Microeconomics I Undergraduate Programs Fernando Branco Second Semester Sessions 8 and 9

Microeconomics IUndergraduate Programs Second Semester Sessions 8 and 9©Fernando Branco Game-theoretical oligopoly models SimultaneousSequential QuantityCournotStackelberg Price Homog.Bertrand Dominant Firm Different. Strategic Complements

Microeconomics IUndergraduate Programs Second Semester Sessions 8 and 9©Fernando Branco 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.

Microeconomics IUndergraduate Programs Second Semester Sessions 8 and 9©Fernando Branco Equilibrium in the Stackelberg oligopoly

Microeconomics IUndergraduate Programs Second Semester Sessions 8 and 9©Fernando Branco –Optimal output level of the follower, given the leader’s decision. –In general, it slopes downward. The followes sets quantity to maximize its profit: Reaction function: Follower’s decision

Microeconomics IUndergraduate Programs Second Semester Sessions 8 and 9©Fernando Branco The leader maximizes its profit, taking in consideration the follower’s decision: Leader’s decision

Microeconomics IUndergraduate Programs Second Semester Sessions 8 and 9©Fernando Branco Stackelberg versus Cournot

Microeconomics IUndergraduate Programs Second Semester Sessions 8 and 9©Fernando Branco Game-theoretical oligopy models SimultaneousSequential QuantityCournotStackelberg Price Homog.Bertrand Dominant Firm Different. Strategic Complements

Microeconomics IUndergraduate Programs Second Semester Sessions 8 and 9©Fernando Branco 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.

Microeconomics IUndergraduate Programs Second Semester Sessions 8 and 9©Fernando Branco 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.

Microeconomics IUndergraduate Programs Second Semester Sessions 8 and 9©Fernando Branco Equilibrium The equilibrium is reached if all firms price at marginal cost. Two suppliers are enough to provide the same outcome as perfect competition.

Microeconomics IUndergraduate Programs Second Semester Sessions 8 and 9©Fernando Branco 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.

Microeconomics IUndergraduate Programs Second Semester Sessions 8 and 9©Fernando Branco Example with different costs Demand: Costs: Equilibrium: –If c < 6: –If c  6:

Microeconomics IUndergraduate Programs Second Semester Sessions 8 and 9©Fernando Branco 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). Bertrand oligopoly in pratice

Microeconomics IUndergraduate Programs Second Semester Sessions 8 and 9©Fernando Branco Game-theoretical oligopy models SimultaneousSequential QuantityCournotStackelberg Price Homog.Bertrand Dominant Firm Different. Strategic Complements

Microeconomics IUndergraduate Programs Second Semester Sessions 8 and 9©Fernando Branco 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.

Microeconomics IUndergraduate Programs Second Semester Sessions 8 and 9©Fernando Branco 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.

Microeconomics IUndergraduate Programs Second Semester Sessions 8 and 9©Fernando Branco 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).

Microeconomics IUndergraduate Programs Second Semester Sessions 8 and 9©Fernando Branco A numeric example Market demand: Dominant’s cost: Costs of the 2 followers: Followers’ supply: Residual demand: Price chosen: Supplies:

Microeconomics IUndergraduate Programs Second Semester Sessions 8 and 9©Fernando Branco Example: graphical analysis Q P QDQD QSiQSi Q* P* MC D QSQS MC S D DRDR

Microeconomics IUndergraduate Programs Second Semester Sessions 8 and 9©Fernando Branco Game-theoretical oligopy models SimultaneousSequential QuantityCournotStackelberg Price Homog.Bertrand Dominant Firm Different. Strategic Complements

Microeconomics IUndergraduate Programs Second Semester Sessions 8 and 9©Fernando Branco 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.

Microeconomics IUndergraduate Programs Second Semester Sessions 8 and 9©Fernando Branco Reaction functions: Costs: Demands: Equilibrium: Simultaneous choice: algebraic example

Microeconomics IUndergraduate Programs Second Semester Sessions 8 and 9©Fernando Branco Simultaneous choice: graphical analysis R2R2 R1R1

Microeconomics IUndergraduate Programs Second Semester Sessions 8 and 9©Fernando Branco Follower’s reaction function: Costs: Demands: Leader’s objectives: Equilibrium: Sequential choices: algebraic example

Microeconomics IUndergraduate Programs Second Semester Sessions 8 and 9©Fernando Branco Sequential choices: graphical analysis R1R1 R2R2

Microeconomics IUndergraduate Programs Second Semester Sessions 8 and 9©Fernando Branco 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.

Microeconomics IUndergraduate Programs Second Semester Sessions 8 and 9©Fernando Branco 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. Incentives to cartels

Microeconomics IUndergraduate Programs Second Semester Sessions 8 and 9©Fernando Branco The cartel objective

Microeconomics IUndergraduate Programs Second Semester Sessions 8 and 9©Fernando Branco 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.