Regulation_mergers.pdf

2.A Horizontal mergers 2.A. Horizontal mergers A. Should we merge into a single firm? DECISIONS WITH NEGATIVE B. Should we form a secret cartel? IMPACTS ON C. Should w...

2.A Horizontal mergers 2.A. Horizontal mergers A. Should we merge into a single firm? DECISIONS WITH NEGATIVE B. Should we form a secret cartel? IMPACTS ON C. Should we try to maintain high prices? CONSUMERS UNDER THE SCRUTINY OF COMPETITION AUTHORITIES ATREX BULVA 19 What do we study in this section? 1. Effects of coordinated decisions 2. Mergers under quantity competition A. No impact on efficiency B. Impacts on efficiency C. Welfare analysis 3. Merger under price competition 20 What if firms coordinate their decisions? Suppose 3 firms in the market: Atrex (1), Bulva (2), and one other (3) Decisions: 0" , 0# , 0$ → 1! (0" , 0# , 0$ ) Competition Each firm " chooses its 0! to maximize 1! (0" , 0# , 0$ ) ⇒ Each firm ignores the externalities it imposes on the other firms. Example: A change in +$ affects ,& (+$ , +& , +' ) and ,' (+$ , +& , +' ). Coordination Suppose firms 1 and 2 coordinate their decisions ⇒ They choose 0" and 0# to maximize 1" (0" , 0# , 0$ ) + 1# (0" , 0# , 0$ ) ⇒ They internalize the externalities they were imposing on one another. They also take into account the effects that +$ has on ,& and that +& has on ,$. 21 Impacts of coordinated decisions How do !0 and !1 change? → Depends on the sign of the externality %&! < 0 (negative externalities) → coordination ↓ 0" and 0# %'" %&! > 0 (positive externalities) → coordination ↑ 0" and 0# %'" How does !2 change? → Depends on the type of strategic interaction % %&$ < 0 (strategic substitutes) %'# %'$ → 0$ moves in the opposite direction than 0" and 0# % %&$ > 0 (strategic complements) %'# %'$ → 0$ moves in the same direction as 0" and 0# 22 Impacts of coordinated decisions (2) Quantity competition Price competition Negative externalities Positive externalities If one firm produces more, it If one firm sets a higher price, it negatively impacts the profit of positively impacts the profit of the other. the other. Strategic substitutes Strategic complements Reaction functions are Reaction functions are upward- downward-sloping; strategies sloping; strategies evolve in the evolve in opposite directions. same direction. ⇒ Firms 1 and 2 decrease their ⇒ Firms 1 and 2 increase their quantity when they coordinate. price when they coordinate. ⇒ Firm 3 reacts by increasing its ⇒ Firm 3 reacts by increasing its quantity. price. This reduces the benefits of This raises the benefits of coordination for firms 1 and 2. coordination for firms 1 and 2. 23 Impacts of coordinated decisions (3) Quantity competition Price competition ⇒ Firms 1 and 2 decrease their ⇒ Firms 1 and 2 increase their quantity when they coordinate. price when they coordinate. BAD FOR CONSUMERS BAD FOR CONSUMERS ⇒ Firm 3 reacts by increasing its ⇒ Firm 3 reacts by increasing its quantity. price. “LESS BAD” FOR CONSUMERS EVEN WORSE FOR CONSUMERS Other things equal, when competing firms coordinate their decisions, the negative impact on consumers is more significant under price competition than under quantity competition. 24 Reminder. Cournot model Consumer chooses the quantities #0 and #1 to maximize 1 1 $ #0 + #1 − #0 + 2)#0#1 + #11 − *0#0 − *1#1 + + 2 FOCs give: 3 3 = 0 ⇔ $ − #0 − )#1 = *0 and = 0 ⇔ $ − #1 − )#0 = *1 34! 34" → Inverse demand functions: *0 #0, #1 = $ − #0 − )#1 3 *1 #0, #1 = $ − #1 − )#0 0 ≤ % ≤ 1 ⟶ Measures link between price and quantity of ! ⟶ Maximum price different goods ⟶ degree of consumer is willing to product substitutability pay for each good % = 0 ⟶ independent goods % = 1 ⟶ homogenous goods 25  Best-response functions max ⇡ (q1 , q2 ) = [p1 (q1 , q2 ) c 1 ] q 1 = (a c1 q1 dq2 ) q1 q1 First-order @⇡ (q1 , q2 ) = 0 , (a c1 q1 dq2 ) q1 = 0 condition @q1 1 max ⇡ (q1 , q2 ) = [p1 (q1 , q2 ) c 1 ] q 1 = (a c1 , q 1 = (a c1 q1dq2 ) ⌘ R1 (q2 ) 2 @R1 (q2 ) d @⇡ (q1, q2) = 0 , (a c1 q1 dq2) q1 =  0@q1 @q2 Firm 1’s best-response (or reaction) function 2 Downward-sloping ✓6$ to choose◆to → Tells firm 1 which quantity 2⇡ q , q → If firm11 expects 6& to increase, @ @⇡ maximize its profit, ( q , 1 2q ) @ ( 1 2 ) , q1it= (aby cdecreasing reacts 1 dq2 ) ⌘6 R1 (q2 ) = = d  20 $ for any quantity 6& that@q firm 2 2 could @q1choose @q1 @q2 @R1 (q2 ) d 1 = 0 q2 = (a c2 dq1 ) ⌘ R2 (q1 ) @q2 2 2 ✓ ◆ 26 @ @⇡ (q1 , q2 ) @ 2 ⇡ (q 1 , q 2 )  @R1 (q2 ) d = 0 Nash equilibrium @q2 2 ✓ ◆ @ @⇡ (q1 , q2 ) @ 2 ⇡ (q 1 , q 2 ) = = d0 We find firm @q 2’s2 best-response @q1 function @q1 @q2 in a similar way 1 q2 = (a c2 dq1 ) ⌘ R2 (q1 ) 2 Nash equilibrium = Intersection of best-response functions '"∗ , '#∗ such that '"∗ = 9" ('#∗ ) & '#∗ = 9# ('"∗ ) Equilibrium 1 2q1 = a c1 d (a c2 dq1 ) 2 , 4q1 = 2a 2c1 da + dc2 + d2 q1 , 4 d 2 q 1 = (2 d) a 2c1 + dc2 (2 d) a 2c1 + dc2 ⇤ , q1 = ⌘ q 1 4 d2 (2 d) a 2c2 + dc1 q2⇤ = 4 d2 27  n firms with di↵erent constant marginal cost ci, i = 1...n Extension to more than 2 firms Notation: Homogenous good (d = 1) Pn – Q = k=1 qk Assumptions - firms with different constant marginal costs: :! Notation: – Q i = Q qi Homogenous product: ; = 1 Notation – Q= Pn – C i=C cP in k=1 qk – C= k=1 ck – Q i=Q qi Problem of firm ii: – C =C ci Problem of firm 5:Pn max ⇡ i (qi , Q i ) = (a ci qi Q i ) qi – C= k=1 ck qi Problem of firm i: @⇡ i (qi , Q imax ) ⇡ i (q i , Q i ) = ( a ci q Q )q q= 0 i , (a c i q i Q i ) i qi =i 0 i @qi @⇡ i (qi , Q i ) 1 0 , (a = c q Q i) qi = 0 ,i qi = (a ci @q Qi i ) i (6) 2 1 28 , qi = (a ci Q i) (6) i (q i , Q i ) = 0 , (a ci qi Q i) qi = 0 @qi na C Nash 1equilibrium , q = (a c i Q ) i i (6) ,Q= n+1 ⌘ Q⇤ 2 1. Sum the best-response 2. Combine Developing (6) and (6) and using (7) (7) gives ver all n firms functions over all firms n X n X 2qi = a ci Q i =a ci Q + qi 1 qi = (a ci Q i) i=1 2 "i=1 # 1 X n n X n X na C ,Q= a ci Q , qi = a ci Q=a ci 2 i=1 i n+1 i=1 i=1 na ci C i n X , qi = a ci , 2Q = na C (Q qi ) n+1 i=1 na + a nci ci na + ci + C i n X n X , qi = n+1 , 2Q = na C Q+ qi i=1 i=1 a nci + C i , qi = ⌘ qi⇤ , 2Q = na C nQ + Q n+1 na C a+C i ,Q= ⌘ Q⇤ (7) qi⇤ 0,a nci + C i 0 , ci  n+1 n 29 , qi = a cina + a nc + ci + n + na 1i+ aci ncna c na C+ ici + C i , qi = , qi = i i = Nash equilibrium (2) na + a nci ci na + ci + C i n+1 n+1 a nci +a C nc i i + ⇤C i , qni + = 1 , qi = ⌘ qi ⌘ qi⇤ n+1 n+1 ✓✓ ◆2◆2 a nci + C i , qi⇤ 3.= Equilibrium ⌘ profit a + C ia + C i Symmetric ⇤ ⇤ firms i+ ⇤ a a ncnc C i i qi ⇡ ✓ = ( p ⇤ ⇤ c ) q ⇤ ⇤ = ◆ i+C qi 0 ,nqai+ nc ⇤ 10 i,+aC nc i i+ 0,C ici 0 , ci  i⇡ i = (p i ci )i q = i 2 n Competitive n ⇡ ⇤ = (p ⇤ c ) q ⇤ = a nc pressure i + C increases i n+ 1 1 nwith + ✓ ◆2 a + C na i CC a + C i number i i of firms.n⇤ + 1 a nc + C , a nci⇤ + C i p⇤⇤0=, c i na ⇤ C a + ⇡ ⇤ = ( p ⇤ c ) q = i i p = a Q =aa Q = an =n + 1 = n + 1 i i i n+1 n+1 n+1 If Ifci c= c for all i = 1... i = c for all i = 1... n, C = nc, C n, C = nc, C i = (n i = (n ⇤⇤ na a + C C a+ a C C i + ci + a Cnci + C i + = a Qp = cai = a C a + = cC = i + c i If c i = a c c nc for = i + all i = i 1... n,⇤ C = ⇤ nc, C ai a=nc n++ (nc (n1()nc.1)So 1c) c a a c ci = cnin=+ 1 +1 n+1 n+1 i n + 1 c = i If c = c for all qi qi== ⇤ p1...cn,= ⇤ cC == nc,nC+i 1= (n 1= ) c. So n + 1 ni + 1 i = p = i n+1 n c+ 1 n + n+1 C a + C i + ci a nci + C qi⇤ = p⇤ c = ⇤ a nc + ( na nc + = 1 ) c a (n✓ 1) c ◆ a c ci = ci = i qi = p ⇤ c = ✓ = 2◆2 1 n+1 n+1 n + 1 n +⇤ 1 n a+ 1c a cn + 1 ⇡ ⇤i⇡= ✓ ◆2 ✓ ◆2 ✓ i = ◆2n + n +11 a nci + C i ⇤ a ⇡c⇤ = a c ⇤ ⇡ i = (p ⇤ ⇤ ci ) q i = ⇡i = i n+1 n+1 n+1 Lerner Lernerindex index a ac c Lerner index p⇤p⇤ c c n+1 a ac c ci = c for all i = 1... n, C = nc, Lerner C i =index (n 1) c. So ⇤a c = = a+nc n+1 = = p⇤ c pn+1 p ⇤ a n+1 a+ncc a+ a +ncnc a nc + (n 1) c a c = a+nc = n+1 ⇤ ⇤ a c p⇤ c n+1 p ⇤ a c a + nc 30 qi = p c= = = a+nc = n+1 Mergers between several firms Model Demand: < ' = = − ' (homogeneous product) - firms with the same constant marginal costs: : Cournot competition Suppose 7 firms consider merging (with 2 ≤ 7 ≤ 9) Assumption: No efficiency gain After the merger, the merged entity continues to produce at cost 7. ⇒ Firms are still symmetric after the merger Number of active firms Before the merger: 9 After the merger: 9 − : non-merged firm + merged entity → 9 − : + 1 firms 31  When is the merger profitable? Compare Cournot equilibrium profits before and after the merger Profit of the Total profits of merged entity merging firms ( (=) after before ( = (%&' ( ( = )* ' ) Slightly larger ! than "# # 32 When is the merger profitable? (2) “80% rule” Mergers between multiple symmetric Cournot competitors (and without any impact on efficiency) are only profitable if they involve at least 80% of the firms in the market. Intuition: Profitability depends on 2 opposite forces 1. By internalising the previous rivalry, the merged entity reduces the quantity produced, which increases its profit. 2. Outside firms react by increasing their quantity, which reduces the profitability of the merger. → The proportion of outside firms must be small enough ( Redo the previous analysis under these assumptions Main result 7 Fixed asset combinations and increasing marginal costs enlarge the 6" scope for profitable mergers in Cournot industries. 41 Synergies Source of efficiency By rationalising its operations, the merged entity can produce at a lower marginal cost. Model < ' = = − ', - firms, @ firms merge Marginal cost before merger: : for all firms Marginal cost after merger Non-merging firms: 7 Merged entity: 7 − + Redo the analysis under these assumptions Main result Mergers between Cournot competitors that do not result in a highly concentrated market are only profitable if they entail sufficiently large synergies. 42 Synergies. Example with 3 firms Suppose firms 1 and 2 consider merging. Before the merger NE : qib = (a − c) /4, π ib = (a − c) 2 /16, p b = (a + 3c) /4 After the merger q3 = 12 (a − c − q12 ) and q12 = 12 (a − c + x − q3 ) € NE : q12a = (a − c + 2x) /3, π12a = (a − c + 2x) 2 /9 p a = (a + 2c − x) /3 a b x b Merger profitable if π >π +π ⇔ 12 1 > 3 2 − 4 ≈ 0,24 2 a−c € x 1 Merger increases consumer surplus if a b p a−c 4 € 43 Synergies. Example with 3 firms (graphically) q3 a−c q12(q3) with synergies € q12(q3) q1(q3) + q2(q3) a −c 2 a −c 3 a −c 4 € q3(q1+q2) = q3(q12) € q1+q2, q12 a −c a −c 2(a −c ) a−c € 3 2 3 44 Welfare analysis of Cournot mergers We use the total surplus criterion Sum of consumer surplus (CD) and total profits (“insiders” and “outsiders” profits). Allow merger if ΔF = ΔCD + ΔΠ) +ΔΠ* > 0 Interplay between Competition-reducing effect of mergers Potential efficiency gains Merger can increase total surplus if efficiency gains are large enough. → ‘Efficiency defence’ But, there also exist levels of synergies that make mergers profitable but, at the same time, detrimental to consumers (or to society as a whole). 45 Welfare analysis of Cournot mergers (2) Example with 3 firms (continued) 0.03 0.25 Not profitable Profitable Not desirable Desirable Merger rejected Merger accepted Lesson. Suppose that mergers among Cournot competitors induce synergies. When a merger does not make the market too concentrated, profitability of the merger is a sufficient condition for welfare improvement. However, if the merger results in a highly concentrated market, it could be profitable and welfare-detrimental at the same time. 46 Mergers under price competition Recall: Price competition Positive externalities If one firm sets a higher price, it Consequences positively impacts the profit of In contrast to quantity the other. competition, there are strong Strategic complements private incentives to merge absent any efficiency gains. Reaction functions are upward- sloping; strategies evolve in the Mergers are necessarily welfare- same direction. reducing if there are no efficiency gains. ⇒ Merging firms increase their price ⇒ Outside firms react by increasing their price as well. This raises the profitability of the merger. 47