Vertical Integration with an Increasing Retail Supply Function. Adekola Oyenuga Department of Economics Norwegian School of Economics and Business Administration Bergen. and Derek Bunn Management Science and Operations department London Business School. NOREL Conference, Stockholm 9 – 10 JUNE 2008.

NOREL Conference, Stockholm2 Tuesday, June 10 The controversial questions: Does vertical integration reduce prices and improve welfare? Or does it raise prices and reduce welfare?

NOREL Conference, Stockholm3 Tuesday, June 10 Alternative arguments Spengler (1950): Vertical integration reduces double marginalization, which would reduce prices and improve welfare. Williamson (1971): Vertical integration reduces the burden of transaction costs in the supply chain, which would also reduce prices and improve welfare. But, Vertical integration may also increase market concentration at the retail level, which would raise retail prices and reduce welfare (the consumer surplus).

NOREL Conference, Stockholm4 Tuesday, June 10 Insights from the literature (1/2) McKenzie (1951), Vernon and Graham (1971), Schmalensee (1973), Hay (1973), Warren-Boulton (1974). When substitution possibilities exist in the use of inputs at the downstream stage (variable proportions). Vertical integration would induce an expansion in the downstream utilization of the intermediate product and of the retail output, which would increase welfare. But vertical integration would also increase monopoly power at the retail level, which would raise prices and reduce welfare. Whether welfare rises or falls following vertical integration depends on which effect dominates.

NOREL Conference, Stockholm5 Tuesday, June 10 Insights from the literature (2/2) Bork (1969), Greenhut and Ohta (1976, 1978). When substitution possibilities do not exist in the use of inputs at the downstream stage (fixed proportions). Vertical integration will not alter the downstream utilization of the intermediate product. Rather, it would reduce the cost of vertical transactions, thereby unambiguously raising welfare.

NOREL Conference, Stockholm6 Tuesday, June 10 But… The generalized nature of these analyses is not readily applicable to more specialized settings. And they ignore unique features which should be considered to meaningfully identify the effects of vertical integration in such environments. Some examples:  A commonly used (retail) distribution network with external effects that results in increasing retail supply costs.  Marketing costs that are rising in the size of the retail demand.  A segmented retail demand. These are familiar features in networked industries such as: telecommunications, electricity, gas, transport and water, etc.

NOREL Conference, Stockholm7 Tuesday, June 10 My questions: How would an increasing retail supply function or / and retail demand segmentation influence the outcome of vertical integration? Would firms still find it economically profitable to vertically integrate?

NOREL Conference, Stockholm8 Tuesday, June 10 The main results: An increasing retail supply function does impose a significant constraint on the welfare gains from vertical integration. If the retail costs rise at a sufficiently high rate (exceeding a critical threshold), then vertical integration will reduce welfare. Compared with vertical separation, vertical integration results in a contraction of the total profit, which raises questions as per whether firms will have sufficient economic incentives to integrate even when this is aggregately beneficial. Welfare is improved by increasing the number of end-user segments, independently of whether vertical integration occurs or not.

NOREL Conference, Stockholm9 Tuesday, June 10 The framework A successive duopoly:  2 symmetric upstream producers (generators) and downstream retailers (power suppliers).  A wholesale market on which they all interact. 2 retail market segments/demands.  e.g. domestic and industrial consumers.  Linear retail demands. Cournot competition at the wholesale and retail levels.  Producers choose wholesale quantities.  Retailers compete for retail market shares.  Solve for Cournot-Nash equilibria at both levels by backward induction. 2 possible ‘states of the market’.  Vertical separation – producers and retailers operate independently.  Vertical integration – producers and retailers merge vertically.

NOREL Conference, Stockholm10 Tuesday, June 10 The vertical structure

NOREL Conference, Stockholm11 Tuesday, June 10 Benchmark analysis: A single end-user segment or retail market (1/2) With vertical separation, Producer i solves: Retailer j solves: The retail linear inverse demand function is: Model the linear retail supply function as: Where ”theta” is the constant rate of increase of the retail costs.

NOREL Conference, Stockholm12 Tuesday, June 10 A single end-user segment (2/2) Solving for the Cournot reaction functions on the wholesale market (with vertical separation): And on the retail market: Which may be solved for the equilibrium quantities and prices at both levels. A similar procedure gives the reaction function on the retail market (with vertical integration) to be: From which we obtain the equilibrium quantities on the wholesale and retail markets, and the retail market price.

NOREL Conference, Stockholm13 Tuesday, June 10 Welfare analysis (1) Comparing the equilibrium profits, prices and quantities obtained under vertical separation with those under integration reveals that: With integration:  The total profit (producer plus retailer’s) falls,  The consumer surplus rises,  Whether the aggregate welfare increases or decreases depends on theta. Welfare rises if: But falls if :

NOREL Conference, Stockholm14 Tuesday, June 10 Two retail markets or end-user segments (1/2) Retailer j now solves: The linear inverse demands: With two retail segments e.g. the domestic and industrial retail demands. And: With the linear retail supply function: Where theta is again the rate of increase of the retail costs.

NOREL Conference, Stockholm15 Tuesday, June 10 The linear inverse demand functions for the two retail market segments

NOREL Conference, Stockholm16 Tuesday, June 10 Two retail markets (2/2) Solving for the Cournot reaction function on the domestic retail market (with vertical separation) gives: and on the industrial retail market: Similar results are obtained under vertical integration. From which we obtain the equilibrium quantities and prices at the wholesale and retail stages.

NOREL Conference, Stockholm17 Tuesday, June 10 Welfare analysis (2) From the analysis with two end-user segments, we can again identify that: With vertical integration:  The total profit falls,  The consumer surplus rises,  Welfare rises if we have: Otherwise it falls provided theta exceeds a defined threshold, which is unchanged from that of the single market analysis.

NOREL Conference, Stockholm18 Tuesday, June 10 Segmentation and Welfare It is desirable to identify the welfare implications of having one or more (two in this case) end-user segments, Proceed by taking the industry structure (vertical separation/vertical integration) as given, and then examine how welfare varies between the cases with one and two retail segments. Moving from one to two retail segments, it is identifiable that:  Total profits rise,  Consumer surplus rises,  Aggregate welfare rises. These results are invariant of vertical separation or vertical integration. Identifiably, retail demand segmentation unambiguously improves welfare, independently of the industry’s vertical structure.

NOREL Conference, Stockholm19 Tuesday, June 10 Some concluding points Welfare will fall with vertical integration when there is an increasing retail supply function and the retail costs rise at a sufficiently high rate i.e. when theta exceeds some critical value. Intuitively, this is because the rise in the consumer surplus from increasing the retail deliveries (due to reduced double marginalization) is countervailed by the drop in total profits following vertical integration. Increasing the number of retail demand segments improves welfare. An explanation for this is that price discrimination becomes more efficient as the number of retail segments increases. The domestic retail price drops while the industrial retail price rises with two retail segments (compared with the case of a single segment). This is because pricing now better reflects consumers’ willingness to pay. Even though vertical integration will improve welfare, i.e. when theta is sufficiently low, the identified drop in total profits suggests that firms may prefer not to integrate.