Recall from last time. Econ 410: Micro Theory. Cournot Equilibrium. The plan for today. Comparing Cournot, Stackelberg, and Bertrand Equilibria
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1 Slide Slide 3 Recall from last time A Nash Equilibrium occurs when: Econ 40: Micro Theory Comparing Cournot, Stackelberg, and Bertrand Equilibria Monday, December 3 rd, 007 Each firm s action is a best response to each other firm s action in an oligopolistic market The Cournot Model of oligopoly assumes Each firm treats the output of its competitors as fixed All firms decide simultaneously the optimal quantity to produce Reaction curves show: The relationship between a firm s optimal output and the amount it thinks its competitor will produce. Slide Slide 4 The plan for today Announcement Chapter, Exercise #3e will be extra credit Those who get this part of the problem completely correct will have 3 additional points (about 5%) added onto their problem set grade Questions about Problem Set Cournot Model Example The Stackelberg and Bertrand Models Oligopoly Wrap-Up Cournot Equilibrium Cournot equilibrium is an example of a Nash equilibrium But, the Cournot equilibrium says nothing about the dynamics of the adjustment process Since both firms adjust their output, neither output would be fixed at all points in time How can we use our knowledge of the Cournot model to see how firms will behave?
2 Slide 5 Slide 7 To make things simple, assume that firms face the same linear demand curve Each firm has the same constant marginal cost, and no fixed costs. How can we compare the Cournot equilibrium with one where the firms colluded (acted together)? Example Let the market demand curve for widgets be equal to P = 50 - Q Market quantity is Q = q +q Marginal cost for each firm is MC =MC =0 Remember: TR MR 50 q q q 50 q q q Setting MR equal to MC: 50 q q 0 Firm s reaction curve gives the optimal amount of q as a function of q It can be found by solving the equation above for q : 40 q q q 0 q Since both firms have identical costs and face the same market demand curve, we know: q 0 q Slide 6 Slide 8 Remember: P = 50 Q, Q = q +q, MC =MC =0 Firm will maximize profit taking firm s quantity as given: Firm s total revenue = P q But, the price firm will receive also depends on the quantity produced by firm : P = 50-(q +q ) TR = [50-(q +q )] q TR MR 50 q q q 50 q q q The reaction curves for each firm are: q =0 (/)q q =0 (/)q Substituting one equation into the other, we can solve for the Cournot Equilibrium: q =0 (/)(0 (/)q ) q =0 0 +(/4)q (3/4)q =0 q *= q * = 3 / 3 Market quantity = q + q = 6 / 3 Market Price = 50-6 / 3 = $3.33
3 Slide 9 Slide How does the Cournot equilibrium to compare to an equilibrium with collusion? What if the firms worked together to act as a monopoly? Quantity produced under monopoly Finding Marginal Revenue TR = PQ = (50-Q)Q = 50Q Q MR = TR/ Q = 50-Q Setting MR=MC 50 Q = 0 Q = 40 Q* = 0 If firms collude, q * = q * = 0 < 3 / 3 Sometimes one firm is able to enter a market before its competitors Example Pharmaceutical firms with patents The Stackelberg model illustrates cases where one firm sets its output before other firms do. Stackelberg Example Assume as before: P = 50-Q MC=$0 Firm sets output first Firm then makes an output decision seeing Firm s output Slide 0 Slide If firms collude, they will produce less output and earn higher profits than in a Cournot equilibrium q M = q M = 0 < 3 / 3 = q, Cournot Price under collusion P = 50 Q = 50 0 = $30 Total profits under collusion TR TC = PQ - MC Q = ($30-$0)0 = $400 Total profits under Cournot equilibrium TR TC = ($3.33-$0)6.66 = $ What should each firm do? Firm Must consider the reaction of Firm Firm Takes Firm s output as fixed Determines output with the Cournot reaction curve: q = 0 - ½(q ) Let s look at Firm s problem: Choose q such that MR = MC = $0 As before, TR = P q = 50 q - q - q q Firm knows Firm will choose output based on its reaction curve. We can use this!
4 Slide 3 Slide 5 Taking Firm s reaction curve into account, Firm finds optimal output Substituting the reaction curve for q : TR = P q = 50 q - q - q [0 - ½(q )] Finding marginal revenue: MR = TR/ q =30-q Setting MR = MC and solving for q *: 30 q = 0 q * = 0 Using the reaction curve, we find q : q * = 0 - ½(q ) = 0 Price Competition Sometimes oligopolies to compete in prices instead of quantities Price Wars The Bertrand Model is used to explain these situations. It assumes: Firms produce a homogeneous good Each firm treats a competitor s price as fixed All firms decide simultaneously what price to charge What will happen as firms compete? Slide 4 Slide 6 What can we learn from the Stackelberg model? Going first gives Firm the advantage Firm s output is twice as large as Firm s Firm s profit is twice as large as Firm s This allows Firm to produce a large quantity. Firm must account for this in order to maximize profit. The Bertrand Model Since goods in the Bertrand model are homogeneous, consumers will buy from the lowest priced seller If firms charge different prices, consumers buy from lowest priced firm only If firms charge the same price, consumers are indifferent as to who they buy from The Nash equilibrium in this case is equal to competitive output Each firm has an incentive to cut prices Both firms set price equal to MC, and both firms earn zero profit
5 Slide 7 Oligopoly Wrap-Up What have we learned about oligopolistic industries? Firm strategy is a critical component of firm decisions in an oligopoly Each firm must account for the decisions of every other firm in the industry Changing assumptions about price, quantity, and entry dramatically affects predicted industry outcomes Quantities range from those of competition to monopoly, based upon initial assumptions Slide 8 For next time We ll spend most of the class reviewing for the final Bring any questions you might have Please bring a # pencil to class You ll be using them to fill out the teaching evaluation form Problem Set Reminder Due this Wednesday Will be graded and handed back at the final Questions for Review are worth point each, while Exercises are worth points.
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