EconS Bundling and Tying

Transcription

1 EconS Bundling and Tying Eric Dunaway Washington State University eric.dunaway@wsu.edu Industrial Organization Eric Dunaway (WSU) EconS 425 Industrial Organization 1 / 39

2 Introduction Let s talk about bundling and tying today. If we group di erent products together and o er a discount for purchasing all of them, can we get more people into the market? Eric Dunaway (WSU) EconS 425 Industrial Organization 2 / 39

3 Bundling is a fairly common practice seen today. Cable companies pair phone, television, and internet services together. Retaurants sell full meals alongside à la carte menu options. By grouping di erent items together, the rm can o er a discount for the package of goods that can entice additional consumers into the market. The key is that these are di erent products. Bundling with the same product is simply second-degree price discrimination. Eric Dunaway (WSU) EconS 425 Industrial Organization 3 / 39

4 Suppose we had two products, 1 and 2. Product 1 could be something like a cheeseburger while product 2 could be an order of french fries. Some consumers may only want product 1, while others may only want product 2. Some might want both products while others want neither. Consumers have unit demand. Now suppose that consumers have a reservation price for both products, and, and that those reservation prices are distributed from 0 to ˆR i for i = 1, 2 where ˆR i is the highest possible reservation price that any consumer has. A consumer with a higher reservation price will purchase their respective good for a higher price. Note: Reservation prices are not observable to the rm in this context. Eric Dunaway (WSU) EconS 425 Industrial Organization 4 / 39

5 Eric Dunaway (WSU) EconS 425 Industrial Organization 5 / 39

6 For a consumer to purchase one of the goods, they must receive a non-negative surplus from the purchase, i.e., R i p i 0 for i = 1, 2 Which is equivalent to saying that their reservation price must be at least as high as the price they are charged, if not higher. Thus, if the rm picks some arbitrary prices, p 1 and p 2, those consumers that have reservation prices equal to or greater than the price will buy the good. Eric Dunaway (WSU) EconS 425 Industrial Organization 6 / 39

7 p 1 Eric Dunaway (WSU) EconS 425 Industrial Organization 7 / 39

8 Purchase Good 1 p 1 Eric Dunaway (WSU) EconS 425 Industrial Organization 8 / 39

9 p 2 Eric Dunaway (WSU) EconS 425 Industrial Organization 9 / 39

10 Purchase Good 2 p 2 Eric Dunaway (WSU) EconS 425 Industrial Organization 10 / 39

11 Purchase Good 2 Purchase Goods 1 and 2 p 2 Purchase Good 1 p 1 Eric Dunaway (WSU) EconS 425 Industrial Organization 11 / 39

12 Let s gure out how much pro t we re making in this case. We ll make it simple by assuming that we have N consumers uniformly distributed along our reservation prices. In this case, the pro t from good 1 is, ˆ p 1 π 1 = N ˆ (p 1 c 1 ) ˆ p 1 ˆ where c 1 is the constant marginal cost of production. Also, is the proportion of consumers that buy good 1. Let s make this simple and assume ˆ = ˆ = 1. Eric Dunaway (WSU) EconS 425 Industrial Organization 12 / 39

13 ˆ p 1 π 1 = N ˆ Plugging in our values, and let N = 1, Similarly, for good 2, we have (p 1 c 1 ) π 1 = (1 p 1 )(p 1 c 1 ) ˆ p 2 π 2 = N (p 2 c 2 ) ˆ = (1 p 2 )(p 2 c 2 ) with total pro t π T = π 1 + π 2 Eric Dunaway (WSU) EconS 425 Industrial Organization 13 / 39

14 Now suppose that the rm could o er a bundle of goods 1 and 2 and sell it at some discounted price p B. For this bundle to make sense, we must have that p B p 1 + p 2. The consumers will have some reservation price R B for the bundle. For simplicity, we ll set R B = +. In the real world, this may not be the case. If the goods are strong complements (I do love fries with my cheeseburger), it s possible that a consumer would be willing to pay more than they would be willing to pay for each good separately. Eric Dunaway (WSU) EconS 425 Industrial Organization 14 / 39

15 If the rm only sold the goods together as a bundle (pure bundling), a consumer would buy the bundle if it gave them non-negative surplus, R B p B 0 + p B 0 Thus, the consumer will purchase the bundle if the sum of their reservation prices is above the bundle price, i.e., + p B Note: If I pick some value for p B, we can plot this function as a line with a slope of 1, = p B Eric Dunaway (WSU) EconS 425 Industrial Organization 15 / 39

16 p B p B Eric Dunaway (WSU) EconS 425 Industrial Organization 16 / 39

17 p B Purchase Goods 1 and 2 p B Eric Dunaway (WSU) EconS 425 Industrial Organization 17 / 39

18 There s actually an interesting consequence created by pure bundling. Some consumers are actually buying a good when their reservation price for that good is below the good s marginal cost. This is quite ine cient. They receive so much extra surplus from the opposite good (the one they value highly), that they are willing to purchase the bundle even though they don t prefer one of the goods at all. We can see this by adding marginal costs to our gure. Eric Dunaway (WSU) EconS 425 Industrial Organization 18 / 39

19 p B Purchase Goods 1 and 2 c 2 c 1 p B Eric Dunaway (WSU) EconS 425 Industrial Organization 19 / 39

20 p B Purchase Goods 1 and 2 c 2 c 1 p B Eric Dunaway (WSU) EconS 425 Industrial Organization 20 / 39

21 We can calculate the pro ts of pure bundling as, π B = N ˆR! 1 1 ˆ 2 p2 B (p B c 1 c 2 ) ˆ ˆ where ˆ ˆ ˆ ˆ 1 2 p 2 B is the proportion of consumers that purchase the bundle. Letting N = 1 and ˆ = ˆ = 1, we have 1 π B = 1 2 p2 B (p B c 1 c 2 ) Eric Dunaway (WSU) EconS 425 Industrial Organization 21 / 39

22 Now let s suppose that the rm o ered both the bundle to consumers as well as the ability to purchase each good separately (mixed bundling). Now, consumers will not only decide whether to buy either good, but they will also choose the option that yields the highest surplus for them, p 1 0 p p B 0 Eric Dunaway (WSU) EconS 425 Industrial Organization 22 / 39

23 p B p 2 p 1 p B Eric Dunaway (WSU) EconS 425 Industrial Organization 23 / 39

24 It s fairly obvious that anyone who would purchase both goods without the bundle will just buy the bundle. From their surpluses, and adding them together, and since p B p 1 + p 2, p 1 0 p p 1 p p B + p 1 p 2 0 Also, we have a group of consumer who originally wouldn t buy either good who will now purchase the bundle. The discount was just enough to put them over. Eric Dunaway (WSU) EconS 425 Industrial Organization 24 / 39

25 p B Purchase Bundle p 2 p 1 p B Eric Dunaway (WSU) EconS 425 Industrial Organization 25 / 39

26 What about the other groups though? Would some of them prefer the bundle over purchasing just their originally preferred product? Let s look at a consumer who originally purchased only good 1 (we can use the same logic for good 2). We know for sure that, p 1 0 Suppose now that they would also purchase the bundle. Thus their surplus from that will also be non-negative, + p B 0 The consumer will simply choose the option that yields a higher surplus. Eric Dunaway (WSU) EconS 425 Industrial Organization 26 / 39

27 p p B 0 The consumer will purchase the bundle if + p B p 1 Rearranging terms, p B p 1 Thus, if they value good 2 (their less preferred good) more than the di erence between the bundle price and the price of good 1 (what they e ectively pay for good 2), they purchase the bundle. Eric Dunaway (WSU) EconS 425 Industrial Organization 27 / 39

28 p B p 2 p B Purchase Good 2 Purchase Bundle p 2 p 1 Purchase Good 1 p B p B p 1 Eric Dunaway (WSU) EconS 425 Industrial Organization 28 / 39

29 The pro ts for all three options under mixed bundling (with their simpli cations) are as follows, ( ˆ p 1 )(p π 1 = B p 1 ) N ˆ ˆ = (1 p 1 )(p B p 1 )(p 1 c 1 ) ( ˆ p 2 )(p π 2 = B p 2 ) N ˆ ˆ = (1 p 2 )(p B p 2 )(p 2 c 2 ) (p 1 c 1 ) (p 2 c 2 ) Eric Dunaway (WSU) EconS 425 Industrial Organization 29 / 39

30 π 3 = N ( 1 ˆ p B + p 2 )( ˆ p B + p 1 ) 2 (p! 1 + p 2 p B ) 2 ˆ ˆ = (p B c 1 c 2 ) (1 p B + p 2 )(1 p B + p 1 ) With total pro ts for the rm of π T = π 1 + π 2 + π (p 1 + p 2 p B ) 2 (p B c 1 c 2 ) Eric Dunaway (WSU) EconS 425 Industrial Organization 30 / 39

31 It s not clear which of the three methods yields the most pro t for the rm. The rm gains more consumers buying the bundle, but it also o ers a discount to the consumers who originally purchased both goods. It all depends on the bundle s price in relation to the individual prices. Mixed bundling, however, will never be worse o than pure bundling. The question, however, is whether to bundle at all. Eric Dunaway (WSU) EconS 425 Industrial Organization 31 / 39

32 Tie-In Sales Another common practice seen in the real world are tie-in sales. Printers come with ink cartridges, Shaving razors come with additional blades, etc. This is a bit di erent from bundling. Tie-in sales usually incorporate the purchase of a single unit of one good, and a variable amount of another good. For instance, you only need a single printer, but you will likely need multiple ink cartridges over time. Eric Dunaway (WSU) EconS 425 Industrial Organization 32 / 39

33 Tie-In Sales In markets like these, the xed product (the printer, in our example) usually comes from a monopolized market, while the variable product (the ink cartridge) comes from a perfectly competitive market. While I can control the production and sale of my own printers, I really can t prevent competitors from creating their own ink cartridges that are compatible with my printer. If the rm could remove their competition among the variable product, they could increase their pro ts. Eric Dunaway (WSU) EconS 425 Industrial Organization 33 / 39

34 Tie-In Sales The rm could create a contract forcing consumers to buy only their variable product. Probably illegal. This is extremely anticompetitive. The rm could alter its xed product such that only their variable product is compatible. This could work, but it s costly. And what prevents their competitors from adapting? The rm could simply not sell the xed product without a purchase of some units of the variable product. This is what we see in the real world. Eric Dunaway (WSU) EconS 425 Industrial Organization 34 / 39

35 Tie-In Sales Suppose we had di erent types of consumers who value the variable product di erently. This di erence is unobservable (as in second-degree price discrimination). To avoid competition in the variable product s market, the rm can simply "bundle" the xed product and varying units of the variable product together. This e ectively removes all competition for the variable product, establishing market power. Eric Dunaway (WSU) EconS 425 Industrial Organization 35 / 39

36 Tie-In Sales At this point, the rm can sell one unit of the xed product (a one time payment) and several units of the variable product (a per-unit payment) to the consumers. Sound familiar? The rm can implement a two-part tari among the consumers and obtain signi cant pro ts, while eliminating their competition. What s interesting, is that since they can eliminate their competition through tie-in sales, they can charge higher than marginal cost for their variable product. Eric Dunaway (WSU) EconS 425 Industrial Organization 36 / 39

37 Summary Bundling allows rms to sell multiple goods together at a discount, including segments of the market that were previously left out. The results on pro ts, however, are ambiguous. Tie-in sales allow a rm to remove competition from a perfectly competitive market that relies on that rm s monopolized market for a xed product. This will increase pro ts for the rm. Eric Dunaway (WSU) EconS 425 Industrial Organization 37 / 39

38 Next Time Game Theory: Simultaneous Move Games This will go beyond what is shown in the textbook. Reading: Eric Dunaway (WSU) EconS 425 Industrial Organization 38 / 39

39 Homework 3-3 Enjoy the weekend. Eric Dunaway (WSU) EconS 425 Industrial Organization 39 / 39