Economics of Management
Strategy
BEE3027
Miguel Fonseca
Lecture 8
Recap
• Whenever you…
– … phone your mum, or switch on the light, or buy
health insurance…
• … you purchase a service or product from a
chain of vertically related industries.
• We’ve looked at vertical integration in the
context of firm boundaries.
Recap
• Today, we focus on the strategic aspect of
vertical integration.
• We will start by looking at the potential for
efficiency gains in a vertical merger.
• We will finish by looking at the potential for the
welfare losses with vertical foreclosure.
Why should a firm acquire a supplier?
• If markets are efficient, firms will sell their
output at marginal cost.
• That means that it is just as cheap to buy from
an external supplier as producing in-house.
• Several problems do occur in the real world:
– Incomplete contracts;
– Hold-up;
– Supplier market may not be perfectly competitive.
Double marginalisation
• Let’s consider the case of an upstream firm (supplier)
producing an intermediate good, and a downstream
firm (retailer) producing a consumer good.
• Demand for the final good is linear: P = a - bQ
• The marginal cost of producing a unit of the
intermediate good is constant and equal to c.
• Let’s first consider if the two firms merge and act as a
single company.
P
Monopoly Solution
a
(a+c)/2
c
MR
(a-c)/2b
Q
The case of separate companies
• Now let’s assume both firms are separate
monopolies.
• Lets call the price the retailer pays the supplier
for each unit be equal to r.
• The retailer will maximise profits:
– Πr = (P- r)Q
– Q* = (a-r)/2b, P*= (a+r)/2.
Double marginalisation (cont.)
• So the demand for the intermediate good is
– Q = (a-r)/2b
• Inverting it as a function of the price of the
intermediate good gives: r = a – 2bQ
(note that this is the same as the retailer’s MR curve)
• So the supplier maximises her profits
[Πs = (r-c)Q] with respect to Q:
• This gives Q = (a-c)/4b. r = (a+c)/2.
Double marginalisation (cont.)
• Recall the optimal output and price by retailer:
Q* = (a-r)/2b, P*= (a+r)/2.
• Plugging r = (a+c)/2 into the equilibrium output
and price of the retailer, we get:
Q* = (a-c)/4b and P* = (3a+c)/4.
• Both the consumer surplus AND the sum of
firms’ profits are lower with separate
companies!
P
Double Marginalization
a
(3a+c)/4
MR for
(a+c)/2
manufacturer
c
MR for
retailer
(a-c)/2b
Q
Double marginalisation (cont.)
• How can this be tackled?
• Two-part tariff (franchising):
– Supplier charges a Fixed fee F to sell the good to
retailer and sells each unit at marginal cost.
– F should not affect retailer price, as the key
condition is that MR = MC.
• Royalty arrangement
– Supplier sells goods at MC but earns a percentage
of profits.
Vertical Foreclosure
• Consider a market in which an upstream firm,
U, produces an input at MC = 0.
• Each unit of input is costlessly converted into a
homogenous unit of a final good by
downstream firms D1 and D2.
• The final good is sold to consumers with
demand function given by:
P = a – bQ, Q =q1+q2
Vertical Foreclosure
Vertical Foreclosure
• Let’s also assume firms engage in Cournot
competition.
• U sells input goods to D1 and D2 by proposing
contract of the form (x, T), where
– x is amount of input, and
– T is payment for bundle.
Vertical Foreclosure
• There are two important cases to consider in
this case:
– Public contracts;
– Secret contracts.
• Public contracts are those in which D1 knows
contractual terms of D2 and vice-versa.
• Secret contracts are those in which neither firm
knows what terms were offered to rival.
Vertical Foreclosure
• If contracts are public, the subgame-perfect
equilibrium of this game is:
– U offers (q m / 2,  m / 2) to both D-firms
– Both D-firms accept.
• Under this offer, both firms:
– Make zero profits net of payment to U if all input is
turned into output and sold at monopoly price.
• If firms reject offer, they also make zero profit.
Vertical Foreclosure
• If contracts are secret, it may not be possible
for U to achieve monopoly profit.
• Suppose D2 accepts (q / 2, / 2) offer from U.
m
m
• If so, it is in U’s and D1’s to agree to a contract
(x*,T*), such that x  q / 2.
*
m
• D2 anticipates this and rejects contract.
Vertical Foreclosure
• The only possible equilibrium is for U to offer
contract (q ,  ), where firms make CournotNash profits.
c
c
• In this contract, neither D-firm has an incentive
to raise outputs.
• The solution for U to achieve maximum profit is
to merge with one of the D-firms.
Vertical Foreclosure
Vertical Foreclosure
• Firm U-D1 sells monopoly quantity through its
downstream subsidiary.
• Since it already captures full monopoly profits, it
has no incentives to supply D2.
Vertical Restraints
• Let’s broaden our analysis further and consider
two possibilities:
– Intra-Brand competition: competition between two
different retailers of the same brand of the product.
– Inter-Brand competition: competition between two
different manufacturers/retailers with different
brands the same or similar product.
Vertical Restraints
• Retailers can invest in advertising, customer
service, consumer education, all of which
enhance consumer willingness to pay.
• Such investments benefit retailer but also its
competitors and the manufacturer;
– Thus the level of investment will be insufficient.
• Vertical restraints can ensure the optimal level
of services.
Vertical Restraints
• Could specify contractually what services should be
provided,
– How does one determine the right level of services? How
does one monitoring the level of services?
• This is an example of the principal-agent problem:
– the manufacturer is the principal,
– the retailer is the agent.
• Solution: Align the agent's payoff function with the
principle's payoff function.
The Principal-Agent Problem
• Assume Q = (A-P)s where s is the service level, then
P = A - Q/s.
– Assume the cost of s is increasing (diminishing marginal
returns to service).
• To maximize joint profits, there is an optimal level of
service and an optimal price to the consumer.
• On his own, the retailer will set price is too high (due
to double marginalization) and the service too low
(due to free riding).
Possible Solutions to the P-A
Problem
• Resale Price Maintenance: Establish a
minimum price that the retailer can set.
– Retailers cannot use price to increase consumer
demand, so they must increase service to compete
with other retailers.
– Works for some services, although not for
advertising.
• Exclusive territories: Designate one retailer for
a certain area.
– Retailer gets all the benefits from services provided.
Manufacturer Competition
• Vertical restraints can help manufacturers
compete against rivals.
– Slotting allowances: fixed fee paid to retailers to obtain shelf
space. Two-part tariff in reverse.
– Exclusive dealing: if the manufacturer provides services
(e.g., training) to retailer which could benefit other
manufacturers.
Pro-competitive Effects of
Vertical Restraints
• Exclusivity: gain economies of scale, lower
distribution costs, achieve optimal level of
services.
• Resale price maintenance: achieve optimal
level of services.
• Royalty and franchise agreements: overcome
double marginalization.
Anti-competitive Effects of
Vertical Restraints
• Exclusivity: facilitate collusion, foreclose
markets to competitors.
• Resale price maintenance: facilitate collusion.
• Royalty and franchise agreements: foreclose
markets to competitors.
Antitrust and Vertical Restraints
• Exclusivity.
– Evaluated under rule of reason: do they harm
welfare/consumers overall. Takes into account
differences between intra- and inter-brand
competition.
• Resale price maintenance.
– Per se illegal.
• Royalty and franchise agreements.
– Some limits on these agreements, evaluated under
rule of reason.