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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:

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Vertical Relations and Restraints

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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

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.





MR for manufacturer


MR for retailer


Double Marginalization

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.





MR for manufacturer


MR for retailer


Double Marginalization

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.

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