Total welfare effects of full market integrations by VSAE

Econometrie

Total welfare effects of full market integrations A lot of national and international business legislation is based on the economic theory of integration of ﬁrms. Firms can integrate by mergers, cartels or other similar constructions. The main subject in this theory is the effect of so-called horizontal integration. Horizontal integration occurs when two or more companies with the same activity merge or enforce a cartel. Effectively this leads to a decrease in the number of active companies in a market and in the extreme case to a monopolist. This reduction in the number of competitors leads to more market power for these companies. Therefore they can increase their proﬁts by lowering their output and selling this for higher prices than before. Result of these changes is a lower total welfare, which is undesirable for the economy.

Besides horizontal integration, there is also the possibility of vertical integration. This vertical integration is a merger or cartel of firms with successive activities in a market. Imagine for example a market for fish. In this market there is a fisherman, this fisherman sells his catch to a fish wholesaler, which in turn sells the fish to a fish store. If two or three of these market players decide to integrate this is called vertical integration. Since an article by J. Spengler, published in 1950, it is a well-known fact that vertical integration of successive monopolists leads to more production and lower prices and therefore total welfare is improving. Other research inspired by this phenomenon showed that vertical integration also leads to more production in less restrictive circumstances. In general, it is stated in the literature that vertical integration is always favorable for total surplus. This is in contrast to horizontal integration, which is in general reducing total surplus. In my thesis I have investigated the relation between the positive effect of vertical integration and the negative effect of horizontal integration. The main question is: Under which circumstances is the net effect of a full market integration welfare improving? Vertical integration of monopolists To illustrate that vertical integration can be better for everybody involved in an economy an example is given below for a simple linear case with two successive monopolies. The output and prices for both monopolists will be calculated and compared to output and price in the integrated market. The demand function is assumed to be linear and marginal costs are zero.

Yvonne Sijm studeerde in december 2004 af in de wiskundige economie aan de UvA. Sinds januari van dit jaar werkt zij als consultant bij Zanders.

Further, the upstream monopolist sells its output, an intermediate good, to the downstream monopolist at a wholesale price w. Given this wholesale price and the demand function the downstream monopolist maximizes its profits, resulting in an output as a function of the wholesale price w. Using this function, the upstream monopolist sets its profit maximizing output. The profits to be maximized by the downstream monopolist are π D (X ) = p (X ) ⋅ X − w ⋅ X = (a − b ⋅ X ) ⋅ X − w ⋅ X

= (a − w ) ⋅ X − b ⋅ X 2 resulting in output a−w XD = or, w=a-2bX. 2b That is, profit maximizing behavior of the downstream firm gives the inverse demand function w(X) for the upstream firm, on which it maximizes its profits. So, profits for the upstream monopolist are π U (X ) = w (X ) ⋅ X = (a − 2b ⋅ X ) ⋅ X and will be maximized by setting output a XU = XD = 4b This output corresponds to the following prices and profits: a 3a a2 w = , p= , πD = , 2 4 16b a2 3a2 πU = , π Total = . 8b 16b When both monopolists decide to integrate, ag-

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Econometrie

a) No integration b) Horizontal integration Figure 1: Different kinds of integration

gregate proﬁts will be maximized. π I (X ) = p (X ) ⋅ X =

(a − b ⋅ X ) ⋅ X

= a ⋅ X − b ⋅ X2

resulting in output a XI = 2b , with corresponding price and profit a a2 . pI = , π I = 2 4b It is obvious that output is higher in the integrated case, that XI is XU. This higher output leads to more profits for the monopolists and higher output also leads to a lower marketclearing price. Like Spengler already concluded, integration of successive monopolists leads to higher total welfare. It is an interesting fact that vertical integration can be good, whereas horizontal integration is usually undesirable for the economy. This has caused other economists to extend this work by investigating vertical integration in more general market structures. In this investigation two different criteria are of interest. A special case is when vertical integration leads to higher consumer surplus and higher profits. This means that vertical integration is better for everyone if Condition 1 holds: Condition 1 a)Integration is socially profitable, i.e. total surplus is higher by means of more output and lower prices. b)Integration is privately profitable, i.e. profit is higher for the integrated company than for the unintegrated companies together. If part a of Condition 1 does not hold, we do not want the integration to occur, because it is not desirable, but if part b does not hold, the companies do not want to integrate because they would be worse off. Vertical integration in an oligopoly If vertical integration of successive monopolists is increasing profits and welfare, it can be expected that the same holds for successive oligopolies. The structure of vertical integra-

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c) Vertical Integration

tion is shown in Figure 1, for clarification this is compared to the unintegrated case and horizontal integration. Note that in this figure three successive oligopolies, or market layers, are shown. Because the number of firms in each layer needs not to be equal, vertical integration can lead to exclusion of one or more firms. See figure 1c. In 1979, Greenhut and Ohta showed in their article “Vertical Integration of Successive Oligopolists” that if vertical integration is profitable for the firms involved it is also welfare improving. They assumed a market with two market layers and an oligopoly in each layer. Comparing the findings on vertical integration with classic theory on horizontal integration an important difference becomes clear. Namely, considering only the cases where integration is profitable for the companies involved and no cost efficiencies or other synergy effects occur, Proposition 1 can be stated. Proposition 1 Compared to the initial state of the market, under Condition 1b: • Vertical integration always leads to higher total welfare • Horizontal integration always leads to lower total welfare This proposition gives rise to the question what happens when there is a combination of horizontal and vertical integration. For example when all companies in a market, upstream and downstream, are integrated. This creates a single monopolist, which is assumed to be undesirable because in general monopolists lead to lower total welfare. But, in this case also vertical integration occurs, which is proved to be favorable for total welfare. Schinkel, Tuinstra and Rüggeberg (2004) have shown that under certain circumstances full market integration can have a net positive effect on total welfare. The trade-off between these negative and positive effects is discussed in the following section. Full market integration

Econometrie

No integration Figure 2: No or full integration

Full Integration

Consider a market with n downstream players and m upstream players, so these players represent oligopolist companies. Market demand is assumed to be linear and is represented by p=a-bX. All companies have constant marginal cost c and d for respectively upstream and downstream firms, and a,b,c,d>0. For this simplified market it can be analyzed what are the changes in profits and welfare if all players decide to fully integrate. Full integration is when all companies in a market form one single monopolist for all activities in the market; this is shown in Figure 2. If there is no integration, all players are maximizing their own profits, this means: • max π(xj)=(w-c)xj for the upstream firms • max π(xi)=(p(X)-w-d)xi for the downstream firms where w is the wholesale price and X =

∑x i =1

∑x . j

(1)

j =1

Equilibrium can be calculated using backward induction. The downstream firms take the wholesale price as given and set their output using market demand. This results in output as a function of the wholesale price. Upstream firms invert this function and can maximize their profits using this inverse demand function. Solving profits for the downstream firms gives the Cournot-Nash equilibrium a−w −d and xiD (w ) = b (n + 1) a−w −d n . ⋅ b n +1 Inverting this gives the inverse downstream demand function, n +1 w (X ) = a − d − bX ⋅ . n Using this, the upstream firms maximize profits using (1), giving a−c −d m x Uj = ⋅ b (n + 1) m + 1 a−c −d n m , X U = m ⋅ x Uj = X D = ⋅ ⋅ b n +1 m +1 X with xi = (2) n X D (w ) = n ⋅ xiD (w ) =

The prices corresponding to this output level are m w = a − d − (a − c − d ) ⋅ m +1 and n m p = a− ⋅ ⋅ (a − c − d ). n +1 m +1 Proﬁts for the downstream and upstream ﬁrms are 2 (a − c − d ) ⋅ n ⋅ ⎛ m ⎞2 , D π Total = ⎟ 2 ⎜ b (n + 1) ⎝ m + 1 ⎠

(a − c − d )

U π Total =

⋅

n m ⋅ . n + 1 (m + 1)2

So total proﬁts are 2 (a − c − d ) ⋅ n ⋅ m ⋅ n + m + 1 . π total = ) 2 2 ( b (n + 1) (m + 1) But, if all players decide to integrate we have a single monopolist maximizing its proﬁt. So under full integration the monopolist chooses output by • max π(X)=(p(X)-c-d)X=(a-c-d-bX)X this results in output a−c −d XI = (3) 2b and price p I = a − bX =

a+c +d a−c −d = +c+d 2 2

with profit 2 (a − c − d ) . πI = 4b For the comparison of consumer surplus we use the rule of thumb that consumer surplus is higher if output is higher and therefore prices are lower. Further, we use that integration only takes place if it is profitable for the companies, so only if their profits are higher. So, if output is higher the consumer surplus and profits are higher, resulting in: Proposition 2 Under condition 1b, If output is higher, total welfare is higher In the non-integrated case we have output XU

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Econometrie

from (2) and in the integrated case we have from (3). So, combining these two results in Condition 2 to hold. Condition 2 Total output is higher under full integration if: n m 1 ⋅ < n +1 m +1 2 Profits without integration are lower or equal to profits with full integration. So, both firms and consumers indeed want to integrate. Therefore it is better for everyone if under Condition 2 a cartel of the whole market is enforced. If a market does not consist of two layers but three or even more, a similar analysis can be made. This results in the more general condition 2’. Condition 2’ Total output is higher under full integration if: K ki 1 < , ∏ 2 i =1 ki + 1 where K is the number of layers and ki is the number of firms in layer i. Non-linear extensions of full integration In the markets discussed above it is assumed that market demand and costs are linear. This gives good insight in the market, but is not very realistic. Therefore the extension is made to more general assumptions in a market with two market layers. First assume the demand function is represented by the nonlinear function p=f(X) with f’(X)<0 and X =

∑x i =1

∑x . j

Marginal costs are again assumed to be constant and ﬁrms are maximizing their proﬁts as before. Given this market demand function it can again be deduced under which conditions full integration is welfare improving. Table 1 can be used to compare the more general case to the case of linear demand by comparing the restrictions to the restricition in Condition 2. Namely, if f’’<0 there are more cases where full integration results in more welfare compared to no integration. For f’’>0 the opposite is true, there are less cases where full integration results in more welfare. Now assume that market demand is again linear, but costs are not. If marginal costs are not constant, distinction has to be made between cartels and mergers. For cartels, the structure of marginal costs does not change the preferences for full integration or not if downstream marginal costs are constant. But if they are not, there are more cases where full integration is desirable if marginal costs are increasing and there are less cases if marginal costs are de-

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Market demand: Linear model, f’’=0

Higher welfare for full integration if: n m 1 ⋅ < n +1 m +1 2

f’’<0

n m 1 ⋅ < +α n +1 m +1 2

α>0

f’’>0

n m 1 ⋅ < −α n +1 m +1 2

α>0

Table 1: Conditions on full integration for nonlinear market demand

creasing. For a merger, the conclusions are the same as for a cartel if marginal costs are increasing. On the other hand, if marginal costs are decreasing total welfare benefits from cost reductions. So, if marginal costs are constant for the downstream firms there are more cases where full integration is desirable. But if downstream marginal costs are also decreasing, there is a trade-off between this negative effect and the positive effect of cost reduction and it depends on the specific cost structure whether full integration is welfare improving. The calculations above all assume that no cost advantages or synergy effects exist. However there can of course be cost advantages or disadvantages for an integrated firm. For example, an integrated firm can reduce its costs by reorganizing overlapping activities. Due to this synergy the firm can produce at lower costs, which will increase total welfare. An example for the opposite effect is when the integrated firm becomes relatively large, leading to ineffective cooperation. This causes the production costs to rise and total welfare to decrease. Ross (1992) assumes that integrated production becomes less efficient and has worked this out for the case of two successive monopolists. In general, total costs for the integrated firm can be written as C(X)+D(X)+η, where η represents the cost advantage or disadvantage. If η<0, there are cost advantages for the integrated firm and there will be more cases where full integration is welfare improving. However, if η>0 the cost disadvantages make less full integration desirable for total welfare. References Greenhut, M.L. and Ohta, H. (1979). Vertical integration of successive oligopolists. American Economic Review, 69, 137-141. Schinkel, M.P., Tuinstra, J. and Rüggeberg (2004). llinois Walls, Working paper, Universiteit van Amsterdam. Spengler, J. (1950). Vertical integration and antitrust policy. Journal of Polictical Economy, 58, 347-352.