THE SIZE OF THE POTENTIAL ENTRANT
If a competitive market becomes monopolized by a colluding group of current suppliers who face a linear demand curve and constant costs, 1 a 5 percent increase in price 2 will maximize profits if the residual demand elasticity of the group is 10. 3 Further, the profit-maximizing level of output is 50 percent of the competitive output supplied by the colluding group. Our reasoning is as follows:
Starting from the initial competitive level of output (Q1) where the constant-cost market supply curve (S) intersects the residual demand curve (D), the colluding group will increase profits by reducing output as long as marginal revenue (MR) remains below constant marginal costs (MC). Profits are maximized at point M, where MR = MC. See Figure C.1.
At any price (P1), the corresponding point on the marginal revenue curve (M) will determine a level of output (Q2) that is one-half the quantity demanded (Q1) at that price. 4 Facing a demand elasticity (E) of 10, the colluding group will maximize profits by increasing P1 by 5 percent. That is, if
substituting E = 10 and dQ/Q = 50 and solving for dP/P yields dP/P = 5. 5 Thus, if a group of firms who initially supplied the competitive output formed a cartel and raised price 5 percent above the competitive level, the profit-maximizing cartel output would not exceed 50 percent of the competitive output.