Econ 815 Dominant Firm Analysis and Limit Pricing

Transcription

1 Econ 815 Dominant Firm Analysis and imit Pricing I. Dominant Firm Model A. Conceptual Issues 1. Pure monopoly is relatively rare. There are, however, many industries supplied by a large irm and a ringe o smaller rivals (IBM, GE, XEROX, Kodak, AT&T, Microsot). The Dominant irm aces a problem that a monopolist does not, the possibility that a price increase will induce some customers to buy rom irms in the ringe o small competitors (Implications or Elasticity) 3. The Dominant Firm, in other words, must take into account the reaction o its ringe competitors. B. Public Policy uestions: 1. Relative to Pure Monopoly, does a market structure compared o a dominant irm and ringe competitors least to higher levels o consumer surplus?. What role should government policy play in ensuring the survival o ringe competitors? (eg, Telecommunications) 3. Should limit pricing be lawul, under what conditions? 4. Why do we observe (or might we observe) a shrinking share o dominant irms over time? What inluence would the irm s discount rate have on this scenario? 5. What has been public policy toward dominant irms? II. The Basic Dominant Firm Model

2 P There is a sunk cost o entry that has already been incurred by the dominant (incumbent) Market Demand Curve Residual Demand Curve P e q D AC e AC(entrant) q e MC(entrant) Residual marginal curve A. Assumptions and Deinitions 1. This is a static limit pricing model; there is no explicit treatment o time.. The post entry price (P e ) will depend on the combined output o the dominant irm and ringe output: q D +q e 3. P e = Price at which q D +q E output will be sold. 4. q e = Proit-Maximizing output o the entrant. 5. Shaded area = entrant s proit. 6. We assume that the potential entrant expects the dominant irm to maintain output at its current level i entry occurs. (i.e., it takes the output level q D as given and then proceeds to maximize proits) 7. I the potential entrant believes this, it can maximize its proit by acting like a monopolist in the segment o the market let or it by the dominant irm. 8. The residual demand curve shows what remains o market demand ater the dominant irm has disposed o its output. 9. The residual marginal revenge curve is derived (in the usual manner) rom the residual demand curve. B. The role o sunk costs 1. De. Sunk Cost: Costs that cannot be recouped once they are incurred (compare and contrast with ixed costs). These may include advertising, expenditures, on development o goodwill and assets speciic to a particular industry, including inormation

3 . Entry always involves some sunk costs. 3. Sunk costs place an entrant at a ixed and marginal cost disadvantage relative to the incumbent [Note Such costs are already sunk and thus unavoidable or the incumbent] 4. The dominant irm [Incumbent] can exploit this disadvantage to maintain its position. C. The Dominant Firm 1. Recognize that i the dominant irm puts enough output on the market, it can push the residual demand curve below the entrant s average cost curve.. That is, the dominant irm, through its choice o output, sets a limit price below which ringe irms will not enter the market, Denote this price by P. P Market Demand Curve Residual Demand Curve Entrant s cost unction C e = F + c e q e AC e = (F/q e ) + c e P AC(entrant) MC(entrant) Residual marginal curve 3. The size o the limit output is determined by two actors. a) Size o the market: The larger the market (rightward shit o the market demand curve), the greater the limit output a dominant irm must produce to preclude entry at the limit price. b) Entrants Average Cost Curve: The greater the extent to which costs are sunk, the greater the entrant s average cost at any output level. An increase in cost sunkedness shits the entrant s average cost curve upward and reduces the limit output. 4. Note: The act that a dominant irm can keep entrants out does not mean that it will choose to do so. A dominant irm will choose the strategy that yields the largest proit. General Example 1. Suppose the market demand curve is

4 P= a b( + q) Where P is the market price, is the output o a dominant irm, and q is the output o the single ringe irm. The dominant irm s cost unction is C() = c, and the cost unction o the ringe irm is C(q) = e + cq, Where e>0 is the sunk costs o entry or expansion. a. What output would the dominant irm produce i it were a monopolist? What price would it charge? I the dominant irm were a monopolist, then q=0. The monopolist s demand unction is given by P=a-b Setting MR=MC yields. m a c (1) a b= c = b m a c a c a+ c m () P = a b = a = = P b b. I the ringe irm observes the dominant irm producing units o output and expects this output level to be maintained, what is the equation o the residual demand curve that the ringe irm expects? P a Market Demand Curve a-b Residual Demand Curve (a/b)- a/b *=+q

5 new vertical intercept (3) P = a b bq (Equation o Residual Demand Curve) treated as a constant c. I the ringe irm maximizes its proit on the residual demand curve, what output will it produce? Equate MR with MC yields (4) [ a b] bq = c (same vertical intercept and twice the slope as inverse demand in (3)) a b c (5) q = Observations (Higher => ower q) =0 => q m monopoly output b Equation (5) is the ringe irm s reaction unction. d. How much output will the monopolist have to produce to keep the ringe out o the market (i.e., to make q=0). What price will this amount or output bring? What is the degree o market power exercised by the monopolist i it chooses to keep the ringe irm out o the market? (i) To keep the ringe out o the market, the monopolist must drive price down to the level where the ringe s proits are equal to zero. et π denote ringe proits where (6) π = ( P c) q e Substituting in or P (7) [ ( ) ] π = a b + q c q e Substituting in or q rom(5) a b c a b c (8) π = a b b c e b b Simpliying and collecting terms yields a b c a b c (9) π = a b c e b a b c a b c (10) π = e b ( ) a b c (11) π = e 4b Set π = 0 and solve or (1) ( a b c) 4b = e

6 (1 ) a b c= 4be (1 ) a c 4be = b a c 4be (13) = b b where the superscript denotes the limit value. Simpliying yields (14) a c e = b b Recognize now that a c b is the (competitive) output level that would be realized i price were set equal to marginal cost. Denote this output level by S; rewriting (14) yields. e (15) = S (suppose e=0)? b Note that is decreasing in e. The higher the sunk costs o the entrant, the lower the limit quantity. (ii) The limit price, P, corresponding to is given by (16) P = a b S e b (16 ) a c e P = a b b b e (16 ) P = a a+ c+ b b e (17) P = c+ b b b (18) P = c+ be (suppose e=0)? (iii) Market Power as indicated by the learner index, lim, is given by lim c+ be c be c (19) = = = 1 c+ be c+ be c+ be Note that the erner Index is increasing in e. Intuition? Suppose e=0=> Dominant Firm has no market power.

7 Summary o Key Findings. a c e 1. = limit quantity b b. P = c+ be limit price lim c 3. = 1 erner index c + be Numerical Example 1. Suppose (1) P= 4000 ( + q ) ; Cq ( ) = 80+ q. Hence, 0 1 a= 4000, b=, c= 1, e= This implies: (1) () (3) = = 79, P = 1+ = 5 0 lim 1 1 = 1 = 1 = 4 = Alternative Solution Method or Numerical Example 1. (1) P= 4000 ( + q ) ; Cq ( ) = 80+ q 0 (i) Derive Fringe reaction unction 1 () P=4000 q 0 0 (3) (4) 1 MR = MC 4000 q = = q q= (ii) Fringe proit 1 1 (5) π = [ P c] q e= 4000 q 1 q

8 (6) π = 3999 (39990 ) (7) π = (8) π = (9) π Set π = = 0 80 (10) = = 40 (11) = 79,900 (1) 1 P = 4000 (79900) = 5 0 lim P c 5 1 (13) = = = 0.8 Market Power erner Index P 5 Numerical Example. 10 (1) P= 1000 ( + q ) () C() = 5 (Dominant Firm Cost Function) (3) C() = 10q (Entrant s Cost Function) Note: We can solve this problem by noting 1 a= 1000, b=, c= 10, e= 0 10 Inverse Market Demand Function

9 P 1000 Residual Demand Curve 10 MC=AC (Entrant)) 5 MC=AC (Dominant irm) 10, The Dominant irm puts the competitive output on the market relative to the entrant s marginal cost.. Recognize now that when = 9900, P =10. Hence, Should the entrant put any positive level o output on the market, P<10 = MC (entrant) Hence, P = =