Competition and Regulation. Lecture 2: Background on imperfect competition

Transcription

1 Competition and Regulation Lecture 2: Background on imperfect competition

2 Monopoly A monopolist maximizes its profits, choosing simultaneously quantity and prices, taking the Demand as a contraint; The rule for profit maximization is always the same MR=MC; Every time he wants to sell a larger quantity he must decrease prices. So the MR of the marginal unit he wants to sell is not the selling price, but less.

3 Figure 1: Marginal revenue for a monopolist

4 Figura 12-7: Linear demand function and marginal revenue A linear demand function produces a linear MR P=A-bQ TR=Q(A-bQ) MR=A-2bQ

5 Monopoly

6 Oligopoly When some firms are active but not too many, the maximizing choice of each firm will depend on strategic considerations; We analyze these through game theory, where agents participate in the games anticipating the payoffs and reactions of other agents; Equilibrium concept is central to discover the market outcome;

7 Collusion under Prisoners dilemma Coop. (P=10) Firm 1 Defect (P=9) Coop. Π 1 = 50 Π 1 = 75 Firm 2 Π 2 = 50 Π 2 = 0 Defect Π 1 = 0 Π 1 = 25 Π 2 = 75 Π 2 = 25 In this game there exist dominant strategies, strategies that are preferable under any circumstances, for both players, here Defect. The equilibrium is easy. Is it optimal for the players?

8 Exclusion of dominated strategies: A game where one firm has no dominant strategy No advert. Firm 1 Advert No Advert. Π 1 = 500 Π 1 = 750 Firm 2 Π 2 = 400 Π 2 = 100 Advert. Π 1 = 200 Π 1 = 300 Π 2 = 0 Π 2 = 200 Firm 1 has a dominant strategy but 2 doesn t. How to find equilibrium? Firm 2 knows that firm 1 cannot play No advert. So we can delete the first column.

9 Oligopoly: Nash equilibrium A Nash equilibrium is a set of strategies, one for each agent in the game, such that every agent maximizes its welfare given the others choice. In other terms from a situation that is a Nash equilibrium no agent has an incentive to move, taking for granted the other agents choices.

10 Dynamic games: Sub-game perfect NE: entry deterrence To play correctly, E must anticipate the response of I in case of entry and compare it to the case of stay out. It all depends on what the I will do after entry. Here it will certainly accomodate. That means entry is profitable.

11 Backward induction In practice the solution to this game can be found by backward induction that is working out the game from the end, deleting every time the paths that are out of equilibrium, the ones that will never be chosen.

12 Oligopoly: Bertrand

13 Bertrand: equilibrium Proof: An equilibrium with p i p j is impossible; The firm offering the higher price gets no demand and wants to lower its price; An equilibrium with p i =p j >c is impossible because both firms will lower their price to capture the whole market and increase their profits; An equilibrium with p i =p j <c is impossible, both firms will exit the market; p i =p j =c is a NE since no one will diverge;

14 Bertand with limited capacity The paradox of marginal cost pricing can be solved by relaxing some assumptions; Asymmetric costs or limited capacity can significantly change the equilibrium (as imperfect substitutability); Limited capacity: Suppose both firms can offer a maximum amount of k< D(p=c) Then the equilibrium p i =p j =c does not exist. Both firm in this situation will try to increase their price above c, because they can still get some demand given that at p=c the other firm will not be able to satisfy the whole demand; The standard bertand equilibrium is not a NE

15 Oligopoly: Cournot Keeping all other assumptions from the former slide but the assumption of price competition, substituting with output competition. For simplicity suppose (inverse) demand is p=1-q where Q= q i +q j

16 Cournot cont.nd. A NE is where both firms are happy with their quantity. That is point C. Analytically, the solution is: q i =(1-c)/3 for i=1, 2 p=(1+2c)/3 Π i =(1-c)/9 for i=1, 2

17 Cournot with n firms

18 Partial substitutability Most real world oligopolies are markets where the goods produced by one firm are not perfectly substitutable with another (brand or quality factors for example). We can capture this idea modifying the demand function as follows: q i =α-βp i +γp j When the price of good-j decreases, the quantity demanded of good-i decreases accordingly because consumers substitute away from i and choose more j. Exc.: Can you find a Nash Equilibrium for a Cournot and a Bertand market for goods i and j?

19 Partial Substitutability Two results emerge: Quantity competition is still less competitive (output is lower than in a Bertrand case) but due to partial substitutability even with Bertrand competition profits are strictly positive; Partial substitutability increases market power