Strategic Interaction Finance 510: Microeconomic Analysis

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 STRATEGIC INTERACTION! 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%

Further, these market shares are not constant over time! 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 (+) Oligopolistic markets rely crucially on the interactions between firms which is why we need game theory to analyze them!

The Airline Price Wars $500 $ Suppose that American and Delta face the given aggregate demand for flights to NYC and that the unit cost for the trip is $200. If they charge the same fare, they split the market P = $500P = $220 P = $500$9,000 $3,600 $0 P = $220$0 $3,600 $1,800 American Delta What will the equilibrium be?

Assume that Delta has the following beliefs about American’s Strategy Probabilities of choosing High or Low price Player A’s best response will be his own set of probabilities to maximize expected utility The Airline Price Wars

Subject to Probabilities always have to sum to one Both Prices have a chance of being chosen

First Order Necessary Conditions

Both always charge $500 Both always charge $220 Both Randomize between $500 and $220 Notice that prices are low most of the time! The Airline Price Wars

Continuous Choice Games – Cournot Competition D There are two firms in an industry – both facing an aggregate (inverse) demand curve given by Aggregate Production Both firms have constant marginal costs equal to $C

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 Note that this is the optimal output for a monopolist!

Further, if Firm two producesIt drives price down to MC

The game is symmetric with respect to Firm two… Firm 1 Firm 2

Firm 1 Firm 2 Monopoly Output Competitive Output There exists a unique Nash equilibrium

A numerical example… Suppose that the market demand for computer chips (Q is in millions) is given by Intel and Cyrix are both competing in the market and have a marginal cost of $20.

Had this market been serviced instead by a monopoly,

With competing duopolies

One more point… Monopoly Duopoly If both firms agreed to produce 1.25M chips (half the monopoly output), they could split the monopoly profits ($62.5 apiece). Why don’t these firms collude?

Suppose we increase the number of firms… Demand facing firm i is given by (MC = c)

Firm i’s best response to its N-1 competitors is given by Further, we know that all firms produce the same level of output. Solving for price and quantity, we get

Expanding the number of firms in an oligopoly Note that as the number of firms increases: Output approaches the perfectly competitive level of production Price approaches marginal cost. Lets go back to the previous example…

D $ CS = (.5)(120 – 53)(3.33) = $112 $112 What would it be worth to consumers to add another firm to the industry? Recall, we had an aggregate demand for computer chips and a constant marginal cost of production.

D $ CS = (.5)(120 – 45)(3.75) = $140 $140 With three firms in the market… A 25% increase in CS!!

Increasing Competition

Now, suppose that there were annual fixed costs equal to $10 How many firms can this industry support? Solve for N

With a fixed cost of $10, this industry can support 7 Firms

Firm 1 Firm 2 The previous analysis was with identical firms. Suppose Firm 2’s marginal costs are greater than Firm 1’s….

Firm 1 Firm 2 Suppose Firm 2’s marginal costs are greater than Firm 1’s…. Firm 2’s market share drops

+ As long as average industry costs are the same as the identical firm case Industry output and price are unaffected! Note, however, that production is undertaken in an inefficient manner! With constant marginal costs, the firm with the lower cost should be supplying the entire market!!

Market Concentration and Profitibility Industry Demand The Lerner index for Firm i is related to Firm i’s market share and the elasticity of industry demand The Average Lerner index for the industry is related to the HHI and the elasticity of industry demand

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 duopolists – both with marginal cost equal to c.

D Cournot Case D Bertrand Case

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?

Bertrand Equilibrium: It only takes two firm’s in the market to drive prices to marginal cost and profits to zero! However, the Bertrand equilibrium makes some very restricting assumptions…  Firms are producing identical products (i.e. perfect substitutes)  Firms are not capacity constrained

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

Imperfect Substitutes Recall our previous model that included travel time in the purchase price of a product Firm 1 Customer Dollar Price Distance to Store Travel Costs Length = 1 Consumers places a value V on the product

Imperfect Substitutes Now, suppose that there are two competitors in the market – operating at the two sides of town Firm 1Customer Firm 2 The “Marginal Consumer” is indifferent between the two competitors. We can solve for the “location” of this customer to get a demand curve

Imperfect Substitutes Firm 1Customer Firm 2

Both firms have a marginal cost equal to c Each firm needs to choose price to maximize profits conditional on the other firm’s choice of price.

Firm 1 Firm 2 Bertrand Equilibrium with imperfect substitutes

Cournot vs Bertrand Firm 1 Firm 2 Firm 1 Firm 2 Suppose that Firm two‘s costs increase. What happens in each case? BertrandCournot

Cournot vs Bertrand Suppose that Firm two‘s costs increase. What happens in each case? Cournot (Quantity Competition): Competition is very aggressive  Firm One responds to firm B’s cost increases by expanding production and increasing market share\  Best response strategies are strategic substitutes Bertrand (Price Competition): Competition is very passive  Firm One responds to firm B’s cost increases by increasing price and maintaining market share  Best response strategies are strategic complements

Stackelberg leadership – Quantity Competition 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 c Firm A chooses its output first Firm B chooses its output second Market Price is determined

Firm B has observed Firm A’s output decision and faces the residual demand curve:

Knowing Firm B’s response, Firm A can now maximize its profits: Monopoly Output

Competitive Output Cournot Output Stackelberg Output Essentially, Firm B acts as a monopoly in the “Secondary” market (i.e. after A has chosen). Firm B earns lower profits!

Sequential Bertrand Competition With identical products, we get the same result as before (P = MC). However, lets reconsider the imperfect substitute case. We already derived each firm’s best response functions Now, suppose that Firm 1 gets to set its price first (taking into account firm 2’s response)

Sequential Bertrand Competition Take the derivative and set equal to zero to maximize profits Note that prices are higher than under the simultaneous move example!!

Sequential Bertrand Competition In the simultaneous move game, Firm A and B charged the same price, split the market, and earned equal profits. Here, there is a second mover advantage!!

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.