Models of Competition Part III: Imperfect Competition Agenda: First let’s review… A continuum of competition: two key questions 3. Models of Imperfect Competition A. Monopolistic Competition B. Cournot Oligopoly C. Stackelberg Oligopoly D. Bertrand Oligopoly 4. Game theory

First let’s review…. What is the profit maximizing condition for perfect competitors? MR = MC What is the profit maximizing condition for a monopolist? MR = MC If supply and demand are: P = 100 + Q and P = 1000 – 2Q What is the equilibrium price and quantity, aggregate producer and consumer surplus for a perfectly competitive firm? (hint: area of triangles!) 100 + Q = 1000 – 2Q Q = 300 P = $400 CS = ½ (600 * 300) = $90,000 PS = ½ (300 * 300) = $45,000 What is the equilibrium price and quantity, producer and consumer surplus and dead weight loss for a monopoly? (hint: draw the graph!) 100 + Q = 1000 - 4Q Q = 180 P = $640 CS = ½ (360 * 180) = $32,400 PS = (360 * 180) + ½ (180*180)= $81,000 DW = ½ (360 * 120) = $21,600

Monopolistic Competition A Continuum of Competition…. Perfect Competition Monopolistic Competition Oligopoly Monopoly Causes of monopoly: Economies of scale (production technology – go back to gnomes), regulation (we don’t want everyone tearing up the roads to lay gas pipe, we want to know who to go to when something blows up) Network externalities, Location (also a form of product differentiation) Patents Of the four assumptions underlying perfect competition, really only two are important: product differentiation and barriers to entry/exit. Pricing power comes from these (assumption #2) and we never have perfect information (transactions costs) Key questions: Is there meaningful product differentiation? Are there significant barriers to entry or exit?

Models of imperfect competition Model Assumptions Limitations Monopolistic Competition Differentiated Products are imperfect substitutes NO barriers to entry Firms act independently, do NOT respond to other firms Oligopoly Products are close substitutes HIGH barriers to entry (including economies of scale) Cournot Firms take other firms’ QUANTITY as given Firms produce equal quantities Stackelberg 2nd mover can NOT respond to 1st mover 1st mover advantage. 1st mover produces same quantity as monopolist. Bertrand Firms simultaneously choose PRICE Price = MC same as perfect competition Game Theory! Firms strategically anticipate and respond to other firms’ actions Few Nash equilibria, context specific implications

Monopolistic Competition: The Chamberlin Model Key features: Many firms Free entry and exit Symmetry – what’s good for one is good for the others equally X Differentiated products make imperfect substitutes Edward Chamberlin Joan Robinson Chamberlin, E.H. (1933) The Theory of Monopolistic Competition: A Re-orientation of the Theory of Value. Harvard University Press, Cambridge MA. Robinson, J. (1933) The Economics of Imperfect Competition, MacMillian, London. Poor Joan was British and a woman and the paper was written in 1933, so as Americans we only refer to the “Chamberlin” model Friedman argued that Chamberlin model added nothing to the model of perfect competition (1953) “The methodology of positive economics,” in Essays in Positive Economics, Chicago: Chicago University Press. Dixit and Stiglitz (1977) “Monopolisitc competition and optimum product diversity” American Economic Review, 67:297 – 308 Symmetry is necessary to make the math models work, not for the intuition, so we won’t focus on that. A matter of degree…. Monopolistic Competition in the History of Economic Thought http://ccso.eldoc.ub.rug.nl/FILES/root/2002/200215/200215.pdf

Monopolistic Competition: The Short Run Joan Robinson Market demand curve Which is more ELASTIC? Firm demand curve P2 Firm demand is more elastic because customers can easily switch to competitors – but if you need (want) a shirt you ultimately get one so market demand is less elastic Q2 Entry of close substitutes Is this firm making a producer surplus? Is this firm making a profit? What will happen in the long run?

Monopolistic Competition: Long-run Implications REVIEW: What is Allocative Efficiency? Is there any producer surplus in the long run? Is there any economic profit in the long run? Is there allocative efficiency in the long run?

What is Allocative Efficiency in a Perfectly Competitive Market? REVIEW: What is Allocative Efficiency in a Perfectly Competitive Market? What can make the supply curve slope up in the long-run? Is there producer surplus in the long run? Is there consumer surplus in the long run? See P&R p. 455 for a graphical comparison of long-run equilibrium in perfect and monopolistic competition

Monopolistic Competition Perfect Competition Monopolistic Competition The value of diversity! Avinash Dixit Joseph Stiglitz

Antoine Augustin Cournot Oligopoly: The Cournot Model Few firms (test yourself: why?) Firms choose quantity at the same time and then the market sets price Products must be relatively close substitutes. 5 75 Antoine Augustin Cournot (1801-1877) KEY: Each firm takes the other’s quantity as GIVEN, which reduces the demand available to them! See P&R p. 459

Antoine Augustin Cournot Oligopoly: The Cournot Model A firm’s RESPONSE FUNCTION expresses its Quantity in terms of the other firm’s Quantity Antoine Augustin Cournot (1801-1877) Recall the general linear demand function: Response functions with MC = 0 Equilibrium is when Q1 = Q2 See P&R p. 461 for a numerical derivation which requires some calculus to get the marginal revenue.

Example: Garden Gnomes…AGAIN! Another firm manages to come up with different technology that also makes Garden Gnomes absorb CO2 and combat global warming. They have a patent too, and conveniently the same cost structure as you. So now the market is a duopoly. (Round Q to nearest whole #) Market demand: QD = 6500 -100P or P = 65 – Q/100 FIRM #1 marginal revenue: 65-2Q1/100 –Q2/100 FIRM #2 marginal revenue: 65-2Q2/100 –Q1/100 FIRM total cost: C(q) = 722 + q2/200 FRIM marginal cost: MC(q) = 2q/200 = q/100 NOTE q = Q1 or Q2 depending on which firm you’re thinking about! What is the response function for Q1 (an expression for Q1 in terms of Q2)? HINT: remember, if in doubt try MR = MC! Q1 = 2167 –Q2/3 How much does Q1 produce? HINT: remember there is symmetry in the response functions since both firms have the same cost structure. Q1 = 2500 –(2500-Q1/3)/3 Q1 = 1,606 3. What is the equilibrium price and quantity for the market? Q = 3,212 P = $32.88

TEST YOURSELF! Compare the equilibrium price, quantity, profit, producer and consumer surplus for the perfectly competitive, monopoly and Cournot Duopoly markets!

Oligopoly: The Stackelberg Model Firm #1 (leader) knows that firm #2 (follower) will take firm #1’s quantity as given following the Cournout model… Demand Function Heinrich Freiherr von Stackelberg 1905 - 1946 Substitute firm #2’s response function assuming MC = 0 What is Firm #1’s Marginal Revenue Function? Firm #1 Demand Function

Oligopoly: The Stackelberg Model Continued What is on the X and Y axis? What kind of functions are graphed? First mover produces the same quantity as a pure monopolist Cournot equilibrium As long as second mover doesn’t respond and push the equilibrium to Cournot How is Stackelberg different from Cournot? First Mover Advantage!!

Joseph Louis François Bertrand Oligopoly: The Bertrand Model Firms choose price and the market sets quantity Each firm takes the other’s price as given Firm #1 Lower Price Same Price Higher Price Joseph Louis François Bertrand  (1822 – 1900) Firm #2 Lower Price all half nothing all all all all half nothing Same Price Price set at MC Same as perfect competition! half half half Higher Price all half nothing nothing nothing nothing Collusion Cartels Dynamic games

A Framework for thinking about problems From Basar & Olsder Dynamic Noncooperative Game Theory (1999) p. 2 One decision maker Many decision makers One decision (a series of independent decisions) Static Mathematical programming, Static optimization Static Game Theory Multiple related decisions Dynamic Optimal control theory, Dynamic optimization Dynamic or differential game theory Game theory – I know that you know, and will respond, and you know that I know and will respond… Applications of game theory: Economics, politics, war, infectious disease, engineering, artificial intelligence, portfolio management, product development

Oligopoly Game 8 Rules of the game: Pick a red or a black card and put it against your chest so no one can see it. I’ll pair you randomly with another player. Show each other your cards and compute your pay-off Play red card: you get 2 (cut your price) Play black card: your opponent gets 3 (keep your price the same) We’ll play 5 rounds – the first two with random partners and the last three with the same partner. Highest earners get .5 bonus point (another .5 for the next game…) 8 (row, column) You do not need to assume anything about the other player or take any of his or her actions as given. Both actions contribute to the outcome.

The Prisoner’s Dilemma Dominant Strategy: You do better no matter what your opponent does. Von Neumann & Morgenstern Maxmin: Pick the best of the worst-case scenarios Row: 10 or 2 > 8 or 0 Column: 10 or 2 > 8 or 0 Nash is a professor at Princeton. Nobel in 1994. 28 page dissertation leading to “The Nash Equilibrium” Von Neumann, J., and O. Morgenstern. 1953. Theory of Games and Economic Behavior 3rd. Ed. Princeton, NJ: Princeton University Press All dominant strategies are Nash, but not all Nash are dominant strategies Nash Equilibrium: No player has an incentive to change strategies. Often one player has a dominant strategy, and the other chooses a dominant strategy given their opponent’s dominant strategy. http://en.wikipedia.org/wiki/John_Forbes_Nash,_Jr.

Standardized Product, Low Barriers → Perfect Competition Standardized Product, High Barriers → Monopoly, Oligopoly Diversified Product, Low Barriers → Monopolistic Competition Diversified Product, High Barriers → Monopoly, Oligopoly