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)/2bPrice = a - b*(a-c)/2b = (a+c)/2Profit = [ (a+c)/2 - c ]*(a-c)/2b = (a-c)2/4b

a

(a+c)/2

c

MR Demand

(a-c)/2b

Monopoly Solution

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)/2bPrice = a - b(a-r)/2b = (a+r)/2Profit = [ (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 Marginalizationa

(3a+c)/4

(a+c)/2

c

MR for retailer Demand

(a-c)/2b

MR for manufacturer

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 Marginalizationa

(3a+c)/4

(a+c)/2

c

MR for retailer Demand

(a-c)/2b

MR for manufacturer

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.