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.
The controversial questions:

Does vertical integration reduce prices and improve
welfare?

Or does it raise prices and reduce welfare?
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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).
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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.
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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.
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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.
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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?
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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.
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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.
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The vertical structure
Intra-firm intermediate
product transfers
under vertical
integration
Producer i
Producer i-
The wholesale market under
vertical separation
Retailer j
Retailer j-
The second retail
market segment
The first retail market
segment
Retail
deliveries
Retail
deliveries
D2
D1
I1
D3
E.g. Domestic consumers
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I3
I2
E.g. Industrial consumers
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Benchmark analysis: A single end-user segment or retail
market (1/2)

With vertical separation, Producer i solves:
max 
qwi

=
p Q q
xrj
j
=p
r
X x
r
wi
-C
q 
wi
rj
- mXr  x rj - p
w
Q x
w
rj
The retail linear inverse demand function is:
p X   A - b X
r

w
w
Retailer j solves:
max

i
r
1
r
Model the linear retail supply function as:
mXr    Xr

Where ”theta” is the constant rate of increase of the retail costs.
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A single end-user segment (2/2)

Solving for the Cournot reaction functions on the wholesale
market (with vertical separation):
q

wi
q  
wi 
rj

1
i
3b   

q
wi 
2
rj 
A  P wQ w x

1
2b   
rj 
2
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:
x x  
rj

'
And on the retail market:
x x  

A C
rj 
A1  C i
'
2b   

x
rj 
2
From which we obtain the equilibrium quantities on the
wholesale and retail markets, and the retail market price.
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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:
  4b

But falls if :
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  4b
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Two retail markets or end-user segments (1/2)

With two retail segments e.g. the domestic and industrial retail
demands.

Retailer j now solves:
max  = p X  x  p X  x
D
I
j
xrj , xrj

r
D
D
I
I
r
rj
r
rj
r
p X
And:
D
r
 A
-d
3
r
r

X
I
r
 p Q x
w
w
D
rj

x
I
rj

X
D
r
X
I
r
With the linear retail supply function:
m

r
-c
2
p X   A
I

D
The linear inverse demands:
r

 X
- m
X
D
r

X
I
r
   X Dr  X Ir 
r
Where theta is again the rate of increase of the retail costs.
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The linear inverse demand functions for the
two retail market segments
P
A3
A2
The domestic
inverse demand
function with
intercept A2 and
slope c.
The industrial
inverse demand
function with
intercept A3 > A2
and slope d < c.
X
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Two retail markets (2/2)
Solving for the Cournot reaction function on the domestic retail
market (with vertical separation) gives:

x x
D
D
rj
rj 

 


D
d  A2  P w Q    A2  A3

w 
x
rj 


2cd  d  c 
2
and on the industrial retail market:

x x
I
I
rj
rj 

 


I
c  A3  P w Q    A2  A3

w 
xrj


2cd  d  c 
2

From which we obtain the equilibrium quantities and prices at
the wholesale and retail stages.

Similar results are obtained under vertical integration.
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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:
 2cd 
  2
 4b

d  c

Otherwise it falls provided theta exceeds a defined threshold, which is
unchanged from that of the single market analysis.
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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.
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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.
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