Oligopoly • Outline: • Salient features of oligopolistic market structures. • Measures of seller concentration • Dominant firm oligopoly • Rivalry among symmetric firms (The Cournot model) • The kinked demand curve
Oligopoly is derived from the Greek work “olig” meaning “few” or “a small number.” Oligopoly is a market structure featuring a small number of sellers that together account for a large fraction of market sales.
Features of oligopoly • Fewness of sellers • Seller interdependence • Feasibility of coordinated action among ostensibly independent firms
Measures of seller concentration • The concentration ratio is the percentage of total market sales accounted for by an absolute number of the largest firms in the market. • The four-firm concentration ratio (CR4) measures the percent of total market sales accounted for by the top four firms in the market. • The eight-firm concentration ratio (CR4) measures the percent of total market sales accounted for by the top eight firms in the market.
Concentration Ratios: Very Concentrated Industries Source: U.S. Bureau of the Census, Census of Manufacturers
Concentration Ratios: Less Concentrated Industries Source: U.S. Bureau of the Census, Census of Manufacturers
Seller interdependence • If Kroger offers deep discounts on soft drinks, will Wal-Mart follow suit? • Northwest Airlines “perks” miles do not expire—how did United, Delta, et al react? • Verizon carries unused minutes over the to next month—implications for Cingular, et. al.? • Some ISP’s now pledge not to sell information to database companies—will this affect AOL? • Alcoa’s decision to add production capacity is conditioned upon the investment plans of rival aluminum producers.
Price-Output Determination in Oligopolistic Market Structures We have good models of price-output determination for the structural cases of pure competition and pure monopoly. Oligopoly is more problematic, and a wide range of outcomes is possible.
Dominant firm price leadership • This is a system of price-output determination we sometimes see in oligopolistic market structures in which there is one firm that is clearly dominant. • General Motors was once the price leader in the U.S. auto industry. • Other “dominant” firms include Du Pont in chemicals, US Steel (now USX), Phillip Morris, Fedex, Boeing, General Electric, AT&T, and Hewlett Packard.
The model • The dominant firm sets the market price and remaining firms sell all they wish at this price. • The demand curve for the price leader is found by subtracting the market demand curve from the supply curve of the remaining sellers in the market.
S u p p l y c u r v e e a d e r ' s f o r s m a l l f i r m s e t d e m a n d ' P * P M C M R * Q Q s O u t p u t Figure 10.1: Dominant Firm Price Leadership D o l l a r s p e r U n i t o f O u t p u t D I n d u s t r y d e m a n d S L d n P* is the price established by the dominant firm D d Q* + QS
Example Let the market demand curve be given by: QD = 248 – 2P The supply curve for 10 small firms in the market is given by: QS = 48 + 3P The dominant firm’s “residual” or net demand curve is given by the market demand curve minus the supply of the 10 other firms, or: Q = QD – QS = 248 – 2P – (48 + 3P) = 200 – 5P The inverse (residual) demand curve facing the dominant firm is given by: P = 40 - .2Q
Assume the dominant firm has a marginal cost function given by: MC = .1Q The dominant firm would maximize its own profits by setting MR = MC. To derive the MR, find the revenue (R) function and take the first derivative with respect to Q: R = P • Q = (40 - .2Q)Q = 40Q - .2Q2 MR = dR/dQ = 40 - .4Q Now set MR = MC and solve for Q 40 - .4Q = .1Q.5Q = 40 Q = 80 Units P = 40 – (.2)(80) = $24 At the price established by the dominant firm, the remaining 10 firms collectively supply 120 units (or 12 units each).
Cournot Model1 • Illustrates the principle of mutual interdependence among sellers in tightly concentrated markets--even where such interdependence is unrecognized by sellers. • Illustrates that social welfare can be improved by the entry of new sellers--even if post-entry structure is oligopolistic. 1 Augustin Cournot. Research Into the Mathematical Principles of the Theory of Wealth, 1838
Assumptions • Two sellers • MC = $40 • Homogeneous product • Q is the “decision variable” • Maximizing behavior Let the inverse demand function be given by: P = 100 – Q  The revenue function (R) is given by: R = P • Q = (100 – Q)Q = 100Q – Q2 
Thus the marginal revenue (MR) function is given by: MR = dR/dQ = 100 – 2Q  Let q1 denote the output of seller 1 and q2 is the output of seller 2. Now rewrite equation  P = 100 – q1 – q2  The profit () functions of sellers 1 and 2 are given by: 1 = (100 – q1 – q2)q1 – 40q1  2 = (100 – q1 – q2)q2 – 40q2 Mutual interdependence is revealed by the profit equations. The profits of seller 1 depend on the output of seller 2—and vice versa
Monopoly case Let q2 = 0 units so that Q = q1—that is, seller 1 is a monopolist. Seller 1 should set its quantity supplied at the level corresponding to the equality of MR and MC. Let MR – MC = 0 100 – 2Q – 40 = 0 2Q = 60 Q = QM = 30 units Thus PM = 100 – QM = $70 Substituting into equation , we find that: = $900
Finding equilibrium Question: Suppose that seller 1 expects that seller 2 will supply 10 units. How many units should seller 1 supply based on this expectation? By equation , we can say: P = 100 – q1 – 10 = 90 – q1  The the revenue function of seller 1 is given by: R = P • q1 = (90 – q1)q1 = 90q1 – q12  Thus: MR = dR/dq1 = 90 – 2q1 
Subtracting MC from MR 90 – 2q1 – 40 = 0  2q1 = 50 q1 = 25 units  Thus the profit maximizing output for seller 1, given that q2 = 10 units, is 25 units. We repeat these calculations for every possible value of q2 and we find that the -maximizing output for seller 1 can be obtained from the following equation: q1 = 30 - .5q2
Best reply function Equation  is a best reply function (BRF) for seller 1. It can be used to compute the -maximizing output for seller 1 for any output selected by seller 2. 60 30 - .5q2 Output of seller 2 30 10 25 30 0 15 Output of seller 1
In similar fashion, we derive a best reply function for seller 2. It is given by: q2 = 30 - .5q1  q2 30 q2 = 30 - .5q1 0 60 q1
So we have a system with 2 equations and 2 unknowns (q1 and q2) : q1 = 30 – .5q2q2 = 30 – .5q1 The solutions are: q1 = 20 units q2 = 20 units q2 Equilibrium is established when both sellers are on their best reply function 60 Seller 1’s BRF 30 Equilibrium Seller 2’s BRF 20 0 20 30 60 q1
Cournot duopoly solution QCOURNOT = 40 Units (20 units each)PCOURNOT = $601 = 2 = $400 Note that: PCOMPETITIVE = $40QCOMPETITIVE = 60 Units Therefore PCOMPETITIVE < PCOURNOT < PMONOPOLY
Implications of the model The Cournot model predicts that, holding elasticity of demand constant, price-cost margins are inversely related to the number of sellers in the market This principle is expressed by the following equation  Where is elasticity of demand and n is the number of sellers. So as n , the price-margin approaches zero—as in the purely competitive case.
Theory of 2 demand curves Sellers in concentrated market structures must form expectations about the likely reaction of rivals before taking action (for example, cutting prices).
If I cut my price to $2.49/gallon, what’s the guy down the street going to do?
Price FD is the “followship” or “constant” market share” demand curve NF is the “non-followship” or “changing market share” demand curve. NF FD 0 Quantity
Which demand curve is relevant? If the firm assumes that rivals will ignore (that is, fail to match) price cuts or increases, then NF is relevant. However, if the firm assumes that rivals will follow any price adjustments, then FD applies.
It is reasonable to assume that rivals will follow price cuts,but not price increases. In that case, the firm faces a “kinked” demand curve
Price Firm faces NF above the kink and FD below the kink. FD K P0 NF 0 q0 Quantity
Incentive to Price At the Kink • Above P0, demand is elastic—hence by raising price revenue will decrease. • Below P0, demand is elastic—hence by decreasing price revenue will decrease. Price > 1 K P0 < 1 0 q0 Quantity
D o l l a r s p e r U n i t o f O u t p u t * P D e m a n d M C ' M C M R * Q O u t p u t Marginal cost can vary in a wide range and the results do not change