Vertical Relations and Restraints
• Many transactions take place between two firms,
rather than between a firm and consumers
• Key differences in these types of transactions:
– Demand for an intermediate good being sold by an
upstream company to a downstream company is
derived from the demand curve the downstream
company faces.
– The buyers of the intermediate good, the downstream
companies, compete with one another.
Types of Vertical
Relationships/Restraints
• Relationships
– Franchise
– Licensed/authorized dealer
– Agent
• Restraints
– Exclusive territories
– Royalty agreements
– Resale price maintenance
Double Marginalization
• Assume there is an upstream firm, the
manufacturer of the product, and a downstream
firm that sells the product in a retail outlet.
• Assume retailers have no costs, just buy the
product and then resell it costlessly.
• Also assume that the marginal cost of
manufacturing the product is constant, c.
• Consumer demand for the product is P = a - bQ.
Double Marginalization, con’t
• If the manufacturer and retailer were an
integrated company, the firm would set
MR=MC to maximize profit:
 a-2bq = c or q = (a-c)/2b
Price = a - b*(a-c)/2b = (a+c)/2
Profit = [ (a+c)/2 - c ]*(a-c)/2b = (a-c)2/4b
Monopoly Solution
a
(a+c)/2
c
MR
(a-c)/2b
Demand
Double Marginalization, con’t
• If the manufacturer and retailer are separate
companies:
– Assume that the price the retailer pays the
manufacturer is r.
– To maximize profit, the retailer sets r = MR:
a-2bq = r or q = (a-r)/2b
Price = a - b(a-r)/2b = (a+r)/2
Profit = [ (a+r)/2 - r ]*(a-r)/2b = (a-r)2/4b
Double Marginalization, con’t
• Thus the retailer’s demand for the
manufacturer’s product is q = (a-r)/2b.
• The inverse demand curve for the
manufacturer is thus r = a-2bq.
– Note that this is the same as the retailer’s
marginal revenue curve.
• So the manufacturer’s MR curve = a - 4bq.
Double Marginalization, con’t
• Setting MR=MC:
 a - 4bq = c, or q = (a-c)/4b
 Price = a - 2b (a-c)/4b = (a+c)/2
(Be sure to use the manufacturer’s demand curve to
get price, not the consumer’s demand curve)
Profit = [(a+c)/2 - c]*(a-c)4b = (a-c)2/8b
• The retailer pays (a+c)2 and sells (a-c)/4b at
P = a-b*(a-c)/4b = (3a+c)/4.
Double Marginalization
a
(3a+c)/4
MR for
manufacturer
(a+c)/2
c
MR for retailer
(a-c)/2b
Demand
Double Marginalization, con’t
• Double Marginalization: both firms mark
the price up above their own costs.
• Both cosumers and firms are better off if the
two firms act in concert to maximize joint
profits.
Double Marginalization
a
(3a+c)/4
MR for
manufacturer
(a+c)/2
c
MR for retailer
(a-c)/2b
Demand
Vertical Restraints as a Response
to Double Marginalization
• Two-part tariff: Fixed cost of F to sell the good,
then goods sold to retailer at marginal cost.
– Retailer sets MR = MC, so the joint profit maximizing
quantity is sold.
– F can be set so that both the manufacturer and the
retailer share profits.
– Classic franchise arrangement.
• Royalty arrangement: Goods sold to retailer at
MC, manufacturer gets percentage of profits.
Level of Competition
• To understand vertical relations and
restraints, need to distinguish between two
levels of competition:
– 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.
Retail Services
• Retailers can invest in advertising, customer
service, consumer education, all of which enhance
consumer willingness to pay.
• Positive externalities from these services (to other
retailers as well as to the manufacturer), thus the
services generally will be underprovided.
• Vertical restraints can ensure the optimal level of
services.
Vertical Agreements to Ensure
Provision of Services
• Could specify contractually what services should
be provided, but determining the right level of
services is hard and monitoring the level of
services is very difficult.
• Classic 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.
Anit-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.