Proof. See Appendix.
Let us now provide an intuition for this result. Under the downstream investment regime, the incentive to invest stems from the cost reduction induced through investment as well as from the effect of investment on competition. Under the upstream investment regime, however, the incentive to invest stems from the increase in total output induced by the investment. With Cournot competition, investment by one downstream firm leads to an output increase by that firm and an output reduction by the rival firm. Hence, the increase in market output is modest. This is beneficial for the downstream investor, but provides only modest investment incentives to the upstream monopolist. Thus, the downstream investment regime always leads to a higher investment level. With Bertrand competi-tion, investment triggers more intense competition and hence, a large increase in market output. This is beneficial for the upstream monopolist, but hurts the downstream com-petitors. So, investment incentives under the upstream investment regime are relatively more pronounced while they are rather weak under the downstream investment regime.
However, the upstream monopolist invests only, when the regulated wholesale margin is large enough to make investment attractive at all. This is only the case, when the fixed upstream cost F is sufficiently large, such that a high upstream margin is needed for the monopolist in order to recoup this cost.
upstream good and hence, upstream profits. The maximization problem under Cournot competition is given by
maxq1 +fi1=w(q1+q2) + (p1(q1, q2)≠w≠(c≠ 1))q1.
This can be rewritten as
maxq1 +fi1=wq2+ (p1(q1, q2)≠(c≠ 1))q1,
which reveals that the production cost of downstream firm 1 is now given only by c≠
1 instead of w+c≠ 1. The independent downstream firm D2 maximizes only its downstream profits, that is,
maxq2 fi2= (p2(q1, q2)≠w≠(c≠ 2))q2.
However, it takes the lower marginal cost of production of the integrated firm through its output choiceq1 into account. The corresponding maximization problems under Bertrand competition are stated in Section B.1 of the appendix. Under VI the same differences as under VS with respect to the different modes of competition persist. Therefore, we omit a more thorough discussion of these differences here and refer to Section 2.3.1. In addition, in the remainder of this chapter we report only the maximization problems and optimality conditions for Cournot competition and refer to Section B.1 of the appendix for the corresponding maximization problems under Bertrand competition.
2.4.2 Investment Stage
Before we analyze the differences in investment among the two modes of competition, we compare investment under the different investment regimes 1 U pstreamV I , DownstreamV I 2 with the socially optimal investment 1 W elf are2 in the following lemma.
Lemma 2.2. [Investment under Vertical Integration] Under vertical integration, invest-ment is always below the socially optimal level, regardless of the investinvest-ment regime and the mode of competition, that is, W elf are> U pstreamV I , DownstreamV I .
Proof. See Appendix.
This result reflects our findings under VS in Section 2.3.2 and Lemma 2.1. Private in-vestors do not take the effect of investment on consumers and the other firm’s profits into account. As market power exists in our model, private investment is always below the socially optimal investment. Again, this result simplifies our subsequent analysis as we have to determine only the investment regime with the highest investment incentives in order to find the ‘best’ regime from a welfare perspective.
Upstream Investment Regime. Under the upstream investment regime, the monopo-list chooses how much to invest in the cost reduction of the downstream firms. It antici-pates downstream industry demand, that is, QC under Cournot competition respectively QB under Bertrand competition, and takes the wholesale price w as given. Thereby, it takes its own downstream profits into account. Hence, under Cournot competition the upstream monopolist maximizes
max
1, 2 +fi1=wQú( 1, 2) + (p1(Qú( 1, 2))≠w≠c+ 1)qú1( 1, 2)≠K
2 21≠K 2 22.
The first term represents the upstream profit and the second term the downstream affil-iate’s profit. Maximization yields the following optimality conditions for investment in the own downstream affiliate’s and the independent downstream firm’s production cost
1 : Y_ __ ] __ _[
wˆQú( 1, 2) ˆ 1
¸ ˚˙ ˝
>0
+ˆp1(q1ú, q2ú) ˆqú2
ˆqú2 ˆ 1q1ú
¸ ˚˙ ˝
strategic ef f ect
+ qú1
¸˚˙˝
quantity ef f ect
≠ K 1
¸ ˚˙ ˝
cost ef f ect
= 0 Z_ __
^ __ _\
(2.5)
2 : Y_ __ ] __ _[
wˆQú( 1, 2) ˆ 2
¸ ˚˙ ˝
>0
+ˆp1(qú1, qú2) ˆqú2
ˆq2ú
ˆ 2qú1+ (pú1≠w≠c+ 1) ˆq1ú ˆ 2
¸ ˚˙ ˝
<0
≠ K 2
¸ ˚˙ ˝
cost ef f ect
= 0 Z_ __
^ __ _\
(2.6)
Investment in each of the two downstream firms boosts the demand for the upstream good just as under VS (the first term in expressions (2.5) and (2.6)). In addition, investment now also affects the downstream affiliate’s profit: First, investment in the own downstream affiliate’s production cost has the same effects on the affiliate’s profit as investment by the downstream affiliate itself. These are the quantity, the strategic and the cost effect.
Second, investment in the downstream rival’s production cost hurts the own downstream affiliate’s profits. That is, it makes the downstream rival more aggressive which leads to lower prices and output for the downstream affiliate. Thus, while investment in the own downstream affiliate 1 is larger than under VS, investment in the downstream rival 2
is lower than under VS. This can be easily seen by comparing the optimality conditions under VI (expressions (2.5) and (2.6)) and under VS (expression (2.1)).
Downstream Investment Regime. Under the downstream investment regime, the downstream firms choose how much to invest into the reduction of their own production cost. They take the access price was given and anticipate their future demand qú1 and qú2 in the subsequent competition stage. Thus, the downstream investment problem is given by
max1 +fi1=wQú( 1, 2) + (p1(Qú( 1, 2))≠w≠c+ 1)q1ú( 1, 2)≠K
2 21≠K 2 22.
for the integrated firm and
max
2 fi2= (p2(Qú( 1, 2))≠w≠(c≠ 2))q2ú( 1, 2)≠K 2 22,
for the independent firm. Maximization with respect to the investments in cost reduction,
1 and 2, yields the following optimality conditions
1 : Y_ __ ] __ _[
wˆQú( 1, 2) ˆ 1
¸ ˚˙ ˝
>0
+ˆp1(q1ú, q2ú) ˆqú2
ˆqú2 ˆ 1q1ú
¸ ˚˙ ˝
strategic ef f ect
+ qú1
¸˚˙˝
quantity ef f ect
≠ K 1
¸ ˚˙ ˝
cost ef f ect
= 0 Z_ __
^ __ _\
(2.7)
2 : Y_ __ ] __ _[
ˆp2(qú1, q2ú) ˆqú1
ˆq1ú ˆ 2qú2
¸ ˚˙ ˝
strategic ef f ect
+ q2ú
¸˚˙˝
quantity ef f ect
≠ K 2
¸ ˚˙ ˝
cost ef f ect
= 0 Z_ __
^ __ _\
(2.8)
Notice that the incentives to invest by downstream firmD1are equal to the incentives un-der the upstream investment regime, holding investment of firmD2constant (expressions (2.5) and (2.7) are identical). The reason for this result lies in the fact that the investment decision stays within the same firm regardless of the specific investment regime. The op-timality condition for investment by downstream firm D2, however, is equivalent to the corresponding condition under VS.
Now we can state the second part of our main result, which compares investment under the upstream investment regime with investment under the downstream investment regime under VI.
Proposition 2.2. [Comparison of Investment Regimes under Vertical Integration] The downstream investment regime always provides an investment outcome closer to the social optimum relative to the upstream investment regime regardless of the mode of competition, that is, W elf are> DownstreamV I > U pstreamV I .
Proof. See Appendix.
Let us now provide an intuition for this result. Under VI, the investment regime does not affect the incentives to invest in the integrated firm’s downstream production cost as the investment decision always stays within the same firm. Thus, the investment regime plays only a role for investment in the independent downstream firm. As was described in this section, investment in the independent downstream firm hurts the integrated firm’s downstream profits while it increases the upstream profits. Hence, under the upstream investment regime the integrated firm’s investment incentives are rather weak. Under the downstream investment regime, however, investment incentives by the independent firm are identical to those under VS, given the integrated competitors investment. In sum, as is shown in the corresponding proof in the appendix, these are always higher than the integrated monopolist’s incentives and hence, the downstream regime always provides a superior result under VI regardless of the mode of competition.
We should shortly mention here how the vertical ownership structure influences the
down-stream firms’ investment activity. VI partly alleviates the double marginalization problem caused through the presence of a positive upstream fixed costF and the linear wholesale price w needed for its recovery. That is, the integrated firm faces a lower marginal cost of production. This leads, for given investments, to higher output by the integrated firm
1qV S1 < q1V I2, lower output by the independent firm 1qV S2 > q2V I2 and higher total output
1QV S < QV I2under both modes of competition for given investments (see Section B.1 in the appendix for the explicit results). The investment levels are influenced according to the same pattern, as firm output is the main determinant of investment. That is, VI causes more investment by the integrated firm1 V S1 < V I1 2, less investment by the independent firm1 V S2 > V I2 2and higher total investment1 V S1 + V S2 < V I1 + V I2 2compared to VS under both modes of competition. This aggravates the static effect of VI and leads to an even larger market output. Hence, in line with previous literature, VI yields a better overall performance compared to VS (compare, e.g., Buehler and Schmutzler, 2008).
Moreover, it is noteworthy that our assumption on linear wholesale prices with a positive upstream margin, caused by our assumption on upstream fixed cost recovery, is central for our results. An increase in the wholesale price, caused by an increase in the upstream fixed cost, stimulates upstream investment incentives and mitigates downstream investment incentives. Hence, only with a sufficiently high wholesale price, the mode of competition starts to matter for determining the ‘best’ investment regime. A linear access price as well as our underlying assumption on upstream capital cost recovery resemble the situation in many regulated network utilities.39 Moreover, notice that a positive regulated upstream margin requires some commitment on the regulator’s side. That is, the wholesale price has to be determined before the investment decision takes place. A similar approach is used by, e.g., Valletti and Cambini (2005). In addition, Valletti (2003) stresses the need, when implementing a regulatory policy, that regulators are endowed with some commitment power over time. A discussion on the commitment value of a regulator’s decision can be found in Guthrie (2006) and Spiller (2005), p. 627-630.
Finally, we should discuss our assumption on upstream cost recovery which is related to the discussion on linear wholesale prices in the preceding paragraph. In our analysis, we have assumed that the revenues from the regulated wholesale price w(F) just cover the upstream capital cost F. The cost of investment, however, is covered by an ex-ante subsidy which is paid whether or not the investment is undertaken. Technically, this subsidy ensures that the wholesale price w(F) is independent of the investment regime.
Consequently, a simple comparison of both investment regimes becomes possible. How-ever, if the wholesale price would also cover the upstream investment cost, the wholesale
39Non-linear tariffs are under suspicion to make discrimination of the downstream competitors possible.
See, e.g., European Commission (2007), p. 58. Moreover, the owners of a regulated infrastructure are generally entitled to revenues in order to recover their cost. See, e.g., §21 EnWG for the case of German energy sector regulation.
price would depend on the investment regime. That is, for a given upstream fixed cost F¯, the wholesale price under the upstream investment regime would be larger than under the downstream investment regime 1wU pstream1F¯2> wDownstream1F¯22. Thus, a simple comparison of investment under both regimes would not be possible. Moreover, such an assumption would lead to an additional spot market distortion under the upstream in-vestment regime. While this would imply an interesting trade-offto analyze, it is beyond the scope of this study.