Vertical Markets: Double Marginalization Todd Kaplan

Question: What is worse for consumers than a Monopolist? Two monopolists. Vertical Markets: An analysis.

Single Monopolist Inverse Demand p=12-q and mc=4. Monopolist profits are (12-q)q-4q=(8-q)q Monopolist produces q=4 and the price is p=12- 4=8. Monopolist profit is 16. Another way of looking at it is Monopoly’s profits=revenue – costs. Choice should set marginal revenue=marginal costs Rev is (12-q)q. MR is 12-2q.

Two Monopolists:Supplier and Retailer. Supplier has marginal costs of 4 and charges price p s to Retailer. Retailer buys q from the supplier at price p s and (charges consumers price p c that would clear the market). Retailer faces demand curve of q=12- p c. Profit of Retailer is (12- q- p s )q Profit of Supplier is q(p s - 4)

Two monopolists Profit of Retailer is (12- q- p s )q –Retailer sets price q= (12- p s )/2 Profit of Supplier is (p s - 4)q Sub. in for q yields (p s - 4)(12- p s )/2 Supplier sets p s =8 Retailer sets q=2, so p c = (12-q)=10 Price to consumers is higher than a single monopolist (10 vs. 8)! Quantity is less as well (2 vs. 4)!

Solutions. Allow the Supplier to buy the Retailer. Allow the Supplier to charge a franchise fee (as with McDonalds). –Supplier charges p s =mc=4. –Supplier charges franchise fee F=16 –What does retailer charge and what are his profits before paying F? –Same as monopolist: p c =8 (q=4), profits 16. –He must pay the franchise fee F. This leaves him w/ no profits. –Supplier gets all the profits. Retailer is barely in business.

Franchise comments In practice, McDonalds actually owns some of restaurants and franchises the rest. Which is McDonald’s more likely to own? –City or highway? There is a moral hazard problem which we will discuss later in the course and is a reason for integration. Profits are also not completely zero since a better owner could make more money than a bad one and McDonalds does not know which is which. This is a traditional Principal-Agent problem On the other hand, a franchise could provide incentives that could be harder to duplicate with a contract and

Vertical Integration (difficulties) We mentioned that the difficulties were –skills investment (buying the franchise is a commitment to a long-term relationship). –Incentive contracts may be harder to design/implement. Another problem is how does this work when it is integrated: transfer pricing. The problem is how is the transfer pricing set. –Example Bellcore

Bellcore example Bellcore was broken off from AT&T. In the late 1980s, they had a lot researchers with PhDs that had started to do their own wordprocessing and graphics rather than using the admin pool. Others had outsourced on their own. At the same time, the pool was laying people off for lack of work to do. Why? The typing pool was trying to cover costs and set a marginal cost of $50/ page. While not paying directly, the researchers preferred spending money on other things. Problem was that it would never be profitable even if rates were reduced. This was because of other transfer pricing that was mispriced: rent, computer time. (Central computer time was relatively expensive for word processing as was non-lab space.)

Exercise A monopoly has marginal cost of 5 and faces a demand of q=20-p. What price should he charge to maximize profits? Let us say it is a vertical market of two firms: supplier and retailer. What would the price would the supplier charge the retailer? What would be the price charged to the end consumer? If the supplier charged a franchise fee in addition to wholesale price, what would they be? Solve the above problem for the general case of marginal cost of c facing demand of q=A-p where (A>c).