Finance 30210: Managerial Economics Strategic Pricing Techniques

Market Structures Recall that there is an entire spectrum of market structures Perfect Competition Many firms, each with zero market share P = MC Profits = 0 (Firm’s earn a reasonable rate of return on invested capital) NO STRATEGIC INTERACTION! Monopoly One firm, with 100% market share P > MC Profits > 0 (Firm’s earn excessive rates of return on invested capital) NO STRATEGIC INTERACTION!

Most industries, however, don’t fit the assumptions of either perfect competition or monopoly. We call these industries oligopolies Oligopoly Relatively few firms, each with positive market share STRATEGIES MATTER!!! Wireless (2002) Verizon: 30% Cingular: 22% AT&T: 20% Sprint PCS: 14% Nextel: 10% Voicestream: 6% US Beer (2001) Anheuser-Busch: 49% Miller: 20% Coors: 11% Pabst: 4% Heineken: 3% Music Recording (2001) Universal/Polygram: 23% Sony: 15% EMI: 13% Warner: 12% BMG: 8%

Market shares are not constant over time in these industries! Airlines (1992)Airlines (2002) American Northwest Delta United Continental US Air American United Delta Northwest Continental SWest While the absolute ordering didn’t change, all the airlines lost market share to Southwest.

Another trend is consolidation Retail Gasoline (1992)Retail Gasoline (2001) Shell Exxon Texaco Chevron Amoco Mobil Exxon/Mobil Shell BP/Amoco/Arco Chev/Texaco Conoco/Phillips Citgo BP Marathon Sun Phillips Total/Fina/Elf

The key difference in oligopoly markets is that price/sales decisions can’t be made independently of your competitor’s decisions Monopoly Oligopoly Your Price (-) Your N Competitors Prices (+) Oligopoly markets rely crucially on the interactions between firms which is why we need game theory to analyze them!

Continuous Choice Games Consider the following example. We have two competing firms in the marketplace.  These two firms are selling identical products.  Each firm has constant marginal costs of production. What are these firms using as their strategic choice variable? Price or quantity? Are these firms making their decisions simultaneously or is there a sequence to the decisions?

Cournot Competition: Quantity is the strategic choice variable D There are two firms in an industry – both facing an aggregate (inverse) demand curve given by Total Industry Production Both firms have constant marginal costs equal to $20

From firm one’s perspective, the demand curve is given by Treated as a constant by Firm One Solving Firm One’s Profit Maximization…

In Game Theory Lingo, this is Firm One’s Best Response Function To Firm 2 0 If firm 2 drops out, firm one is a monopolist!

What could firm 2 do to make firm 1 drop out?

3 1 Firm 2 chooses a production target of 3 Firm 1 responds with a production target of 1

The game is symmetric with respect to Firm two… Firm 1 chooses a production target of 1 Firm 2 responds with a production target of 2

Firm 1 Firm 2 Eventually, these two firms converge on production levels such that neither firm has an incentive to change We would call this the Nash equilibrium for this model

Recall we started with the demand curve and marginal costs

The markup formula works for each firm

Had this market been serviced instead by a monopoly,

Had this market been instead perfectly competitive,

MonopolyPerfect Competition 2 Firms

D $ CS = (.5)(120 – 70)(2.5) = $62.5 $62.5 What would it be worth to consumers to add another firm to the industry? Recall, we had an aggregate demand and a constant marginal cost of production. Monopoly $120

D $ CS = (.5)(120 – 53)(3.33) = $112 $112 Recall, we had an aggregate demand and a constant marginal cost of production. Two Firms

Suppose we increase the number of firms…say, to 3 Demand facing firm 1 is given by (MC = 20) The strategies look very similar!

D $ CS = (.5)(120 – 45)(3.75) = $140 $140 With three firms in the market… Three Firms

Expanding the number of firms in an oligopoly – Cournot Competition Note that as the number of firms increases: Output approaches the perfectly competitive level of production Price approaches marginal cost. N = Number of firms

Increasing Competition

Firm 1 Firm 2 The previous analysis was with identical firms. Suppose Firm 2’s marginal costs increase to $30 50%

Firm 2 Suppose Firm 2’s marginal costs increase to $30 If Firm one’s production is unchanged

Firm 1 Firm 2 Firm 2’s market share drops Firm 1’s Market Share increases 42% 58%

The previous analysis (Cournot Competition) considered quantity as the strategic variable. Bertrand competition uses price as the strategic variable. D Q* P* Should it matter? Just as before, we have an industry demand curve and two competing duopolies – both with marginal cost equal to $20. Industry Output

D Quantity Strategy D Bertrand Case Firm level demand curves look very different when we change strategic variables If you are underpriced, you lose the whole market If you are the low price you capture the whole market At equal prices, you split the market

Price competition creates a discontinuity in each firm’s demand curve – this, in turn creates a discontinuity in profits As in the cournot case, we need to find firm one’s best response (i.e. profit maximizing response) to every possible price set by firm 2.

Firm One’s Best Response Function Case #1: Firm 2 sets a price above the pure monopoly price: Case #3: Firm 2 sets a price below marginal cost Case #2: Firm 2 sets a price between the monopoly price and marginal cost Case #4: Firm 2 sets a price equal to marginal cost What’s the Nash equilibrium of this game?

However, the Bertrand equilibrium makes some very restricting assumptions…  Firms are producing identical products (i.e. perfect substitutes)  Firms are not capacity constrained MonopolyPerfect Competition 2 Firms

An example…capacity constraints Consider two theatres located side by side. Each theatre’s marginal cost is constant at $10. Both face an aggregate demand for movies equal to Each theatre has the capacity to handle 2,000 customers per day. What will the equilibrium be in this case?

If both firms set a price equal to $10 (Marginal cost), then market demand is 5,400 (well above total capacity = 2,000) Note: The Bertrand Equilibrium (P = MC) relies on each firm having the ability to make a credible threat: “If you set a price above marginal cost, I will undercut you and steal all your customers!” At a price of $33, market demand is 4,000 and both firms operate at capacity

With competition in price, the key is to create product variety somehow! Suppose that we have two firms. Again, marginal costs are $20. The two firms produce imperfect substitutes. D Example:

Recall Firm 1 has a marginal cost of $20 Each firm needs to choose price to maximize profits conditional on the other firm’s choice of price. Firm 1 profit maximizes by choice of price D Firm 1’s strategy $30 Firm 2 sets a price of $50 Firm 1 responds with $55

Firm 1 Firm 2 With equal costs, both firms set the same price and split the market evenly

MonopolyPerfect Competition 2 Firms

Firm 2 Suppose that Firm two‘s costs increase. What happens in each case? Bertrand $30 With higher marginal costs, firm 2’s profit margins shrink. To bring profit margins back up, firm two raises its price

Firm 1 Firm 2 Suppose that Firm two‘s costs increase. What happens in each case? With higher marginal costs, firm 2’s profit margins shrink. To bring profit margins back up, firm two raises its price A higher price from firm two sends customers to firm 1. This allows firm 1 to raise price as well and maintain market share!

Cournot (Quantity Competition): Competition is for market share  Firm One responds to firm 2’s cost increases by expanding production and increasing market share  Best response strategies are strategic substitutes Bertrand (Price Competition): Competition is for profit margin  Firm One responds to firm 2’s cost increases by increasing price and maintaining market share  Best response strategies are strategic complements Firm 1 Firm 2 Firm 1 Firm 2 BertrandCournot

Stackelberg leadership In the previous example, firms made price/quantity decisions simultaneously. Suppose we relax that and allow one firm to choose first. Both firms have a marginal cost equal to $20 Firm 1 chooses its output first Firm 2 chooses its output second Market Price is determined

Firm 2 has observed Firm 1’s output decision and faces the residual demand curve:

Knowing Firm 2’s response, Firm 1 can now maximize its profits: Firm 1 produces the monopoly output!

MonopolyPerfect Competition 2 Firms (67%) (33%)

Sequential Bertrand Competition We could also sequence events using price competition. Both firms have a marginal cost equal to $20 Firm 2 chooses its price first Firm 2 chooses its price second Market sales are determined

Recall Firm 1 has a marginal cost of $20 From earlier, we know the strategy of firm 2. Plug this into firm one’s profits… Now we can maximize profits with respect to firm one’s price.

Sequential Bertrand Competition MonopolyPerfect Competition 2 Firms

Cournot vs. Bertrand: Stackelberg Games Cournot (Quantity Competition):  Firm One has a first mover advantage – it gains market share and earns higher profits. Firm B loses market share and earns lower profits  Total industry output increases (price decreases) Bertrand (Price Competition):  Firm Two has a second mover advantage – it charges a lower price (relative to firm one), gains market share and increases profits.  Overall, production drops, prices rise, and both firms increase profits.