Consumption, Production, Welfare B: Monopoly and Oligopoly (partial eq) Univ. Prof. dr. Maarten Janssen University of Vienna Winter semester 2013

2 Profit maximisation Monopolist P Q ATC MC D MR QMQM PMPM Profit ATC Pricing rule Profit π = P(Q)Q – C(Q) When is monopoly outcome Pareto inefficient?

3 On which part of demand curve is the monopolist’s price? P Q Q Demand Elastic Inelastic MR Total Revenue (€) Total revenue=PQ Marginal revenue =

Oligopoly: between monopoly and perfect competition On demand side always many consumers who take prices as given On supply side – Under perfect competition, firms take prices as given (problems with increasing returns to scale) – Under monopoly, one firm takes effect on price into account (look at previous formulaes) – Middle ground: what if there are some firms (more than one, not many) Have to take actions, reactions into account (game theory) Subtleties important, for example, what are the decision variables (price or quantity) of the firms Here, two basic models: Cournot (quantity) and Bertrand (price)

5 Cournot Model 2 (or more) firms Market demand is P(Q) Firm i cost is C(q) Firm i acts in the belief that all other firms will put some amount Q -i in the market. Then firm i maximizes profits obtained from serving residual demand: P’ = P(Q) - Q -i For each output produced by the others, firm is the monopolist for the residual demand

6 Demand and Residual Demand Market demand P(Q)=P(q 1,Q -1 =0) q1q1 P(q 1 ) P(q 1, Q -1 =10) P(q 1, Q –1 =20)

7 Cournot Reaction Functions Firm 1’s reaction (or best-response) function is a schedule summarizing the quantity q 1 firm 1 should produce in order to maximize its profits for each quantity Q -1 produced by all other firms. Since the products are (perfect) substitutes, an increase in competitors’ output leads to a decrease in the profit- maximizing amount of firm 1’s product (  reaction functions are downward sloping). Check for monopoly

8 Profit maximisation Monopolist for different demands P Q ATC MC D MR QMQM PMPM Profit ATC Pricing rule Profit π = P(Q)Q – C(Q) When is monopoly outcome Pareto inefficient? D‘ MR’

9 Cournot Model A firm can only decide bout what it will produce. It has to take as given what others produce. What others produce is, however, relevant. The problem Max{(P(q i +Q -i ) q i – C(q i )} defines the best-response (or reaction) function of firm i to a conjecture Q -i as follows: P’(q i +Q -i )q i + P(q i +Q -i ) – C’(q i ) = 0 Linear case on blackboard Q -i qiqi qiMqiM qjqj r1r1 qi*(qj)qi*(qj) Firm i’s reaction Function Q -i =0

10 Cournot Equilibrium Situation where each firm produces the output that maximizes its profits, given a conjecture about the output of rival firms Conjectures about what the others produce are correct No firm can gain by unilaterally changing its own output

11 Cournot Equilibrium q2q2 q1q1 q1Mq1M r1r1 r2r2 q2Mq2M Cournot equilibrium q 1 * maximizes firm 1’s profits, given that firm 2 produces q 2 * q 2 * maximizes firm 2’s profits, given firm 1’s output q 1 * No firm wants to change its output, given the rival’s Beliefs are consistent: each firm “thinks” rivals will stick to their current output, and they do so!

Rewriting optimal decision rule

13 Properties of Cournot equilibrium The pricing rule of a Cournot oligopolist satisifes: Cournot oligopolists exercise market power: – Cournot mark-ups are lower than monopoly markups – Market power is limited by the elasticity of demand More efficient firms will have a larger market share. The more firms, the lower will be each firm’s individual market share and market power.

Symmetric Cournot competition with N firms; linear case

15 Bertrand Model 2 (or more) firms – Firms produce identical products at constant marginal cost. – Each firm independently sets its price in order to maximize profits Consumers enjoy – Perfect information – Zero transaction costs

16 Bertrand Equilibrium Firms set P 1 = P 2 = MC! Why? Suppose MC < P 1 < P 2 Firm 1 earns (P 1 - MC) on each unit sold, while firm 2 earns nothing Firm 2 has an incentive to slightly undercut firm 1’s price to capture the entire market Firm 1 then has an incentive to undercut firm 2’s price. This undercutting reasoning continues... Equilibrium: Each firm charges P 1 = P 2 = MC

17 Bertrand Paradox Two firms are enough to eliminate market power – If firms are symmetric, market power is eliminated entirely – If firms are asymmetric (MC 1 < MC 2 ), market power is substantially reduced Solutions (in course on Industrial Organization): – Capacity constraints – Repeated interaction – Product differentiation – Imperfect information