Vertical Differentiation

EconS 425 - Vertical Di¤erentiation Industrial Organization Eric Dunaway (WSU) EconS 425 Industrial Organization 1 / 41 Product Di¤erentiation Firms may want to o¤er di¤erent versions of the same product. By diversifying their product line, they can attract di¤erent consumers with varying tastes and (of course) extract more pro…t from the market. At the same time, if there were multiple …rms in a market, they may want to di¤erentiate their products to increase their market power. We’ll talk about this at a later time (we’ll need some game theory). Eric Dunaway (WSU) EconS 425 Industrial Organization 3 / 41 Product Di¤erentiation Product di¤erentiation can also be quite subtle. Is Cougar Gold sold in Pullman the same as Cougar Gold sold in Spokane? No. There are additional costs involved to ship Cougar Gold from one location to another. We can actually treat these two products (while identical in appearance) as separate. Eric Dunaway (WSU) EconS 425 Industrial Organization 4 / 41 Product Di¤erentiation Product Di¤erentiation often leads to price discrimination. Be careful, however. We may see situations where di¤erent groups are charged di¤erent prices, yet there is not price discrimination going on. For example, suppose gas were being sold in Pullman for $3 a gallon, while it was being sold for $2 a gallon in Colfax (ignore taxes, etc.). Now suppose the marginal cost for gas was $2 in Pullman and $1 in Colfax. In this case, the prices merely take into consideration the di¤erence in marginal costs. To determine if price discrimination is happening, we want to see if the net prices (price less costs) di¤er across markets. Eric Dunaway (WSU) EconS 425 Industrial Organization 5 / 41 Product Di¤erentiation Product di¤erentiation easily satis…es our necessary conditions for price discrimination. By o¤ering di¤erent versions of a good, we can design it such that di¤erent consumers want to purchase di¤erent goods. This will cause consumers to sort themselves into their own groups, even if we can’t observe their characteristics. Also, a group will want their product more than the other, reducing the chance of arbitrage. Eric Dunaway (WSU) EconS 425 Industrial Organization 6 / 41 Product Di¤erentiation We classify product di¤erentiation into two broad categories, vertical and horizontal. We separate them based on how consumers view quality. With Vertical Di¤erentiation, consumers can all agree "what quality is," but they have di¤erent willingnesses to pay for quality. Examples: Lexus vs. Toyota, Banana Republic vs. GAP vs. Old Navy. With Horizontal Di¤erentiation, consumers can’t agree on what quality is, and have di¤erent preferences for di¤erent characteristics. Example: Di¤erent kinds of Colgate toothpaste. Eric Dunaway (WSU) EconS 425 Industrial Organization 7 / 41 Vertical Di¤erentiation Today, we’ll focus on vertical di¤erentiation. If a …rm can o¤er di¤erent versions of the same product that vary in their quality, how should they price them? We will use some technniques that we saw in second-degree price discrimination, namely the participation and incentive compatibility constraints. They’re a bit easier in this context. Eric Dunaway (WSU) EconS 425 Industrial Organization 8 / 41 Vertical Di¤erentiation Let’s start with a simple model. A …rm can produce two versions of a good, one of low quality and one of high quality. The marginal costs of producing these goods are cL and cH , respectively and cL < cH . The quality of the goods is predetermined (exogenous). We’ll relax this later. There are N1 consumers who value both versions of the good less (the low type), and N2 consumers who value both versions of the good more (the high type). We are unable to observe any di¤erences between the consumers. Perhaps the high type has more income than the low, or the low type is just a cheapskate. Consumers have unit demand (They will only buy one unit, or none at all). Eric Dunaway (WSU) EconS 425 Industrial Organization 9 / 41 Vertical Di¤erentiation The low type consumer has a reservation price of V1L for the low quality good, and V1H for the high quality good. Likewise, the high type consumer has a reservation price of V2L for the low quality good and V2H for the high quality good. We can rank the valuations as following. V1H V2H > V1L > V1H V2H > V2L V2L > V1L thus we know that the high type values both versions of the good more than the low type, and both consumers value the high quality good more than the low quality good. We’ll also assume that all reservation prices are above their respective costs, otherwise it would be ine¢ cient for a consumer to buy the product. We’ll also assume ViH Eric Dunaway (WSU) ViL > cH EconS 425 cL for i = 1, 2 Industrial Organization 10 / 41 Vertical Di¤erentiation If the …rm knows everything about the consumers except for which consumer is which, the …rm has three viable options: O¤er only the high quality good, and sell it to both types of consumer. O¤er only the high quality good, and sell it to only the high type. O¤er both types of good, and target a di¤erent type of consumer with each. Eric Dunaway (WSU) EconS 425 Industrial Organization 11 / 41 Vertical Di¤erentiation If the …rm o¤ers only the high quality good, but wants to sell it to both types of consumers, the most they can charge is V1H . Anything higher than that, and it would be better for the low type consumer to not buy the good. The …rm’s pro…t level is π 1 = (N1 + N2 )(p H cH ) (N1 + N2 )(V1H cH ) = Consumer 1 receives no surplus, while consumer 2 receives a surplus of V2H V1H . Eric Dunaway (WSU) EconS 425 Industrial Organization 12 / 41 Vertical Di¤erentiation Next, the …rm could o¤er only the high quality good, but sell it only to the high type consumer. In this case, it can charge a much higher price, V2H , but it loses out on all of the low type consumers. The …rm’s pro…t level is π 2 = N2 ( p H cH ) N2 (V2H cH ) = Neither consumer receives any surplus in this case. High types pay their whole valuation, while the low types don’t buy. Eric Dunaway (WSU) EconS 425 Industrial Organization 13 / 41 Vertical Di¤erentiation Lastly, the …rm could o¤er both types of good, and target the high quality to the high type and the low quality to the low type. We have to be aware, though, that one consumer may want to purchase the product not intended for them. This requires us to use participation and incentive compatibility constraints. As before, we’ll have two participation constraints and two incentive compatibility constraints, one for each type of consumer. Again, only one participation constraint and one incentive compatibility constraint will bind in equilibrium. I’ll spoil it and tell you that the participation constraint for the low type and the incentive compatibility constraint for the high type bind. EconS 425 Industrial Organization 14 / 41 Vertical Di¤erentiation Our constraints are V1L p L | {z } = 0 (PC1 ) Consumer 1’s surplus V2H p H | {z } V2L p L | {z } = Consumer 2’s surplus if they buy high quality (IC2 ) Consumer 2’s surplus if they buy low quality We can rearrange these to solve for prices, p L = V1L pH = V2H V2L + V1L |{z} pL Eric Dunaway (WSU) EconS 425 Industrial Organization 15 / 41 Vertical Di¤erentiation p L = V1L pH = V2H V2L + V1L Now, we can calculate pro…ts for the …rm, π 3 = N1 ( p L = N1 (V1L c L ) + N2 ( p H cL ) + N2 (V2H cH ) V2L + V1L cH ) Once again, the low type consumer receives no surplus, but the high type receives a surplus of V2L V1L Eric Dunaway (WSU) EconS 425 Industrial Organization 16 / 41 Vertical Di¤erentiation Which of the three cases should the …rm choose? The one that gives the most pro…ts, of course! We can compare the pro…t levels across cases, and see which ones are the best, given what we know about our consumers. Starting with the …rst two cases, the …rm would rather only sell the high quality good to the high type consumer instead of selling to both consumers if π2 > π1 N2 (V2H cH ) > (N1 + N2 )(V1H EconS 425 cH ) Industrial Organization 17 / 41 Vertical Di¤erentiation N2 (V2H cH ) > (N1 + N2 )(V1H cH ) We can rearrange this expression to obtain N2 (V2H V1H ) > N1 (V1H cH ) This expression is actually quite intuitive. The left-hand side, N2 (V2H V1H ), is the amount of extra pro…t the …rm can squeeze out of the high type if the …rm sells only to them. The right-hand side, N1 (V1H cH ), is how much pro…t the …rm would get from the low type by including them in the market. EconS 425 Industrial Organization 18 / 41 Vertical Di¤erentiation N2 (V2H V1H ) > N1 (V1H cH ) This condition is not guaranteed to hold. If N1 is much larger than N2 , i.e., there are a lot more low types than high types, the condition is unlikely to hold. If the high type has a much larget reservation price than the low type relative to the marginal cost, the condition is likely to hold. It is a case by case basis that you will have to analyze. Eric Dunaway (WSU) EconS 425 Industrial Organization 19 / 41 Vertical Di¤erentiation What about the third case where the …rm o¤ers both products? It would be better for the …rm to do this (assuming π 2 > π 1 ) if π3 > π2 N1 (V1L cL ) + N2 (V2H V2L + V1L cH ) > N2 (V2H cH ) which rearranges to N1 (V1L Eric Dunaway (WSU) cL ) > N2 (V2L EconS 425 V1L ) Industrial Organization 20 / 41 Vertical Di¤erentiation N1 (V1L cL ) > N2 (V2L V1L ) Again, this also has some great interpretation, The left-hand side, N1 (V1L cL ) is how much pro…t the …rm makes by letting the low type into the market and selling them the low quality good. The right-hand side, N2 (V2L cH ) is how much pro…t the …rm loses to consumer surplus to the high type, since it has to lower the price they charge due to incentive compatibility. Naturally, the …rm chooses whichever method yields the highest pro…ts (again, it depends on parameters). Eric Dunaway (WSU) EconS 425 Industrial Organization 21 / 41 Vertical Di¤erentiation Let’s make the model a little harder. So far we’ve let quality be determined outside of the model, but now were going to let the …rm choose the quality they o¤er along with the price. We need add a few things to the model. The …rm can choose the quality, sj of both of its j products. Quality is costly. To add quality to a product, the …rm must pay some cost function c (s ) which is increasing (always going up) and convex (getting steeper). Higher quality adds a lot of cost to the …rm. The consumer valuation of the product is θ i s j , where θ i is consumer i’s preference for quality. Let θ 2 > θ 1 , so the high type values quality more than the low type. Eric Dunaway (WSU) EconS 425 Industrial Organization 22 / 41 Vertical Di¤erentiation Going back to our three cases, if the …rm sells a single quality of the good to all consumers, its pro…t maximization problem is max (N1 + N2 )(p c (s )) p,s subject to two participation constraints θ1 s p 0 (PC1 ) θ2 s p 0 (PC2 ) of which only one will bind, PC1 . Eric Dunaway (WSU) EconS 425 Industrial Organization 23 / 41 Vertical Di¤erentiation θ1 s p=0 (PC1 ) From this participation constraint, we can solve for price as a function of quality, p = θ1 s and substitute this back into our maximization problem max (N1 + N2 )(p p,s max (N1 + N2 )(θ 1 s s Eric Dunaway (WSU) EconS 425 c (s )) c (s )) Industrial Organization 24 / 41 Vertical Di¤erentiation max (N1 + N2 )(θ 1 s s c (s )) From here, we take a …rst-order condition with respect to s to obtain, (N1 + N2 )(θ 1 c 0 (s )) = 0 which reduces to c 0 (s ) = θ 1 Thus, when the …rm sells one quality of good to the whole market, it sets that marginal cost of quality equal to the low type’s preference for quality (Their marginal willingness to pay for quality). Again, the low type receives no surplus, while the high type receives a surplus of (θ 2 θ 1 )s . Eric Dunaway (WSU) EconS 425 Industrial Organization 25 / 41 Vertical Di¤erentiation For the case where the …rm sells a single quality of good, but only caters to the high type, its maximization problem is max N2 (p p,s c (s )) subject to a single participation constraint, θ2 s p 0 (PC2 ) which will bind in equilibrium. Eric Dunaway (WSU) EconS 425 Industrial Organization 26 / 41 Vertical Di¤erentiation Our results are very similar to those in the …rst case. We will …nd that p = θ2 s from our participation constraint, and in equilibrium, c 0 (s ) = θ 2 the marginal cost of quality will now equal the high type’s preference for quality (Their marginal willingness to pay). No consumer will have any surplus either (since the low type doesn’t buy the product). Eric Dunaway (WSU) EconS 425 Industrial Organization 27 / 41 Vertical Di¤erentiation Lastly, we have our third case, where the …rm o¤ers more than one quality of the good. To make this case a little bit easier, I’m going to impose c (s ) = 12 s 2 . The …rm’s pro…t maximization problem is, max N1 (p1 max N1 p1 p 1 ,p 2 ,s1 ,s2 p 1 ,p 2 ,s1 ,s2 c (s1 )) + N2 (p2 1 2 s 2 1 c (s2 )) + N2 p2 1 2 s 2 2 with two participation and two incentive compatibility constraints. Again PC1 and IC2 bind. Eric Dunaway (WSU) EconS 425 Industrial Organization 28 / 41 Vertical Di¤erentiation Our binding constraints are θ 1 s1 p1 = 0 θ 2 s2 p2 = θ 2 s1 (PC1 ) p1 (IC2 ) which we can solve for p1 and p2 to obtain p1 = θ 1 s1 p2 = θ 2 s2 (θ 2 θ 1 ) s1 Notice that the low type is charged their valuation, while the high type is charged less than their valuation. Eric Dunaway (WSU) EconS 425 Industrial Organization 29 / 41 Vertical Di¤erentiation Substituting these values back into the pro…t maximization problem, max N1 p1 max N1 θ 1 s1 p 1 ,p 2 ,s1 ,s2 s1 ,s2 1 2 s 2 1 1 2 s 2 1 + N2 p2 + N2 θ 2 s 2 1 2 s 2 2 (θ 2 θ 1 ) s1 1 2 s 2 2 and calculate …rst-order conditions for s1 and s2 to obtain, N1 ( θ 1 Eric Dunaway (WSU) s1 ) N2 ( θ 2 θ1 ) = 0 N2 ( θ 2 s2 ) = 0 EconS 425 Industrial Organization 30 / 41 Vertical Di¤erentiation N1 ( θ 1 s1 ) N2 ( θ 2 θ1 ) = 0 N2 ( θ 2 s2 ) = 0 Solving for s1 and s2 , we have s1 = θ1 s2 = θ2 N2 (θ 2 N1 θ1 ) Again, notice that the low type receives a lower quality than the e¢ cient level (c 0 (s ) = s, and si = θ i is the e¢ cient level) while the high type receives the e¢ cient level. Eric Dunaway (WSU) EconS 425 Industrial Organization 31 / 41 Vertical Di¤erentiation The results of vertical di¤erentiation are very similar to those we saw with menu pricing. In menu pricing, the low type was given a smaller quantity of the good, while in vertical di¤erentiation, the low type is simply given a lower quality good. The low type pays their valuation in both cases, while the high type pays a lower price to ensure incentive compatibility. Eric Dunaway (WSU) EconS 425 Industrial Organization 32 / 41 Vertical Di¤erentiation It’s really interesting that the …rm gives the low type a purposefully lower quality good. The book has a great quote on this from 1849 (well before these ideas were formalized): "It is not because of the few thousand francs which would have to be spent to put a roof over the third-class seats that some company or other has open carriages with wooden benches. What that company is trying to do is prevent the passengers who can pay the second class fare from travelling third class; it hits the poor, not because it wants to hurt them, but to frighten the rich. And it is again for the same reason that the companies, having proved almost cruel to the third-class passengers and mean to the second-class ones, become lavish in dealing with …rst-class passengers. Having refused the poor what is necessary, they give the rich what is super‡uous. (Jules Dupuit, 1849)" Eric Dunaway (WSU) EconS 425 Industrial Organization 33 / 41 Vertical Di¤erentiation What Dupuit was explaining is incentive compatibility. If they improved the third-class seats, many passengers who could a¤ord second-class tickets would likely ride third-class in order to save some money. Thus the quality is kept so low to guarantee that those passengers pay the second-class price. On the other hand, since they can’t lower the second-class quality relative to …rst-class, they have to make …rst-class extravagant in order to ensure that …rst-class passengers wouldn’t rather ride second-class. Basically, it’s not because the train operator is cheap, it’s because they want to get the most pro…t out of their passengers as possible. Eric Dunaway (WSU) EconS 425 Industrial Organization 34 / 41 Vertical Di¤erentiation Purposely lowering the quality of a product is actually very common today. If a …rm wants to sell to a segment of the market that is excluded due to the price being too high, they can o¤er a lower quality version of that product. They have to make sure that the low quality product doesn’t take from their high type consumers, though. Eric Dunaway (WSU) EconS 425 Industrial Organization 35 / 41 Vertical Di¤erentiation Example: Table vs. Cooking wine. Many people like to use wine while cooking. Wine, however, can be an expensive ingredient for a meal. As a wine …rm, if you wanted to o¤er a cheap type of wine speci…cally marketed for cooking, you run into the problem where consumers may want to drink that wine instead of the more expensive table wine meant for drinking. How do you solve this problem? You take the table wine, purposely damage it by adding enough salt to it to make it undrinkable, then sell it as cooking wine. Other examples: Laser printers, student versions of software, iPhone 5C, etc. Eric Dunaway (WSU) EconS 425 Industrial Organization 36 / 41 Vertical Di¤erentiation What’s interesing about the case of cooking wine is that the marginal cost to produce the low quality product is actually higher than the marginal cost to produce the high quality product, i.e., cL > cH . Intuitively, you can’t make the low quality product without starting from the high quality product, so it has to be more expensive. Remember from our …rst example that the …rm will want to o¤er both qualities if N1 (V1L cL ) > N2 (V2L V1L ) and thus, a "purposely damaged" product like this will be harder to implement in this case. Eric Dunaway (WSU) EconS 425 Industrial Organization 37 / 41 Vertical Di¤erentiation N1 (V1L cL ) > N2 (V2L V1L ) However, if the high type consumer puts a very low valuation on the low quality good (V2L , think of a master chef wanting to use cooking wine rather than table wine) relative to the low type’s valuation (V1L ), this constraint can still hold, implying that it might be better for the …rm to sell both qualities of the good. The interesting thing is that if purposely damaging a good allows more consumers into the market, it actually reduces deadweight loss. Eric Dunaway (WSU) EconS 425 Industrial Organization 38 / 41 Summary Vertical Di¤erentiation is a useful tool to a …rm in order to implement price discrimination. If quality can be varied, the …rm can get consumers to self-select into the best product for themselves. Eric Dunaway (WSU) EconS 425 Industrial Organization 39 / 41 Next Time A brief explanation of horizontal di¤erentiation, then budling and tying. I don’t like the book’s coverage of horizontal di¤erentiation, so skip over section 6.2 for now; we’ll cover it in more depth after we do game theory. Reading: 6.3. Eric Dunaway (WSU) EconS 425 Industrial Organization 40 / 41 Homework 3-1 Consider a …rm that wants to o¤er two di¤erent qualities of a good marketed to a low type and a high type consumer. The …rm cannot tell the di¤erence between the two consumers, but knows that the high type values the good twice as much as the low type, i.e., θ 1 = 1 and θ 2 = 2. In order to produce quality in their product, the …rm faces the cost function c (s ) = 13 s 3 where s is the quality level. The proportion of low type consumers is γ and the proportion of high type N1 N1 consumers is 1 γ where γ N 1 +N 2 = N . 1. Set up the …rm’s pro…t maximization problem and list all four constraints. 2. Assume PC1 and IC2 bind. Calculate the equilibrium qualities and prices o¤ered to each type of consumer. 3. For what values of γ does the …rm o¤er any quality at all to the low type consumer? (Hint: look at s1 ). Eric Dunaway (WSU) EconS 425 Industrial Organization 41 / 41