and
P = price.
?If price is increased by a proportionality factor of 1.05,
(2) Q2 = A[(1.05)P1]-21 and the demand function suggests that the quantity demanded must decrease by a proportionality factor equal to
(3) Q2/Q1 = (A/A)(1.05P1/P1)-21 = (1.05)-21 = 1/(2.786) = .36.
For expositional purposes, we use .35.
Thus, if a group of firms who initially supplied the competitive output formed a cartel and set a price 5 percent above the competitive level (Q1), the cartel output (Q2) would be 35 percent of the competitive output (Q1). Thus, if a nearby pipeline can expand output in the new market by at least 65 percent, the nearby pipeline is a potential entrant and must be included in the cartel.
The constant elasticity case is therefore more restrictive in the sense that it requires a noncolluding firm to be larger in size (65 percent versus 50 percent) to pose a competitive threat to the cartel if denied membership. Except in the long run, the larger size requirement tends to reduce the number of potential entrants, thereby limiting the size of the colluding group, and therefore it tends to increase the ability of the cartel to set a monopoly price and earn supracompetitive profits.
In Chapter 5, "The Intermediate Run", the number of competitive markets is estimated using both demand elasticity assumptions. Since divertible gas is limited in the intermediate run, the larger size requirement implicit in the constant elasticity case is expected to reduce the number of potential entrants and, in turn, reduce the number of competitive markets.