reduce competition increase market power cost savings economies of scale and scope cost savings Oliver Williamson: the efficiency defense

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1 Mergers Why merge? reduce competton ncrease market power cost savngs economes of scale and scope Why allow mergers? cost savngs Olver Wllamson: the effcency defense Merger wthout cost savngs Before merger: an n-frm olgopoly After a merger of two frms: an (n 1)-frm olgopoly Before merger: Each of the mergng frms had a market share of 1/n, totallng 2/n After merger: the merged frm has a market share of 1/(n 1). The prce may have ncreased somewhat from the merger, but hardly enough to compensate for a loss n market share. So why merge? Why not just expand? Tore Nlssen Strategc Competton Lecture 12 Slde 1

2 The Perry-Porter model There s a factor of producton whose total supply s fxed n the ndustry. f you want to expand, then you need access to more of ths factor, whch you can only obtan from other frms n the ndustry. Example: human captal, knowledge on operatons. A merger combnes productve resources that are not avalable outsde the ndustry. A frm ownng a fracton k of that captal stock and producng output n quantty x has costs C(x, k). c C x, k = x 2k C c = x x k Total costs: ( ) 2 Margnal costs: The more k you have, the lower are your margnal costs. A larger frm s able to make better use of ts larger amount of the fxed-supply factor. When two frms merge, the merged entty now has hgher k then the two separate frms, and therefore lower costs. Now, the merged frm obtans a market share n excess of 1/(n 1) because of ts cost beneft. For suffcently hgh c, ths makes a merger proftable. Tore Nlssen Strategc Competton Lecture 12 Slde 2

3 Merger polcy n general, welfare analyses of mergers are complex even wthn rather smple models. An alternatve: a suffcent condton for a merger to be welfare mprovng The Farrell-Shapro crteron A merger affects the mergng frms the non-mergng frms consumers When a merger s proposed, then presumably t s proftable for the mergng frms. So the competton authorty when lookng for a suffcent condton for a welfaremprovement - can lmt the analyss to the merger s effect on () non-mergng frms, and () consumers the external effect of a merger Cost savngs affect to a large extent only the mergng partes. So focusng on the external effect, we do not need to assess vague statements about cost savngs from a merger. f the merger leads to a hgher prce, then non-mergng frms beneft, and consumers suffer. But what s the total external effect? Tore Nlssen Strategc Competton Lecture 12 Slde 3

4 Cournot competton X total output n the ndustry x frm s output y all other frms output: y = X x Frm s costs: c (x ) nverse demand: p(x) Frm s frst-order condton: p(x) + x p (X) - c x(x ) = 0. p(x + y ) + x p (x + y ) - c x(x ) = 0 Frm s response to a change n other frms output: Total dfferentaton wrt x and y : dx p' + xp" = R = dy 2 p' + xp" c xx From whch we fnd frm s response to a change n total output: dx = R dy dx (1 + R ) = R (dx + dy ) = R dx dx '( ) " R p X + x p ( X) = = = λ < 0 dx 1 + R c x p' X xx ( ) ( ) Tore Nlssen Strategc Competton Lecture 12 Slde 4

5 Welfare effects of a merger Two sets of frms: nsders O outsders An nfntesmal merger dx a small exogenous change n ndustry output Change n welfare from ths merger: dw = pdx dc + p c dx x O changes n output assessed at market prce p. c nsders total costs Note: dx = λ dx for each outsder frm From an outsder frm s FOC: p c x = x p (X) dw = ( pdx + X dp dc ) X dp + p' ( X ) λxdx O ( ) '( ) dw dπ = X p' X dx + p X λxdx O dw dπ = λx X p' ( X ) dx = λs s Xp' ( X ) dx O O Here, p < 0 and, typcally, dx < 0. So the external effect of a merger (the accumulaton of many nfntesmal mergers) s postve f and only f: λs> s! O An upper bound on the mergng frms jont (pre-merger) market share n order for ther merger to mprove welfare. Tore Nlssen Strategc Competton Lecture 12 Slde 5

6 Examples 1. Constant margnal costs, lnear demand c xx = 0, p = 0 λ = 1. Before merger: all frms of equal sze. The external effect s postve f the set of mergng frms s less than half of all frms: s m < n/2 < s O But: wll t always be proftable? 2. The Perry-Porter model, quadratc costs, lnear demand k λ = c + k FOC for frm : c x p + x p C (x ) = 0 p x x = 0 p = k λ x s λ = = p ε The external effect s postve f: 1 2 s < s ε O The sze of the external effect depends on how concentrated the non-mergng part of the ndustry s! A merger s more lkely to be welfare-enhancng f the rest of the ndustry s concentrated. A merger among small frms leads to the other, bg, frms to expand, whch s good. Tore Nlssen Strategc Competton Lecture 12 Slde 6

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