1 / 12

Price-Output Determination in Oligopolistic Market Structures

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. Cournot Model 1.

kura
Download Presentation

Price-Output Determination in Oligopolistic Market Structures

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. 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.

  2. 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

  3. 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 [1] The revenue function (R) is given by: R = P • Q = (100 – Q)Q = 100Q – Q2 [2]

  4. 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 [5] 2 = (100 – q1 – q2)q2 – 40q2[6] Mutual interdependence is revealed by the profit equations. The profits of seller 1 depend on the output of seller 2—and vice versa

  5. 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

  6. 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]

  7. 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]

  8. Best reply function 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 Output of seller 2 30 10 25 30 0 15 Output of seller 1

  9. In similar fashion, we derive a best reply function for seller 2. It is given by: q2 = 30 - .5q1 [13] q2 30 q2 = 30 - .5q1 0 60 q1

  10. 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

  11. Cournot duopoly solution QCOURNOT = 40 Units (20 units each)PCOURNOT = $601 = 2 = $400 Note that: PCOMPETITIVE = $40QCOMPETITIVE = 60 Units Therefore PCOMPETITIVE < PCOURNOT < PMONOPOLY

  12. 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 [14] 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.

More Related