# Overview 11/6/2014. Herfindahl Hirshman index of market concentration ...

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1 Overview Market Structure and Competition Chapter 3 explores different types of market structures. Markets differ on two important dimensions: the number of firms, and the nature of product differentiation. As special cases, we will analyze: competitive markets (many sellers), oligopoly markets (few sellers), and monopoly markets (just one seller). Herfindahl Hirschman Index of Market concentration Herfindahl Hirshman index of market concentration HHI S S S firm firm... firmn Market share for each firm in the industry. Examples ) Monopoly, S=00 HHI = 00 0, 000 ) Very fragmented market, s =.00 for each of the,000 firms in the industry. HHI=,000(.00). 00 Hence HHI ranges from 0 to 0,000 Close to Perfect comp Monopoly

2 Oligopoly Market Models we use to examine Oligopoly markets Firms choose their actions simultaneously A small number of firms sell products that have virtually the same attributes, performance characteristics, image. Example: U.S. salt industry where Morton Salt, Cargill, and IMC sell virtually the same product. Cournot If competition in quantities Bertrand If competition in prices Stackelberg We will consider competition in quantities Homogeneous Products (no product differentiation) Firms choose their actions sequentially Later on, we will allow for product differentiation. Cournot Oligopoly Model Cournot model refers to a homogenous products oligopoly. In the Cournot model, firms simultaneously and independently choose their production level. The market price adjusts to equilibrium after each firm sets the quantity it will produce. Main characteristics: ) N= firms ) Firms compete in quantities 3) They both simultaneously submit their quantities The residual demand curve illustrates the relationship between the market price and a firm s quantity when rival firms hold their outputs fixed. This demand curve is simply the market demand curve shifted inward by the exact amount the rival produces.

3 Given that my rival has already sold 50 units, the demand curve I face has been reduced by 50 units at every price. S0, taking into account this reduced demand (Residual Demand), I act as a monopolist, setting Coming from Residual demand D 50 MR50 Similarly for any other output my rival produces (50,40,30.) This describes my Best Response Function (Reaction Function) since it describes what is my profit maximizing output decision, q, is a function of my rival s output level, q and we write it down as q q MC Example Market demand: p00 Q p00 q q MC 0 Find optimal q where q = 50. Firm s residual demand is p 00 q50 50 q MR associated to this residual demand is MR 50 q MR res = MC 50 q 0 40 q q 0 Qq q Optimal q when rival produces q = 50 Depicting Firm s BRF Let us now find the optimal q for any arbitrary q (not only q 50, as above) q Since demand is p 00 q q, Firm s residual demand is p 00 q q Setting MR = MC, we obtain: 00 q q \$0 90 q q 90 qq q 45 This is Firm s BRF 45 / 90 q 3

4 Alternative approach Note that, alternatively, we can find BRF by directly solving firm s profit maximization problem: max(00 q) q * q 0q q TR=p*q TC=c* Taking first order conditions with respect to q, we obtain: ( 00 q) q 0 0 Solving for q, yields 90 q q q) q 45 ( which coincides with the BRF we found using the other approach. Firm s BRF In order to find BRF : Residual demand is p=(00 q ) q MR for this Residual Demand is MR00 q q Setting MR = MC, we obtain: 00 q q 0 This production level is given (firm cannot control it) Solving for q, we find firm s best response function Figure Depicting Firm s BRF q 90 Slope: / 45 Trick: Rotate the page to draw this BRF using the same axes as for BRF q 4

5 This image cannot currently be displayed. /6/04 Putting BRF and BRF together q q * BRF q * q* = q* (It happens in the 45 line for this exercise, but it doesn t need to). 45 BRF This is the Cournot Equilibrium (where BRF crosses BRF ) 90 q Find Cournot Equilibrium in this example q BRF q 45 Trick : q q q BRF q q 45 Market Price is hence: q 3 q 45 q 45 In symmetric Duopolies, where both firms cost function coincide And solving for q, we obtain q=30 p 00 q q \$40 Equilibrium profits in the Cournot model are hence pqcq \$ \$900 Similarly for firm, π =\$900 What would happen if firms and coordinate their production decisions, i.e., if the collude as in a cartel that maximizes their joint profits? They would like to replicate what a single monopolist would do, producing Q m Each firm producing half of Q m, since their costs coincide. Let s see that next 5

6 What are the Monopoly P and Q in this setting? PQ 00 Q MR MC 00 Q0 Q45 units q =.5 q =.5 In a cartel that maximizes joint profits each firm should produce half of monopoly output since they are symmetrical in costs Hence, p 00 Q00 45 \$55 Therefore, profits in the cartel become pqcq \$ \$,0.5 Similarly for firm, π =\$,0.5. Aggregate profits are, hence,,0.5+,0.5=\$,05. Comparisons of Cournot vs. Collusion under a cartel that replicates monopoly outcomes \$55 P \$45 Q monopoly monopoly P Q \$,05 Profits Cournot Cournot monopoly \$40 q q \$60 Profits Profits \$,800 Why is the last inequality occurring? Because when firm q, it produces a decrease in p. Such a decrease in prices entails a reduction in firm s profits which firm doesn t consider when selecting q Since all firms do that, aggregate profits are lower under Cournot (when firms do not coordinate their output decisions) than under monopoly (or cartel, where firm coordinate their output choices). Extending the Cournot model to N firms Let s try Learning by Doing Exercise 3. Residual demand for firm p a b q X p a bx bq where X p abq,mc \$ c q j j Then we can set MR=MC as follows: Solving for q MR abx bq c = MC abx c ac q q X b b This is BRF (similar for all other N firms) 6

7 By symmetry q q... q, which implies that X q q... q ( N q N 3 N ) a c q ( N ) q b And by rearranging X a c q N q b qn q a c b q Nq a c a c q N b b a c q N b where q is a firm s optimal output in a Cournot market with N firms For instance, in our previous numerical example where p=00 Q, i.e., a=00 and b=, and where c=0 and N= firms, entails an individual output (per firm) of a c q N b units Individual output as a function of N For instance, when a=00 and b=, so that p(q)=00 q, as in the demand curve of our previous numerical example; and c=0, then q becomes: q N N which is decreasing in the number of firms, N. q which is exactly the amount we found before when dealing with N= firms

8 Note that if N= firms compete in this oligopoly What about total (aggregate) output, Q? As in Perfect Competition As in Monopoly Aggregate output as a function of N Aggregate output when a=00 and b=, so that p(q)=00 q, and c= Q N N N N And what about Market Prices? if N= if N= if N= 8

9 Prices as a function of N Prices when a=00 and b=, so that p(q)=00 q, and c=0. 00 N 90 p 0 0 N N N Hence, prices decrease as more firms compete in the market, approaching p=mc=\$0 when N is large. p We used IEPR in monopoly markets Can we use it in oligopoly markets as well? Yes! Cournot IEPR In monopoly p MC p In Cournot p MC p N Q, P Q, P N Mark Up ( market power) Therefore, the more firms there are, the less market power each firm has. Note that this IEPR is the same as the Monopoly IEPR, except (/N) is added to the right hand side. As N approaches infinity the market approaches perfect competition Indeed, if N, the right hand side of the IEPR collapses to zero, and thus Bertrand Model Let us now analyze competition in prices; which we refer to as the Bertrand model of price competition. As opposed to the Cournot model, in which firms competed in quantities. Will the equilibrium results coincide? No, let s see why. 9

10 Bertrand Model Consider that firm sets a price p=\$40. What price will its rival, firm, set? Firm (Samsung) must set P <\$40 (otherwise it sells nothing) Once Samsung has set a price of \$39, then its rival must set a price p<\$39, e.g., \$38. But then Samsung should respond by setting a price lower than \$38 since otherwise it sells nothing. Repeating this process.. Example: Set P =\$39, losing area A, but gaining B The process can be repeated until prices reach p=mc. (Setting a price p<mc would imply losses). Bertrand Conclusions So, the Bertrand model even with N= firms we have competitive industry prices This didn t happen when firms compete in quantities (a la Cournot) (and N=). Example: a c p c 3 Let s next show this result by systematically going over all possible price pairs (p,p ) different from (c,c), i.e., whereby both firms price coincides with their common cost, c. We will demonstrate that they cannot be equilibria of the of the Bertrand model of price competition. In particular, we will show that they are unstable prices in the sense that at least one firm has incentives to deviate to another price. For presentation purposes: We will first examine asymmetric price pairs, p p, and then We examine symmetric price pairs, where p =p 0

11 No Asymmetric Equilibrium ) p p c ) p p (similar to above) c c p p Profitable deviation of firm Symmetric equilibrium ) p p c c ~ p p p, and similarly for firm 3) p p c c c p p Profitable deviation of firm ) p p c is the unique equilibrium in the Bertrand Model of Price Competition. p p 4) p p c (similarly) c p p Cournot vs Bertrand: How can their equilibrium predictions be so different? ) Capacity constraints: Cournot capacity is set firstly, then competition (LR capacity competition) Bertrand enough capacity to satisfy all market demand if necessary (SR price comp.) ) Firm s beliefs about the reaction of its competitor: Cournot model competitors cannot adjust their production very much. e.g. mining or chemical processing Bertrand model all my competitors have enough production capacity to steal my customers. e.g. US airlines in the early 000s Stackelberg Model Competition is in quantities: One firm acts as a quantity leader, choosing its quantity first, with other firms acting as followers. ) Leader and Follower ) The leader maximizes profits taking as given the follower s BR (Reaction) function Procedure: We first find the followers BR function, and then plug that into the leaders residual demand Example in the next slide.

12 Consider an inverse demand curve P 00 Q00 qq st MC \$0 step q Follower (firm s) BRF q 45 (Same BRF as in Cournot) nd step Leader (firm s) residual demand: q q p 00 q q 00 q (45 ) 55 q Hence, the MR associated with this residual demand is q MR q MC \$0 Setting MR=MC yields 55 q 0 45 q We can now find the output of the follower Plugging q =45 into BRF Evaluating profits in the Stackelberg model Hence, the profits of the leader (firm ) are pqcq \$ \$,350 While the profits of the follower (firm ) are only pq cq \$ \$675 This is usually referred to as the leader s advantage. Let us next compare prices, output, and profits in the Stackelberg and Cournot models. Before starting our comparison, we first need to find the price in the Stackelberg model of sequential quantity competition: p 00 q q \$3.50

13 Conclusions PRICE Profit for leader \$,350= Profit for the follower P stackelberg =\$3.50<P cournot =\$40 LEADER FOLLOWER TOTAL OUTPUT \$675= =45 =30 =.5 =30 =\$900 =\$900 =60 Intuitively, the leader produces a large amount, pushing the follower to produce a small amount. This allows the leader to capture larger profits than the follower. This result is usually referred to as First mover advantage. Note that this output difference is not due to different costs. Both firms have the same costs, yet the leaders position helps him flood the market, leaving little room (residual demand) for the follower to capture. Note that the leader doesn t serve the entire market (inducing the follower to produce nothing, q =0), but instead q >q >0. Comparing output and prices across different models: We can place aggregate output levels and their corresponding prices in a standard linear inverse demand curve p(q) = a bq. Query # Stackelberg duopolists, Firm and Firm, face inverse market demand P = 50 Q. Both have marginal cost, MC = \$0. If the follower takes the leader s output as fixed at Q, what is the equation of its reaction function? a) 30 Q Q b) 5 Q Q c) 5 Q Q Q d) 5 Q 3

14 Query # Answer Answer D The Stackelberg model of oligopoly pertains to a situation in which one firm acts as a quantity leader, choosing its quantity first, with all other firms acting as followers and making their decision after the leader. To find the follower s reaction function, we first find its residual demand: P 50 QMarket or P 50 QQ This is the follower s residual demand curve, where the parenthesis highlight the terms the follower views as given. (50 Q) is the vertical intersect, and is the slope. The corresponding Marginal Revenue Curve is P 50 Q Q The corresponding MR keeps the same vertical intercept but doubles the slope Then just equate the Marginal Revenue Curve to Marginal Cost, MC = \$ Q Q Q 50 Q 0 Q 30 Q Pages 50, 50 5 Q 5 Q Dominant Firms ) One dominant firm with a large market share dominates the market (has a significant market share compared to others) ) Many small firms (Market competitive fringe) Example: Light bulb market GE (7%), Sylvania (7%) Steel Market US Steel Aluminum Market Alcoa Dominant Firm ) D M and S Fringe, and MC for every firm is equal (same access to technology). ) Residual demand for the dominant firm, D R, is D R = D M S fringe When S Fringe = 0 D R coincides with D M (see segment of D M for prices between zero and \$5, where D M =D R ). Interpretation 4

15 Dominant Firm 3) MR R associated to D R MR R = MC determines the equilibrium Q for the dominant firm In this case that occurs at Q R = 50 units 4) Market price: from D R not from D M, hence, p=\$50 5) Profit = pmcq R \$, 50 6) Fringe firms supply an output of 5 units when p = \$50 Exercise Exercise on Dominant Firms d Consider a demand curve: Q 0 0 p MC=5 (dominant firm s MC) 00 firms in the fringe, each firm with MC 500q a) Supply of firms in the Fringe, S F. p 5 MC p 5 00q q 00 since c = 5) p 5 S F 00 p 0 00 a) We now find the residual demand for the dominant firm, Dem R (Q R ) D M S F p (which is positive as long as p > 5 S F D M S F c) Profit maximizing output for the dominant firm since Q R =0 p, then the inverse demand is Summarizing the results in the exercise Total Industry Supply: 30+5=35 units setting MR R =MC, we obtain This is the MR associated with the res. demand (double slope) Fringe Market Share: 5/35 = 4.9% Dominant Firm Market Share: 30/35 = 85.7% Price is then Fringe supply is 5

16 Product Differentiation Vertical differentiation: two products with differences in their quality Duracell vs. Store brand batteries At a given price (e.g., \$5), ALL costumers regard one good superior to another. Horizontal differentiation: two products with differences in some attributes, a matter of substitutability. Pepsi vs. Coke (some consumers like one more than the other even if their prices coincide.) Horizontal differentiation Weak H.D. Strong H.D Demand is insensitive to own price (steep) Demand is sensitive to own price (flat) rival s price rival s price (small inward shift) (Large inward shift) Weak vs. Strong Differentiation Graph A: Weak HD: firm demand curve is very flat and therefore is very sensitive to its own price. p q along D 0 In addition, price rival strong leftward shift in the demand curve, indicating that demand is sensitive to its rival s price. Graph B: Strong HD: firm demand is less sensitive to its own price. p slight q D 0 (insensitive to its own price) In addition, price rival slight leftward shift in the demand curve ( q), indicating that demand is insensitive to its rival s price. Bertrand Competition with Horizontal Product Differentiation H.D. entails that demands for Coke and Pepsi are different Which do you like the most? It s a matter of taste, not quality: Coke : Q 644p p MC \$5 Pepsi : Q 505 p p MC \$4 6

17 These demand functions were estimated by a group of leading economists. Procedure: Find Pepsi s profit maximizing price p for any arbitrary price of Coke, p This gives you BRF, as p (p ) Similarly, find Coke s profit maximizing price p for any arbitrary price of Pepsi, p This gives you BRF, as p (p ) Substitute one BRF into another, and find optimal prices p and p a) What is Coke s profit maximizing price p when p = \$8 ) Find Residual Demand for Coke ) Find MR, and set it equal to MC 3) Substitute back into the demand function (For Coke) (For Pepsi) b) What is Coke s profit maximizing price p for any arbitrary p? ) Residual Demand for Coke Coke s BRF p (p ) = (p /4) p BRF ) Find MR, and set it equal to MC 3) Substitute back into the demand function BRF FIGURE 0.5 /4 p q 7

18 Practice how to find BRF by setting MR R MC for Pepsi Pepsi s price Similarly for Pepsi, we can find its BRF as p Superimposing both BRF S p With H.D. BRF 7 Slope = /0 p Remember to use the same axis as in the previous figure p Coke s price In order to find the crossing point of BRF and BRF, plug one inside the other A few more points \$.56 = =\$8.6 Because: Note that their price markups are different but unambiguously large: Coke And outputs are (plugging prices on the demand function): (Coke) (Pepsi) Pepsi That is, product differentiation softens price competition as opposed to the Bertrand Model with no product differentiation, where p=mc and Profits=0 8

19 Another application of product differentiation Channel Tunnel between Dover, UK and Callais, France. Application Channel Tunnel: The author estimated the reaction function of each firm (only data for trucks) obtaining the following figure. Equilibrium occurs at the crossing point: 87 for the channel and 50 for the ferries. Competing against the traditional ferries operating in the same route. 87 Cournot Model of Horizontal Product Differentiation What if firms still sell a horizontally differentiated product, but rather than competing in prices (as in the Coke vs Pepsi example), they compete in quantities? firms Simultaneously competing in quantities Selling horizontally differentiated products, Exercise 3.9 in your textbook for practice. Query # Which of the following is true in markets with horizontally differentiated products? a) Bertrand competitors will generally earn zero profits in equilibrium. b) Firms always act as monopolists when products are horizontally differentiated. c) IEPR does not apply to markets with horizontal product differentiation. d) Bertrand competitors will generally earn positive profits in equilibrium. 9

20 Query # Answer Answer D Bertrand competitors will generally earn positive profits in equilibrium. The IEPR does apply to markets with horizontal product differentiation. Pages Query #3 Let firm A face demand curve QA 00 PA 0.5PBand firm B face demand curve QB 00 PB 0.5PA. Products A and B both have constant marginal cost of production of 0 per unit (and no fixed cost). Each firm acts as a Bertrand competitor. What is firm B s profit maximizing price when firm A sets a price of \$70 for its good? a) \$70 b) \$7.5 c) \$74 d) 76.5 Query #3 Answer Answer B The Demand Curves can be rewritten as: Q A = ( P B ) P A Q B = ( P A ) P B Plugging P A = 70 into the equation for Q B we obtain: Q B = ( (70)) P B P B = 35 Q B Then, we can find the associated Marginal Revenue Curve MR = 35 Q B Same vertical intercept as P B but double slope Equate MR and MC, MC = \$0 35 Q B = 0 Q B = 6.5 Now that we know Q B, we can plug this back into our original demand curve to find P B. Q B = ( P A ) P B 6.5 = ( (70)) P B P B = \$7.5 Page 5 0

21 Monopolistic Competition (free entry) Many firms. Sell a horizontally differentiated product. Example: restaurants in Seattle Entry and exit are possible but, unlike P.C. markets, the product is horizontally differentiated. Short run, but Profits attract entry In the short run, profits might be positive, but In the long run, firms are attracted to positive profits, and economic profits become zero. (Accounting profits are positive, but just comparable to those in order industries). Long Run Monopolistic Competition and Price Elasticity Few firms are attracted to enter Many firms are attracted to enter Low mark up High Mark Up P=AC No Profits! Decreases customers of your restaurant as entry occurs. Fewer sales per firm. Ex. Liquor Stores, Hardware Stores Ex. Flower shops, Jewelry stores True at Chicago or Pittsburgh, probably true in Spokane and Seattle Ultimately, we observe more flower shops than liquor stores.

22 Can prices go up as a consequence of the entry of more firms? Yes! Can prices actually go up as a consequence of the entry of more firms? Yes! Consider the following figure where: The market is initially in a long run equilibrium at a price of \$50, and with each firm facing demand curve D (point A). Technological improvement reduces the average cost curve of all firms, from AC to AC Firms now start earning positive short run profits, which attract the entry of more firms. Due to entry, the demand curve for each firm shifts inwards, from D to D In the new long run equilibrium (point B) firms don t make profits. Prices are higher than at the initial equilibrium (point A). They increase from \$50 to \$55. 4 th Short nd Run Profits B A 3 rd Entry st step Of course, this doesn t need to be the case: Prices could also fall as more firms enter the industry. nd Short run Profits A B st AC Application 3.8: Primary Physicians as an example of Monopolistic Competition 9 metropolitan areas in the U.S. An increase in the number of physicians per square mile was associated with an increase in the average price per office visit. Notice that an increase in the number of physicians is equivalent to the entry of new competitors in this industry (local market of physicians). D AC D Entry (3 rd ) Fall in prices, from A to B

23 Application 3.8: Primary Physicians as an example of Monopolistic Competition Why? Search costs: comparison shopping becomes more difficult as you increase the number of physicians. Additional confirmation: physicians prices were higher in markets in which a large proportion of the population had recently moved (and thus had poorer information about local doctors) than in markets in which households were more settled. Hence, the entry of new doctors in this market lead to an inward shift in the demand curve of each doctor (from D to D ), leading prices up, as in the figure we described three slides ago. 3

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