EconS Vertical Pricing Restraints 2

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1 EconS Vertical Pricing Restraints 2 Eric Dunaway Washington State University eric.dunaway@wsu.edu Industrial Organization Eric Dunaway (WSU) EconS 425 Industrial Organization 1 / 38

2 Introduction Let s continue our discussion of vertical pricing restraints. Last time, we established a basic model with one upstream monopolist and one downstream monopolist. We saw that the upstream rm had several methods available to funnel pro ts from the downstream rm to itself without vertically integrating while still correcting for double marginalization. Eric Dunaway (WSU) EconS 425 Industrial Organization 2 / 38

3 When the market structure of the downstream rm is a monopoly, it s fairly simple for an upstream monopolist to impose retail price maintenance agreements on the downstream rm. They can set a price cap, and capture all of the pro t for themselves, while removing double marginalization. They can impose a two-part pricing scheme (franchising), and have the same outcome. Likewise, when the downstream market is perfectly competitive, a simple RPM agreement allows the rms to function as a cartel. The upstream rm can franchise out to the downstream rms and impose a price oor to minimize competition. Eric Dunaway (WSU) EconS 425 Industrial Organization 3 / 38

4 Interestingly, downstream markets that deal in imperfect competition are the most challenging to control for an upstream rm. Suppose we had a downstream market consisting of two rms that could price discriminate among its consumers. Let a proportion α < 1 of consumers be naturally lazy. They don t care which rm has the lowest price, but simply shop at the rm that is closest to them. For simplicity, we ll assume that each rm receives 2 α of these consumers. The remaining proportion 1 α are mobile comparison shoppers. They check the prices of both rms and shop at whichever rm has the lower price. The rms compete for these consumers in Bertrand competition. The rms are able to price discriminate between the two types of consumer (don t ask me how). Eric Dunaway (WSU) EconS 425 Industrial Organization 4 / 38

5 Like before, the upstream rm has a constant marginal cost of c U while the downstream rms have constant marginal costs of c D. The downstream rms must also purchase one unit of the upstream rm s output at a price of p U to use as an input. Market demand in the downstream market is Q D = a p D Starting with the lazy consumers, we know that α 2 of them shop for each rm, thus their segment of the total market demand Q, is q D L = α 2 QD = α 2 (a pd L ) and setting up their pro t maximization problem, max p D L (p D L c)q D L = (p D L p U c D ) a 2 (a pd L ) Eric Dunaway (WSU) EconS 425 Industrial Organization 5 / 38

6 max p D L (p D L p U c D ) a 2 (a pd L ) Taking a rst-order condition, π D L pl D = α 2 and solving this expression for pl D the upstream price, a 2p D L + p U + c D = 0 pl D = a + pu + c D 2 which is identical to the monopoly price. gives us our price as a function of This should make sense, since the rms don t have to compete for these consumers. Essentially, the lazy consumers are forced to pay monopoly prices due to their laziness. Eric Dunaway (WSU) EconS 425 Industrial Organization 6 / 38

7 The mobile comparison shoppers, on the other hand, get the bene ts of Bertrand competition. Each rm o ers them a price equal to their marginal cost, p D M = pu + c D and half of the mobile comparison shoppers shop at each rm. For the upstream rm, this situation is a bit tougher. What can it do to capture the pro ts from the downstream market? For comparison purposes, if the upstream rm vertically integrated into both of the downstream rms, the total pro ts would be π U V = (a cu c D ) 2 4 which is the maximum pro t available in this market. Eric Dunaway (WSU) EconS 425 Industrial Organization 7 / 38

8 Suppose the upstream rm decided to franchise out to both downstream rms by implementing a two-part pricing scheme. It would set p U = c U and set a xed entry price (franchise fee) equal to the pro ts of the downstream rm. For the lazy consumers, we d see the optimal markup and no double marginalization, leading to pro ts of π D L = α (a c U c D ) For the mobile comparison shoppers, we still wouldn t see any markup. Since competition between those consumers is erce, the downstream price is p D M = cu + c D and there are no pro ts. Eric Dunaway (WSU) EconS 425 Industrial Organization 8 / 38

9 Thus, the upstream rm s total pro t is the franchise fee it receives from both downstream rms, π U = 2π D L = α (a cu c D ) 2 4 < π U V and unless all of the consumers are lazy (α = 1), this yields lower pro ts than optimal. What s going on here? While the downstream rms are able to price discriminate, the upstream rm cannot. They can t specify which of their inputs goes to each consumer and adjust the price accordingly. Going back to our lessons on price discrimination, the upstream rm can t identify di erent markets for their consumers. Eric Dunaway (WSU) EconS 425 Industrial Organization 9 / 38

10 At the same time, the upstream rm could try to target the mobile comparison consumers and charge a price of p U = p M c D, where p M is the vertically integrated monopoly price. The mobile comparison consumers would pay the monopoly price in this case, and downstream pro ts would be π D M = 1 α (a c U c D ) The lazy consumers, however, would see their price marked up again to a level far above the monopoly price, and their downstream pro ts would be π D L = α (a c U c D ) Eric Dunaway (WSU) EconS 425 Industrial Organization 10 / 38

11 This leaves total pro ts for the upstream rm of π U = 2π D M + 2π D L = (1 α) (a cu c D ) 2 4 3α (a c U c = D ) 2 1 < π U V α (a cu c D ) 2 16 and unless all consumers are mobile comparison shoppers (α = 0), this yields lower pro ts than optimal. Again, the upstream rm can t price discriminate. If they target one type of downstream consumer, the other will either receive a price that is too low or too high to achieve maximum pro ts. Eric Dunaway (WSU) EconS 425 Industrial Organization 11 / 38

12 We could try to correct for this ine ciency by using a two-part tari. We ll lower the price of the franchise fee, but raise the price per unit. The upstream monopolist s pro t maximization problem becomes, h max (p U c U )(a p U c D ) 1 α + α i + α (a pu c D ) 2 p U 2 4 Maximizing this problem leads to a unit price of p U = 2(1 α)(a cd ) + (2 α)c U 4 3α Eric Dunaway (WSU) EconS 425 Industrial Organization 12 / 38

13 p U = 2(1 α)(a cd ) + (2 α)c U 4 3α This is actually a really interesting function. As α approaches 0, i.e., as all consumers become mobile comparison shoppers, the price approaches p U = p M c D, the price we would want to charge just that segment of the market. The franchise fee also approaches 0 in this case. As α approaches 1, i.e., as all consumers become lazy, the price approaches p U = c U, the price we would want to charge just the lazy consumers. The franchise fee approaches π U V in this case. However, for any value of α between 0 and 1, pro ts are strictly less than the optimal level. Eric Dunaway (WSU) EconS 425 Industrial Organization 13 / 38

14 π U* V π U 0 1 α Eric Dunaway (WSU) EconS 425 Industrial Organization 14 / 38

15 Thus, our two-part tari won t lead to the maximum amount of pro t as long as there are at least two di erent types of consumers. Our price ceiling won t work either, as competitive pressure will lower the price the mobile comparison consumers receive. So how do we x this? What if we combined the two? Eric Dunaway (WSU) EconS 425 Industrial Organization 15 / 38

16 Suppose the upstream rm set a minimum price of p M and utilized standard two-part pricing. In this case, the upstream rm sets p U = c U and and lazy consumers see a natural price markup to p M. At the same time, a binding price oor requires the mobile comparison consumers to pay p M. If the upstream rm sets a franchise fee of πu V 2 for each downstream rm, it can capture all of the pro ts for itself. With a combination of two-part pricing and a retail price maintenance agreement, the upstream rm can exert its control over the downstream markets. Eric Dunaway (WSU) EconS 425 Industrial Organization 16 / 38

17 As seen, sometimes it s necessary for the upstream rms to utilize multiple techniques to ensure the optimal price is charged in the downstream market while funnelling most of the pro ts to themselves. We see these techniques used a lot in the real world, especially among franchises. They pay a yearly fee to the upstream supplier for the right to sell under the brand name. They are limited in how they can price to consumers to minimize competition. Let s look at some other situations where RPM agreements can optimize a market. Eric Dunaway (WSU) EconS 425 Industrial Organization 17 / 38

18 In many downstream markets, retail services are vital to the success of a product. Magazines and snacks are strategically located next to registers to promote impule buying. Experts are employed by the rms to make recommendations. In general, anything a retailer does to promote the sale of the product has bene ts for the upstream rm, but comes at a cost to the downstream rm. That being said, the upstream rm is very interested in these retail services being available to the consumers, but has no direct control over them. Eric Dunaway (WSU) EconS 425 Industrial Organization 18 / 38

19 Suppose that the downstream market is able to provide a certain level of retail services, s, at a cost of φ(s). We ll say that φ(s) is increasing and convex in s (this means that both its rst and second derivatives are positive). We assume this so that retail services have diminishing marginal returns, i.e., they lose e ectiveness as the service level increases. Our demand function is now a function of both the market price and the retail service level, q(p, s) = s(a p)n where N is the number of consumers in the market. If we solve for our inverse demand function, we would have Q p = a sn Intuitively, the level of retail services attens out the demand curve, but leaves the highest willingness to pay alone. Eric Dunaway (WSU) EconS 425 Industrial Organization 19 / 38

20 a p D q Eric Dunaway (WSU) EconS 425 Industrial Organization 20 / 38

21 a p D q Eric Dunaway (WSU) EconS 425 Industrial Organization 21 / 38

22 There is a socially optimal amount of retail services to provide to a market. To calculate this value, we must balance the consumer and producer surplus gained by the consumers and upstream rm with the producer surplus lost by the downstream rm. The downstream rm must incur the cost of these retail services. To make this calculation simple, assume that both the upstream and downstream markets are perfectly competitive. If we assume that the upstream market has a constant marginal cost of c U and the downstream market must purchase one unit of the upstream rm s output and pay φ(s) for retail services, our equilibrium price is p = c U + φ(s). In this case, we don t have any producer surplus (perfectly competitive market) and all surplus goes to the consumers. Eric Dunaway (WSU) EconS 425 Industrial Organization 22 / 38

23 a p CS c U D q Eric Dunaway (WSU) EconS 425 Industrial Organization 23 / 38

24 a p CS c U + ϕ(s) D q Eric Dunaway (WSU) EconS 425 Industrial Organization 24 / 38

25 a p Gain c U + ϕ(s) c U Loss D q Eric Dunaway (WSU) EconS 425 Industrial Organization 25 / 38

26 The socially optimal amount of retail services is when the amount of surplus gained is equal to the amount lost, or when the marginal bene t of an additional unit of surplus is equal to its marginal cost. When the market is perfectly competitive, both the upstream and downstream rms set price equal to marginal cost and produce the socially optimal amount of retail services. Since consumers desire these services, the downstream rms compete to provide them. Interestingly, when we have a vertically integrated monopolist, they charge the monopoly price, but they still provide close to the socially optimal amount of retail services. As it turns out, the socially optimal amount of retail services is also close to the pro t maximizing amount for the vertically integrated rm. Eric Dunaway (WSU) EconS 425 Industrial Organization 26 / 38

27 Suppose now that both the upstream and downstream rms acted as monopolists. We could go through and calculate all our values, using what we know about the demand functions and costs. What we ll nd is that if the upstream rm makes positive pro t, i.e., p U > c U, we ll have our typical problem of double marginalization. We ll also see that the downstream rm provides less than the socially optimal level of retail services. Why? Since the nal price the consumers pay is greater than the monopoly price, the realized pro t is lower than the monopoly pro t. To cut back on its costs, the downstream rm lowers the provision of retail services. As we know, the incentives for the upstream and downstream rms di er, and this di erence can cause issues with social optimality. Eric Dunaway (WSU) EconS 425 Industrial Organization 27 / 38

28 Can a RPM agreement x this? If the upstream rm mandates a maximum price of p M on the downstream rm and sells to them at a price of p U = p M φ(s ), where s is the socially optimal amount of retail services, the downstream rm will charge the monopoly price, but again, provide less than the optimal amount of retail services. Again, the downstream rm can increase its own pro t by cutting back on the retail services, so they do. Thus, the RPM agreement won t work. What about two-part pricing? Eric Dunaway (WSU) EconS 425 Industrial Organization 28 / 38

29 Suppose the upstream rm implemented a standard two-part pricing scheme with a constant unit price of p U = c U and a franchise fee of π M. In this case, the downstream rm sets its price to p M and chooses the socially optimal amount of retail services, s. Thus, the two-part pricing scheme can lead to maximum pro t for the upstream rm. A note, however: If the downstream rm is a monopolist, it does have a lot of bargaining power and will likely demand a share of π M for itself. The point is that this arrangement can lead to an e cient level of retail services and the maximum pro t available. Eric Dunaway (WSU) EconS 425 Industrial Organization 29 / 38

30 Now, suppose the downstream market is perfectly competitive. Like before with our monopolist, if the upstream rm tries to make pro t o the downstream rms, i.e., p U > c U, the downstream rms will set their price to p D = p U + φ(s), and the level of retail services will be below the socially optimum level. Again, the downstream rms cut costs by reducing retail services. Two-part pricing won t work in this case, either. There are no pro ts in the downstream market to claim as a franchise fee. What about an RPM? Eric Dunaway (WSU) EconS 425 Industrial Organization 30 / 38

31 If the upstream rm created a RPM such that each rm was required to charge p M as a minimum, and set its own price such that p U = p M φ(s), then all of the rms in the downstream market would charge the monopoly price. Remember that competitive downstream rms like this, as it s e ectively collusion. At the same time, the downstream rms would also choose the socially optimal amount of retail services. Even though the rms don t compete against eachother in prices due to the RPM, they still compete in retail services. These become the de ning factor in this market, which makes the upstream supplier quite happy. Eric Dunaway (WSU) EconS 425 Industrial Organization 31 / 38

32 Lastly, retail services create the possibility for a "free rider" problem. A free rider problem is when a person can receive a good without paying for it, so why would they pay for it? This is common among public goods. Roads, national defense, and the o ce co ee pot are all examples of free rider goods. Take Best Buy. They employ several experts on all of the appliances and consumers electronics that they sell in their store as a retail service. What prevents you from receiving a free recommendation from those experts, then purchasing the same product for less on Amazon? Eric Dunaway (WSU) EconS 425 Industrial Organization 32 / 38

33 We must remember that the retail service of expert advice comes at a cost to the rm employing them. Firms that do not provide these experts can thus sell the product at a reduced price. Naturally, there are incentives to reduce the provision of retail services when faced with free riding by competing rms. The upstream rm would not like this at all. Eric Dunaway (WSU) EconS 425 Industrial Organization 33 / 38

34 Fortunately, RPM agreements can mitigate this e ect. By removing the ability for one rm to undercut the other, there is no incentive for one rm to free ride on another s retail services. The key is that the upstream rm does not want competition in prices, but they do want competition in retail services. The upstream rm can t control the downstream s choice of retail services, but they can prevent them from being concerned about the price in their market. Leaving retail services the only thing downstream rms are concerned about. Eric Dunaway (WSU) EconS 425 Industrial Organization 34 / 38

35 Downstream rms, then, depend on these RPM agreements, as well, and it leads to strong relationships between manufacturers and retailers. In several industries, the upstream rms depend on their downstream partners for consumer feedback. For example, the fashion industry needs the expert opinions of the retail service providers to determine how to design their product going forward. Without protection from free riders, these relationships are much harder to sustain. Eric Dunaway (WSU) EconS 425 Industrial Organization 35 / 38

36 Summary Through RPM agreements and franchising, upstream rms can handle most situations that are present in a downstream market. The relationship between upstream and downstream rms is critical when determining the provision of retail services. Eric Dunaway (WSU) EconS 425 Industrial Organization 36 / 38

37 Next Time Uncertainty, non-price vertical restraints, and aftermarket sales. Reading: Chapter Eric Dunaway (WSU) EconS 425 Industrial Organization 37 / 38

38 Practice Problem Suppose we had an upstream and downstream monopolist. The upstream monopolist pays a constant marginal cost of c U and the downstream rm must simply purchase from the upstream rm at a price of p U. The downstream rm can also o er retail services at a cost of s 2. Market inverse demand in the downstream market is as follows, q p = D a s 1. If the upstream and downstream rms vertically integrate, what is the equilibrium level of retail services? 2. If no vertical integration occurs, what is the equilibrium level of retail services? 3. Compare parts 1 and 2. What happens to retail services? Eric Dunaway (WSU) EconS 425 Industrial Organization 38 / 38