# A-State ECON 6313 - Oligopoly (32 pages)

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## Oligopoly

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- School:
- Arkansas State University
- Course:
- Econ 6313 - Managerial Economics

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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 Industry or Product Refrigerators Motor vehicles Soft drinks Long distance telephone Laundry machines Breakfast foods Vaccuum cleaners Running shoes Beer Aircraft engines Domestic air flights Tires Aluminum Soap Pet food CR4 CR8 94 94 94 92 91 88 80 79 77 72 68 66 64 60 52 98 98 97 97 NA 93 96 97 94 83 82 86 88 73 71 Source U S Bureau of the Census Census of Manufacturers Concentration Ratios Less Concentrated Industries Industry or Product Fast food Personal computers Office furniture Toys Bread Lawn equipment Machine tools Paint Newspapers Furniture Boat building Concrete Women s dresses CR4 CR8 44 45 45 41 34 40 30 24 22 17 14 8 6 57 63 59 58 47 57 44 36 34 25 22 12 10 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 priceoutput 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 Figure 10 1 Dominant Firm Price Leadership Dollars per Unit of Output D Industry demand S Supply curve for small firms d Leader s net demand P P d MC P is the price established by D the dominant firm MR Q Qs Q QS Output 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 Augustin Cournot Research Into the Mathematical Principles of the Theory of Wealth 1838 1 Assumptions 1 Two sellers 2 MC 40 3 Homogeneous product 4 Q is the decision variable 5 Maximizing behavior Let the inverse demand function be given by P 100 Q 1 The revenue function R is given by R P Q 100 Q Q 100Q Q2 2 Thus the marginal revenue MR function is given by MR dR dQ 100 2Q 3 Let q1 denote the output of seller 1 and q2 is the output of seller 2 Now rewrite equation 1 P 100 q1 q2 4 The profit functions of sellers 1 and 2 are given by 1 100 q1 q2 q1 40q1 2 100 q1 q2 q2 40q2 5 6 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 5 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 4 we can say P 100 q1 10 90 q1 7 The the revenue function of seller 1 is given by R P q1 90 q1 q1 90q1 q12 8 Thus MR dR dq1 90 2q1 9 Subtracting MC from MR 90 2q1 40 0 10 2q1 50 q1 25 units 11 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 12 Best reply function Output of seller 2 Equation 12 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 30 10 0 15 25 30 Output of seller 1 In similar fashion we derive a best reply function for seller 2 It is given by q2 30 5q1 13 q2 30 0 q2 30 5q1 60 q1 So we have a system with …

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