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Microeconomics I

Microeconomics I. Undergraduate Programs Fernando Branco 2006-2007 Second Semester Sessions 8 and 9. Game-theoretical oligopoly models. Stackelberg oligopoly. There are a few suppliers; Outputs are differentiated or homogeneous;

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Microeconomics I

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  1. Microeconomics I Undergraduate Programs Fernando Branco 2006-2007 Second Semester Sessions 8 and 9

  2. Game-theoretical oligopoly models

  3. Stackelberg oligopoly • There are a few suppliers; • Outputs are differentiated or homogeneous; • One supplier (the leader) decides its output before the others. • The other suppliers (followers) decide after observing the leader’s decision.

  4. Equilibrium in the Stackelberg oligopoly

  5. Reaction function: Follower’s decision • The followes sets quantity to maximize its profit: • Optimal output level of the follower, given the leader’s decision. • In general, it slopes downward.

  6. Leader’s decision • The leader maximizes its profit, taking in consideration the follower’s decision:

  7. Stackelberg versus Cournot

  8. Game-theoretical oligopy models

  9. Bertrand oligopoly • There are a few suppliers; • Outputs are homogeneous (and provided with constant marginal cost); • Suppliers take price decisions simultaneously; • Buyers have complete information and no transaction costs; • There are entry barriers.

  10. Supplier decisions • Buyers purchase the output from the lowest price supplier. • If one supplier knew other’s price, what price would like to choose? • A price just slightly below the other’s, as long as it is not below the marginal cost.

  11. Equilibrium • The equilibrium is reached if all firms price at marginal cost. • Two suppliers are enough to provide the same outcome as perfect competition.

  12. Cost differences • What would happen if supplier have different marginal costs? • Example • If the difference is small, the equilibrium price is equal to the marginal cost of the less efficient supplier; otherwise, the more efficient supplier price at its monopoly level.

  13. Demand: • Costs: • If c < 6: • If c 6: Example with different costs • Equilibrium:

  14. Bertrand oligopoly in pratice • It is not easy to find example of Bertrand oligopolies in practice. • The suppliers’ profits would be zero. • Hence, sppliers try to find eays to increase their profits (for example differentiation of collusion).

  15. Game-theoretical oligopy models

  16. The dominant firm oligopoly • The are a few suppliers; • Outputs are homogeneous; • One supplyer sets the price (the dominant firm); • Other suppliers are price takers, and adust their supply to the price set.

  17. Followers’ decisions • Suppliers from the competitive fringe follow the dominant firm’s price. • Each maximizes its profit. • Hence, these suppliers decide as in perfect competition: • They adjust the supply to equalize marginal cost to price.

  18. Dominant firm’s decision • The dominant firm sets the price to maximize its profit: • The dominant firm acts as a monopolist on the residual demand (the demand left after subtracting the supply of the followers).

  19. A numeric example • Market demand: • Dominant’s cost: • Costs of the 2 followers: • Followers’ supply: • Residual demand: • Price chosen: • Supplies:

  20. QS MCS D DR P* MCD QSi QD Q* Example: graphical analysis P Q

  21. Game-theoretical oligopy models

  22. Price choices with differentiation • The strategic interactions are similar to those in Cournot oligopolies (simultaneous choices) or Stackelberg oligopolies (sequential choices) • Main difference: reaction curves slope uprwards. • Algebraic example.

  23. Simultaneous choice: algebraic example • Demands: • Costs: • Reaction functions: • Equilibrium:

  24. R1 R2 Simultaneous choice:graphical analysis

  25. Sequential choices: algebraic example • Demands: • Costs: • Follower’s reaction function: • Leader’s objectives: • Equilibrium:

  26. R1 R2 Sequential choices: graphical analysis

  27. Collusion and cartels • Suppliers may collude to decrease competitive pressure. • Ina cartle, suppliers decide production quotas and/or set prices, to increase profits. • Example: OPEC.

  28. Incentives to cartels • Supplies may increase profits. • Problem similar to that of a multi-unit supplier that needs to decide how to split the activities. • Additionally, compensatory payments may be needed to enforce the cartel.

  29. The cartel objective

  30. Limits to cartels • Legal limits: • Work implicit collusion. • Instability of cartels: • If one supplier knows the quantity of the other, it will want to make its choice to be on its reaction curve. • This creates an instability in the cartels.

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