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Strategic Pricing: Theory, Practice and Policy Professor John W. Mayo mayoj@georgetown.edu

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Prices, Industry Supply & Demand, and the Role of Industrial Organization mc ac D $ CS = Consumer Surplus Pricing above competitive levels imposes economic welfare losses S

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Monopoly and Competition mc ac D mr $ cs Prices are higher under Monopoly than competition

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The Role of Market Structure in Pricing Suppose that: Market Demand Q=1000-1000P MC = $.28 How do optimal prices compare depending on Market Structure and the nature of competition?

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Perfect Competition MC D 720 Q Industry P=.28 Regardless of Market demand Price is driven by the equality Of price and marginal cost

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Monopoly MC D 720 Q Firm P=.28 mr P=.64 360 π = PQ -.28Q π = [1 – (1/1000Q)]Q -.28Q π = Q -.001Q 2 -.28Q So, taking the first derivative And setting equal to 0: Dπ/dQ = 1 -.002Q -.28 =0 Q = 360 Plugging into the demand function P=.64.

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The Role of Industrial Organization on Pricing Competition v. Monopoly Strategic Interactions Among Competitors Oligopoly Few competitors Barriers to entry Possible reactions to price/output changes: Competitors match price decreases, but not price increases Model: Sweezy oligopoly Price is determined by market output. Each competitors set output to maximize profit given the output of rivals Model: Cournot Oligopoly Firms constantly seek to undercut competitors’ prices Model: Bertrand oligopoly Price leadership (One or more firm calls out price and others follow) Model: Dominant Firm-Competitive fringe Models most typically rely upon Nash equilibrium concept Each firm is optimizing given the behavior of its rivals

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Sweezy Oligopoly D1 D2 mr1 mr2 Q P Suppose price is initially at P 0. If competitors follow price decreases, but not increases, then a kinked demand results P0P0

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Sweezy Oligopoly D1 D2 mr1 mr2 Q P Implications: prices are non-responsive to changes in mc over a range – consider mc1 and mc2 mc1 mc2

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Nash equilibrium In a Nash equilibrium, each firm is optimizing, given the behavior of other firms John Nash 1994 Nobel Laureate

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Cournot Oligopoly Price is determined by total market output (relative to demand) So my strategy must account for the output of rivals If duopoly: Q1* =r1(Q2) and Q2* = r2(Q1)

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Cournot Model: Nash equilibrium as number of firms changes mr1 D1 With an initial equilibrium of Qm,Pm, consider the output of a second firm. The second firm takes the output of Firm 1 as given, then optimizes on the Residual demand curve (the lower Half of the original demand) mr2 Pm P2 The result is P2. What is Firm 1’s reaction? Qm $ Q Assume mc=0 Qc

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Cournot Model: Nash equilibrium as number of firms changes mr1 D1 mr2 Pm P2 The result is P2. What is Firm 1’s reaction? Firm 1, then takes the output of firm 2 as given and reduces its output. Why? Because firm 2 has taken ¼ of market.

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Cournot Quantity Adjustments

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Reaction Functions In Cournot, each firm seeks to maximize profit given the output of its rival. So, we can examine how firm 1’s output changes as firm 2 has different outputs. Denote Q 1 *(Q 2 ) Q1Q1 Q2Q2 Note that in our previous example, increases in Q 2 were met with reductions in Q 1 Q1*(Q2) Similarly, for Q2*(Q1) Cournot- Nash equilibrium Q2*(Q1)

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Cournot: A linear demand example Suppose that market demand is P= 30-Q and MC 1 =MC 2 = 0. What is firm 1’s reaction function? Revenue for firm 1 = PQ 1 = (30-Q)Q 1 = (30 – Q 1 - Q 2 )Q 1 = 30Q 1 – Q 1 2 – Q 1 Q 2 Thus, MR = 30-2Q 1 -Q 2 Set MR=MC and solve for Q 1 : Q 1 = 15 - 1/2Q 2 Similarly, Q 2 = 15-1/2Q 1

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Cournot: linear demand (cont.) Q1 Q2 Q 1 = 15 - 1/2Q 2 Q 2 = 15 - 1/2Q 1 Solving the reaction functions simultaneously: 10 How does this compare with a Competitive equilibrium for the firms? How does this compare with the case of Collusion?

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Stackelberg Consider that firms compete in quantities, but now… Suppose that instead of firms choosing outputs simultaneously, one firm is the leader and output is sequential

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Stackelberg If firm 1 goes first, then it will maximize profit given the reaction function of firm 2 Recall that in our example Rev 1 = PQ 1 = 30Q 1 – Q 1 2 –Q 1 Q 2 But firm 1 knows how firm 2 will react to its output, so substituting in the reaction function from 2, we get Rev 1 = 15Q 1 -1/2Q 1 2, so MR = 15 –Q 1, so Q1* = 15, Q2* = 7.5. Why is the equilibrium different from simultaneous Cournot?

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Bertrand Oligopoly Homogeneous Differentiated

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Dynamic Pricing Considerations Cournot and Bertrand are static What if playing (in competition with) a rival repeatedly?

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Pricing: Dynamic considerations Suppose rivals announce intention to raise price If cooperate, then your profits are $10 per period, forever. If “cheat”, then profits increase (say to $50) this period with zero thereafter.

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Pricing: Dynamic considerations Look at NPV of cooperative behavior compared to NPV of non-cooperative behavior Assume infinitely repeated NPV = 0 + ’ t * (1/(1+r)) t = [(1 + r)/r] 0 NPV CO = 10 + 10 * (1/(1+r)) t = 10 + 10*1/r NPV NC = 50 + 0 * (1/(1+r)) t = 50 NPV CO > NPV NC if r <.25 In this example, if very impatient, cheat. Otherwise cooperate with price increase. Pricing strategy will depend upon discount rates and the relative payoff from defection

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IF competing in long-run Folk Theorem – says that with a low discount rate, any price between MC and P M can be equilibrium Engendering cooperation Focal prices [Knittle and Stango (AER 2003)] Standardize timing of price changes Pre-announcement of price changes (upward) Trigger Strategies (tit-for-tat; grim trigger) Most Favored Customer Clause Match rivals’ price (create “whistle blowing” consumers) “Giant now honoring Safeway coupons”

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Price Ceilings as Focal Points Knittle and Stango study the credit card market 1450 bank-issued cards 90 % of states in late 70s/early 80s had interest rate ceilings (18% was most common) Find tacit collusion consistent with price ceilings serving as focal points Tacit collusion is more likely when: (a) concentration is higher (b) costs are higher (c ) firms are larger (d) but lower when demand is high

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