Decreasing average total costs (natural monopoly) (which is USPS? Google? The water company?)

Transcription

1 Market Power The simplest departure from the price-taking equilibrium model is when agents (firms) stop treating price as out of their control: they have market power and are free to design the market as they please. Why does market power occur? Legal, technological, or resource barriers to entry Decreasing average total costs (natural monopoly) (which is USPS? Google? The water company?) The Monopolist: Linear demand We ll work with a simple version of the quasilinear representative consumer model, where u(q, m) = aq b 2 q2 + m, and the budget constraint is pq + m = w. Then the consumer s problem is max aq b q 2 q2 pq + w, which gives the simple, linear demand curve p(q) = a bq. The Monopolist: Linear demand What would happen in the price-taking equilibrium? marginal cost, so that a bq = c, and q = a c. b Set price equal to The Monopolist: Linear demand The monopolist s problem, then, is max p(q)q C(q) F q where C(q) are variable costs and F is the fixed or sunk cost. variable costs, max(a bq)q cq F q So the FONC is a bq bq c = 0, With linear 1

2 and the profit-maximizing quantity is exactly half the efficient quantity. q = a c 2b, The Monopolist: General rule What is the monopolist doing, in general? The FONC for is or max p(q)q C(q) F q p(q) c (q) + p (q)q = 0 Marginal profit from the marginal sale Change in revenue for all inframarginal sales p(q) + p (q)q c (q) = 0. Marginal Revenue Marginal Cost The Monopolist: General rule The Monopolist: Lerner index 2

3 To get more economic intuition on the magnitude of the problem, we ll convert the first-order condition into a Lerner index: p(q) c (q) p(q) Lerner index = dp(q) dq q p(q) = 1 dq(p) p dp q(p) = 1 ε d (q), where ε d (q) is the price elasticity of demand. The Lerner index then says that the fraction of the price that is attributable to market power p(q) c (q) is proportional to the inverse of the price elasticity of the demand curve. Less elastic goods will have larger margins, higher profits, and more inefficiency. Monopolists facing more inelastic demand make more money, and the losses to society are greater. Unit Demand In many cases, each consumer either buys a good or doesn t: a washing machine per year, a new car, a ticket to a particular concert,... In this case, we imagine the household has a mean value for the good, v, and they purchase at a price p if v ε p v p ε where ε is a taste shock that explains why some people buy and some don t. The cumulative distribution function, F (ε), of a random variable ε given the probability that the random variable is below some threshold: P r{ε x} = F (x). For example, standard Normal CDF is Then demand is The Unit Monopolist P r{ε x} = Φ(x) = The monopolist then solves: x 1 2π e x2 /2 dx. P r{ε v p} = F (v p) = D(p) max F (v p)(p c), p which has the first-order necessary condition or F (v p) f(v p)(p c) = 0, p c = 3 F (v p) f(v p)

4 Probit Demand If we know about the households their income xi,income, their education level xi,education, household head age xi,age, etc. we take the list of characteristics xi,k and multiply by coefficients αk to model their mean utility: K αk xik εi βp, k=1 This yields a statistical model of demand for household i! K D(p, xi ) = Φ αk xik βp k=1 and the market demand curve D(p) = N D(p, xi ) = N i=1 i=1 Φ K! αk xik βp k=1 Probit Demand: Application We randomized prices for a health product in Senegal Households call in, ask us to run an auction for them; we send out a proposal for bids; suppliers have an hour to bid; we pass the lowest bid to the household, who accepts or rejects At a variety of different prices, we get to see whether households in different neighborhoods at different times buy the product or not How do we estimate demand? What are the profit- and welfare-maximizing prices and quantities? Mechanical versus manual desludging 4

5 Probit Demand: Result 750 Quantity (Units) Price (USD) Addressing Monopoly Encourage entry (e.g., research subsidies) or break up the monopolist (e.g., AT&T) Price controls (e.g., ATC pricing) Oligopoly Most industries are actually not monopolies or perfectly competitive, but somewhere in the middle: firms have price power, but don t control the whole market Why do oligopolies arise? Standard barriers to entry Product differentiation The relevant policy concerns are usually about mergers and collusion Oligopoly What happens when there are N > 1 firms instead of just one, where each knows it has market power? We imagine each firm takes the quantity choices of its opponents as fixed and selects its own quantity to maximize its profits We then find the quantity choices for all the firms at which each firm s forecasts about its opponents are correct 5

6 This is called a Cournot Equilibrium or a Nash equilibrium: it s just like a pricetaking equilibrium, except that what you take as given instead of the price are the choices of your opponents. Oligopoly Suppose all the firms are the same, so firm i of N s costs are just C(q i ) = cq i. Then a typical firm i faces the problem max (a b(q 1 + q q i q N )) q i cq i q i Firm i takes the quantities of the other firms as given, and chooses his quantity to maximize the above profit function, giving the FONC N a bq i c = 0. j=1 q j Now, since the firms are all the same, we ll look for a solution where they all do the same thing: q i = q for all i, so that (a Nq ) bq c = 0. Oligopoly This gives q = 1 N + 1 a c, b which is between the monopoly ((a c)/2b) and perfectly competitive (a c) quantities. The total quantity produced in the market is Nq, or and the price is Q = N a c N + 1 b p = a N N + 1 (a c) = a 1 N N N + 1 c. Notice, as N gets large, p gets closer and closer to c: the perfectly competitive outcome. Oligopoly: Convergence to perfect competition If the price for N firms is p 1 N = a N N N + 1 c, 6

7 consider the quantity p N c, which is p N c = 1 a constant (a c). N + 1 N So the oligopoly price converges to the competitive price (c) at a rate of 1/N: this is really fast. At 10 equally competitive firms, you re about 1/10-th the distance from the competitive price; at 100, you re about 1/100 the distance. In the presence of competition, oligopoly prices converge to competitive ones at a speed of O(1/N), so the best regulatory policy is usually to encourage competition. Oligopoly: Merger analysis and the HHI But firms don t want entry: they want to merge. Why? Economize on fixed costs (welfare-enhancing) Increase market power by pooling patents/resources (welfare-reducing) Increase market power by reducing competition (welfare-reducing) The Herfindahl-Hirschman Index is intended to be a measure of industrial concentration, defined as N HHI = where s i is i s share of total industry production, q i /Q. If all the firms have a small market share, they presumably have little market power, and HHI is closer to zero. If a single firm does the vast majority of the production, then HHI is closer to one. So this gives a zero-to-one-measure of the competitiveness of an industry. Oligopoly: Merger analysis and the HHI The Department of Justice actually uses the HHI to decide whether a proposed merger presents a threat to competition. The Horizontal Merger Guidelines state: i=1 An H below 0.01 indicates a highly competitive industry An H below 0.15 indicates an unconcentrated industry An H between 0.15 to 0.25 indicates moderate concentration An H above 0.25 indicates high concentration If the industry is moderately or highly concentrated, or if a merger would lead to a large increase in the HHI, the DOJ will typically investigate or challenge the merger. s 2 i 7

8 Oligopoly: Merger analysis and the HHI For our simple model, each firm produces q = (a c)/(b(n + 1)), so s i = 1/N. Then we have N ( ) 2 1 HHI = = 1 N N, Then the guidelines say: i=1 An H with 100 or more firms indicates a highly competitive industry An H with more than 7 firms indicates an unconcentrated industry An H between 4 to 7 firms indicates moderate concentration An H with fewer than 4 firms indicates high concentration Oligopoly: Merger analysis and Market Definition Here is a case that makes the issue of market definition clearer: In 2007, the FTC challenged a merger between Whole Foods and Wild Oats, arguing that they were premium natural and organic supermarkets, distinct from conventional supermarkets. Apart from Whole Foods and Wild Oats, the only other PNOS identified by the FTC were Earth Fare in southeastern states and New Seasons in Oregon. Whole Foods/Wild Oats argued that they were basically a really nice supermarket The Whole Foods CEO hadn t helped when he previously said, Safeway and other conventional retailers... cant really effectively focus on Whole Foods Core Customers without abandoning 90 percent of their own customers The merger was ultimately allowed, since the case was nutty Merger analysis and Market Definition An important feature of the case was: Based largely on testimony and studies from the defendants experts, the court found that conventional stores such as Safeway, Delhaize America, Krogers, and others had repositioned themselves to offer more natural and organic products and would operate to constrain Whole Foods in the post-merger market. It found that grocery shoppers are price sensitive and frequently engage in cross-shopping, i.e., buying various grocery items from different stores in their local areas, and purchasing many, if not the majority, of their items at conventional stores. ABA analysis of ruling Things went differently in FTC v Staples, when Staples tried to acquire Office Dept in the late 1990 s: 8

9 The court ruled that office superstores were a distinct market The merger was blocked, since it would have reduced the market to three firms and considerably increased concentration Oligopoly: Merger analysis and the HHI Pros: Cons: The HHI is intuitive: larger market shares usually means more market power Gathering and computing market share data is easy The guidelines seem reasonable The entire economic analysis will hinge on market definition, and this has had lasting implications The HHI somewhat arbitrary: it s not really tied to consumer welfare in any way Market power might not necessarily be driven by market share, or small produces might be taking the most advantage of their consumers Market Power Monopolists are the most powerful kind of market designer: that usually comes at a cost to society Regulatory solutions can constrain a monopolist s power, but can t generally restore efficiency In markets with a lot of competition, the situation improves: competitors bid prices down on one another, pushing the outcome towards perfect competition 9