• Reduce competition – Increase market power • cost savings – Economies of scale and scope Why allow companies to consolidate in Europe? • Merger without cost savings
output in quantity x has costs C(x, k). Total costs: C(x,k)= c x2 ∂C c 2k Marginal costs: ∂x = k x
Merger policy
Cournot competition X – total output in the industry Firm i’s costs: ci(xi) Inverse demand: p(X) Firm i’s firstorder condition: p(X) + xip’(X)  cix(xi) = 0. ⇒ p(xi + yi) + xip’(xi + yi)  cix(xi) = 0 ⇒ Firm i’s response to a change in other firms’ output: Total differentiation wrt xi and yi: dxi =Ri =− p'+xip" dy 2p'+x p"−ci i ixx Firm i’s response to a change in total output: dxi = Ridyi ⇒ dxi(1 + Ri) = Ri(dxi + dyi) =RidX ⇒ dxi = Ri =p'(X)+xip"(X)=−λ<0 dX 1+ R ci(x )− p'(X ) i i xx i • Before merger: Each of the merging firms had a market share of 1/n, totalling 2/n • Before merger: an nfirm oligopoly • After a merger of two firms: an (n – 1)firm oligopoly • Before merger: Each of the merging firms had a market share of 1/n, totalling 2/n • After merger: the merged firm has a market share of 1/(n – 1). • Before merger: an nfirm oligopoly • After a merger of two firms: an (n – 1)firm oligopoly • Before merger: Each of the merging firms had a market share of 1/n, totalling 2/n • After merger: the merged firm has a market share of 1/(n – 1). Why merge? • reduce competition – increase market power • cost savings – economies of scale and scope Why allow mergers? • cost savings ƒ Oliver Williamson: the efficiency defense Merger without cost savings • Before merger: an nfirm oligopoly • After a merger of two firms: an (n – 1)firm oligopoly • Before merger: Each of the merging firms had a market share of 1/n, totalling 2/n • After merger: the merged firm has a market share of 1/(n – 1). • The price may have increased somewhat from the merger, but hardly enough to compensate for a loss in market share. So why merge? Why not just expand? Tore Nilssen – Strategic Competition – Lecture 12 – Slide 1The PerryPorter model • There is a factor of production whose total supply is fixed in the industry. • If you want to expand, then you need access to more of this factor, which you can only obtain from other firms in the industry. • Example: human capital, knowledge on operations. A merger combines productive resources that are not available outside the industry. A firm owning a fraction k of that capital stock and producing output in quantity x has costs C(x, k). Total costs: ( ) 2 , 2 c C x k x k = Marginal costs: C c x x k ∂ = ∂ • The more k you have, the lower are your marginal costs. • A larger firm is able to make better use of its larger amount of the fixedsupply factor. • When two firms merge, the merged entity now has higher k then the two separate firms, and therefore lower costs. Now, the merged firm obtains a market share in excess of 1/(n – 1) because of its cost benefit. For sufficiently high c, this makes a merger profitable. Tore Nilssen – Strategic Competition – Lecture 12 – Slide 2Merger policy • In general, welfare analyses of mergers are complex – even within rather simple models. • An alternative: a sufficient condition for a merger to be welfare improving • The FarrellShapiro criterion A merger affects • the merging firms • the nonmerging firms • consumers When a merger is proposed, then – presumably – it is profitable for the merging firms. So the competition authority – when looking for a sufficient condition for a welfareimprovement  can limit the analysis to the merger’s effect on (i) nonmerging firms, and (ii) consumers → the external effect of a merger Cost savings affect to a large extent only the merging parties. So focusing on the external effect, we do not need to assess vague statements about cost savings from a merger. If the merger leads to a higher price, then nonmerging firms benefit, and consumers suffer. But what is the total external effect? Tore Nilssen – Strategic Competition – Lecture 12 – Slide 3Cournot competition X – total output in the industry xi – firm i’s output yi – all other firms’ output: yi = X – xi Firm i’s costs: c i (xi ) Inverse demand: p(X) Firm i’s firstorder condition: p(X) + xi p’(X)  c i x(xi ) = 0. ⇒ p(xi + yi ) + xi p’(xi + yi )  c i x(xi ) = 0 ⇒ Firm i’s response to a change in other firms’ output: Total differentiation wrt xi and yi : ' " 2 ' " i i i i i i dx p x p R dy p x p c + = = − + − xx From which we find firm i’s response to a change in total output: dxi = Ri dyi ⇒ dxi (1 + Ri ) = Ri (dxi + dyi ) = Ri dX ⇒ ( ) ( ) ( ) ( ) ' " 0 1 ' i i i i i i xx i dx R p X x p X dX R c x p X λ + = = = − + − < Tore Nilssen – Strategic Competition – Lecture 12 – Slide 4Welfare effects of a merger Two sets of firms: I – insiders O – outsiders An infinitesimal merger • dXI – a small exogenous change in industry output Change in welfare from this merger: I i I x i i O dW pdX dc p c dx ∈ = − + ⎡ − ⎤ ∑⎣ ⎦ • changes in output assessed at market price p. • c I – insiders’ total costs • Note: dxi = – λi dXI for each outsider firm • From an outsider firm’s FOC: p – c i x = – xi p’(X) ⇒ ( ) ' ( ) I I I I i i i O dW pdX X dp dc X dp p X λ x dX ∈ = + − − + ∑ ' ' ( ) ( ) I I I i i O dW dπ λ X p X dX p X x dX ∈ − = − + ∑ i I ' ' ( ) ( ) I i i I I i i I I i O i O dW dπ λ x X p X dX λ s s Xp X dX ∈ ∈ ⎡ ⎤ ⎡ ⎤ − = − = − ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ ⎣ ⎦ ∑ ∑ Here, p’ < 0 and, typically, dXI < 0. So the external effect of a merger (the accumulation of many infinitesimal mergers) is positive if and only if: i i I i O λs s ∈ ∑ > ! → An upper bound on the merging firms’ joint (premerger) market share in order for their merger to improve welfare. Tore Nilssen – Strategic Competition – Lecture 12 – Slide 5Examples 1. Constant marginal costs, linear demand c i xx = 0, p” = 0 → λI = 1. Before merger: all firms of equal size. The external effect is positive if the set of merging firms is less than half of all firms: ⇔m < n/2 I i O s ∈ < ∑ i s • But: will it always be profitable? 2. The PerryPorter model, quadratic costs, linear demand i i i k c k λ = + FOC for firm i: p + xi p’ – C’(xi ) = 0 ⇔ 0 i i i c p x x k − − = ⇔ i i x p λ = ⇔ i i i x s p λ ε = = The external effect is positive if: 1 2 I i i O s s ε ∈ < ∑ • The size of the external effect depends on how concentrated the nonmerging part of the industry is! • A merger is more likely to be welfareenhancing if the rest of the industry is concentrated. • A merger among small firms leads to the other, big, firms to expand, which is good. Tore Nilssen – Strategic Competition – Lecture 12 – S Why merge? • reduce competition – increase market power • cost savings – economies of scale and scope Why allow mergers? • cost savings ƒ Oliver Williamson: the efficiency defense Merger without cost savings • Before merger: an nfirm oligopoly • After a merger of two firms: an (n – 1)firm oligopoly • Before merger: Each of the merging firms had a market share of 1/n, totalling 2/n • After merger: the merged firm has a market share of 1/(n – 1). • The price may have increased somewhat from the merger, but hardly enough to compensate for a loss in market share. So why merge? Why not just expand? Tore Nilssen – Strategic Competition – Lecture 12 – Slide 1The PerryPorter model • There is a factor of production whose total supply is fixed in the industry. • If you want to expand, then you need access to more of this factor, which you can only obtain from other firms in the industry. • Example: human capital, knowledge on operations. A merger combines productive resources that are not available outside the industry. A firm owning a fraction k of that capital stock and producing output in quantity x has costs C(x, k). Total costs: ( ) 2 , 2 c C x k x k = Marginal costs: C c x x k ∂ = ∂ • The more k you have, the lower are your marginal costs. • A larger firm is able to make better use of its larger amount of the fixedsupply factor. • When two firms merge, the merged entity now has higher k then the two separate firms, and therefore lower costs. Now, the merged firm obtains a market share in excess of 1/(n – 1) because of its cost benefit. For sufficiently high c, this makes a merger profitable. Tore Nilssen – Strategic Competition – Lecture 12 – Slide 2Merger policy • In general, welfare analyses of mergers are complex – even within rather simple models. • An alternative: a sufficient condition for a merger to be welfare improving • The FarrellShapiro criterion A merger affects • the merging firms • the nonmerging firms • consumers When a merger is proposed, then – presumably – it is profitable for the merging firms. So the competition authority – when looking for a sufficient condition for a welfareimprovement  can limit the analysis to the merger’s effect on (i) nonmerging firms, and (ii) consumers → the external effect of a merger Cost savings affect to a large extent only the merging parties. So focusing on the external effect, we do not need to assess vague statements about cost savings from a merger. If the merger leads to a higher price, then nonmerging firms benefit, and consumers suffer. But what is the total external effect? Tore Nilssen – Strategic Competition – Lecture 12 – Slide 3Cournot competition X – total output in the industry xi – firm i’s output yi – all other firms’ output: yi = X – xi Firm i’s costs: c i (xi ) Inverse demand: p(X) Firm i’s firstorder condition: p(X) + xi p’(X)  c i x(xi ) = 0. ⇒ p(xi + yi ) + xi p’(xi + yi )  c i x(xi ) = 0 ⇒ Firm i’s response to a change in other firms’ output: Total differentiation wrt xi and yi : ' " 2 ' " i i i i i i dx p x p R dy p x p c + = = − + − xx From which we find firm i’s response to a change in total output: dxi = Ri dyi ⇒ dxi (1 + Ri ) = Ri (dxi + dyi ) = Ri dX ⇒ ( ) ( ) ( ) ( ) ' " 0 1 ' i i i i i i xx i dx R p X x p X dX R c x p X λ + = = = − + − < Tore Nilssen – Strategic Competition – Lecture 12 – Slide 4Welfare effects of a merger Two sets of firms: I – insiders O – outsiders An infinitesimal merger • dXI – a small exogenous change in industry output Change in welfare from this merger: I i I x i i O dW pdX dc p c dx ∈ = − + ⎡ − ⎤ ∑⎣ ⎦ • changes in output assessed at market price p. • c I – insiders’ total costs • Note: dxi = – λi dXI for each outsider firm • From an outsider firm’s FOC: p – c i x = – xi p’(X) ⇒ ( ) ' ( ) I I I I i i i O dW pdX X dp dc X dp p X λ x dX ∈ = + − − + ∑ ' ' ( ) ( ) I I I i i O dW dπ λ X p X dX p X x dX ∈ − = − + ∑ i I ' ' ( ) ( ) I i i I I i i I I i O i O dW dπ λ x X p X dX λ s s Xp X dX ∈ ∈ ⎡ ⎤ ⎡ ⎤ − = − = − ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ ⎣ ⎦ ∑ ∑ Here, p’ < 0 and, typically, dXI < 0. So the external effect of a merger (the accumulation of many infinitesimal mergers) is positive if and only if: i i I i O λs s ∈ ∑ > ! → An upper bound on the merging firms’ joint (premerger) market share in order for their merger to improve welfare. Tore Nilssen – Strategic Competition – Lecture 12 – Slide 5Examples 1. Constant marginal costs, linear demand c i xx = 0, p” = 0 → λI = 1. Before merger: all firms of equal size. The external effect is positive if the set of merging firms is less than half of all firms: ⇔m < n/2 I i O s ∈ < ∑ i s • But: will it always be profitable? 2. The PerryPorter model, quadratic costs, linear demand i i i k c k λ = + FOC for firm i: p + xi p’ – C’(xi ) = 0 ⇔ 0 i i i c p x x k − − = ⇔ i i x p λ = ⇔ i i i x s p λ ε = = The external effect is positive if: 1 2 I i i O s s ε ∈ < ∑ • The size of the external effect depends on how concentrated the nonmerging part of the industry is! • A merger is more likely to be welfareenhancing if the rest of the industry is concentrated. • A merger among small firms leads to the other, big, firms to expand, which is good. Tore Nilssen – Strategic Competition – Lecture 12 – S Why merge? • reduce competition – increase market power • cost savings – economies of scale and scope Why allow mergers? • cost savings ƒ Oliver Williamson: the efficiency defense Merger without cost savings • Before merger: an nfirm oligopoly • After a merger of two firms: an (n – 1)firm oligopoly • Before merger: Each of the merging firms had a market share of 1/n, totalling 2/n • After merger: the merged firm has a market share of 1/(n – 1). • The price may have increased somewhat from the merger, but hardly enough to compensate for a loss in market share. So why merge? Why not just expand? Tore Nilssen – Strategic Competition – Lecture 12 – Slide 1The PerryPorter model • There is a factor of production whose total supply is fixed in the industry. • If you want to expand, then you need access to more of this factor, which you can only obtain from other firms in the industry. • Example: human capital, knowledge on operations. A merger combines productive resources that are not available outside the industry. A firm owning a fraction k of that capital stock and producing output in quantity x has costs C(x, k). Total costs: ( ) 2 , 2 c C x k x k = Marginal costs: C c x x k ∂ = ∂ • The more k you have, the lower are your marginal costs. • A larger firm is able to make better use of its larger amount of the fixedsupply factor. • When two firms merge, the merged entity now has higher k then the two separate firms, and therefore lower costs. Now, the merged firm obtains a market share in excess of 1/(n – 1) because of its cost benefit. For sufficiently high c, this makes a merger profitable. Tore Nilssen – Strategic Competition – Lecture 12 – Slide 2Merger policy • In general, welfare analyses of mergers are complex – even within rather simple models. • An alternative: a sufficient condition for a merger to be welfare improving • The FarrellShapiro criterion A merger affects • the merging firms • the nonmerging firms • consumers When a merger is proposed, then – presumably – it is profitable for the merging firms. So the competition authority – when looking for a sufficient condition for a welfareimprovement  can limit the analysis to the merger’s effect on (i) nonmerging firms, and (ii) consumers → the external effect of a merger Cost savings affect to a large extent only the merging parties. So focusing on the external effect, we do not need to assess vague statements about cost savings from a merger. If the merger leads to a higher price, then nonmerging firms benefit, and consumers suffer. But what is the total external effect? Tore Nilssen – Strategic Competition – Lecture 12 – Slide 3Cournot competition X – total output in the industry xi – firm i’s output yi – all other firms’ output: yi = X – xi Firm i’s costs: c i (xi ) Inverse demand: p(X) Firm i’s firstorder condition: p(X) + xi p’(X)  c i x(xi ) = 0. ⇒ p(xi + yi ) + xi p’(xi + yi )  c i x(xi ) = 0 ⇒ Firm i’s response to a change in other firms’ output: Total differentiation wrt xi and yi : ' " 2 ' " i i i i i i dx p x p R dy p x p c + = = − + − xx From which we find firm i’s response to a change in total output: dxi = Ri dyi ⇒ dxi (1 + Ri ) = Ri (dxi + dyi ) = Ri dX ⇒ ( ) ( ) ( ) ( ) ' " 0 1 ' i i i i i i xx i dx R p X x p X dX R c x p X λ + = = = − + − < Tore Nilssen – Strategic Competition – Lecture 12 – Slide 4Welfare effects of a merger Two sets of firms: I – insiders O – outsiders An infinitesimal merger • dXI – a small exogenous change in industry output Change in welfare from this merger: I i I x i i O dW pdX dc p c dx ∈ = − + ⎡ − ⎤ ∑⎣ ⎦ • changes in output assessed at market price p. • c I – insiders’ total costs • Note: dxi = – λi dXI for each outsider firm • From an outsider firm’s FOC: p – c i x = – xi p’(X) ⇒ ( ) ' ( ) I I I I i i i O dW pdX X dp dc X dp p X λ x dX ∈ = + − − + ∑ ' ' ( ) ( ) I I I i i O dW dπ λ X p X dX p X x dX ∈ − = − + ∑ i I ' ' ( ) ( ) I i i I I i i I I i O i O dW dπ λ x X p X dX λ s s Xp X dX ∈ ∈ ⎡ ⎤ ⎡ ⎤ − = − = − ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ ⎣ ⎦ ∑ ∑ Here, p’ < 0 and, typically, dXI < 0. So the external effect of a merger (the accumulation of many infinitesimal mergers) is positive if and only if: i i I i O λs s ∈ ∑ > ! → An upper bound on the merging firms’ joint (premerger) market share in order for their merger to improve welfare. Tore Nilssen – Strategic Competition – Lecture 12 – Slide 5Examples 1. Constant marginal costs, linear demand c i xx = 0, p” = 0 → λI = 1. Before merger: all firms of equal size. The external effect is positive if the set of merging firms is less than half of all firms: ⇔m < n/2 I i O s ∈ < ∑ i s • But: will it always be profitable? 2. The PerryPorter model, quadratic costs, linear demand i i i k c k λ = + FOC for firm i: p + xi p’ – C’(xi ) = 0 ⇔ 0 i i i c p x x k − − = ⇔ i i x p λ = ⇔ i i i x s p λ ε = = The external effect is positive if: 1 2 I i i O s s ε ∈ < ∑ • The size of the external effect depends on how concentrated the nonmerging part of the industry is! • A merger is more likely to be welfareenhancing if the rest of the industry is concentrated. • A merger among small firms leads to the other, big, firms to expand, which is good. Tore Nilssen – Strategic Competition – Lecture 12 – S 
Welfare effects of a merger Two sets of firms: I – insiders O – outsiders • dXI – a small exogenous change in industry output Change in welfare from this merger: dW=pdX −dcI + I⎣⎦ ∑ i∈O ⎡p−ci⎤dx xi • changes in output assessed at market price p. ⇒()∑() dW= pdX +Xdp−dcI −Xdp+ p' X λxdX ii iiI III i∈O p'(X)λxdX ∑ i∈O Here, p’ < 0 and, typically, dXI < 0. So the external effect of a merger (the accumulation of many infinitesimal mergers) is positive if and only if: ∑λisi >sI ! i∈O → An upper bound on the merging firms’ joint (premerger) market share in order for their merger to improve welfare. dW−dπI =−X p'(X)dX + II ⎢iiI⎥I⎢iiI⎥I ⎣ i∈O ⎦ ⎣ i∈O ⎦
1. Constant marginal costs, linear demand cixx =0,p”=0→λI =1. Before merger: all firms of equal size. The external effect is positive if the set of merging firms is less than half of all firms: ∑ sI< si⇔m<n/2 i∈O • But: will it always be profitable? λi = ki c+ki FOC for firm i: λi = xi = si pε
