Reexamining the Schmalensee effect

Kim, Jeong-Yoo Working Paper Reexamining the Schmalensee effect Economics Discussion Papers, No. 2017-3 Provided in Cooperation with: Kiel Institute for the World Economy – Leibniz Center for Research on Global Economic Challenges Suggested Citation: Kim, Jeong-Yoo (2017) : Reexamining the Schmalensee effect, Economics Discussion Papers, No. 2017-3, Kiel Institute for the World Economy (IfW), Kiel This Version is available at: https://hdl.handle.net/10419/149753 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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Licensed under the Creative Commons License - Attribution 4.0 International (CC BY 4.0) Discussion Paper No. 2017-3 | January 30, 2017 | http://www.economics-ejournal.org/economics/discussionpapers/2017-3 Reexamining the Schmalensee effect Jeong-Yoo Kim Abstract The author reexamines the Schmalensee effect from a dynamic perspective. Schmalsensee’s argument suggesting that high quality can be signaled by high prices is based on the assumption that higher quality necessarily incurs higher production cost. In this paper, the author argues that firms producing high-quality products have a stronger incentive to lower the marginal cost of production cost because they can then sell larger quantities than low-quality firms can. If this dynamic effect is large enough, then the Schmalensee effect degenerates and, thus, low prices signal high quality. This result is different from the Nelson effect relying on the assumption that only the high-quality product can generate repeat purchase, because the result is valid even if low-quality products can also be purchased repeatedly. The author characterizes a separating equilibrium in which a highquality monopolist invests more to reduce cost and, as a result, charges a lower price. Separation is possible due to a difference in quantities sold in the second period across qualities. JEL D82 L15 Keywords Experience good; quality; signal; Schmalensee effect Authors Jeong-Yoo Kim, Department of Economics, Kyung Hee University, Seoul, Korea, [email protected] This research was begun when the author was visiting POSTECH in 2015. Citation Jeong-Yoo Kim (2017). Reexamining the Schmalensee effect. Economics Discussion Papers, No 2017-3, Kiel Institute for the World Economy. http://www.economics-ejournal.org/economics/discussionpapers/2017-3 1 Introduction Recently, a smartphone named Luna was launched in Korea. The retail price was $380, half the price of most premium phones—and it offered higher-quality specs than most of its mid-range peers, comparable to Samsung’s earlier flagship product, the Galaxy S5. Luna’s processor, the Snapdragon 801 by Qualcomm, supported a 2.5 GHz Quadcore while many mid-range smartphones such as BandPlay and the Grand Max by Samsung Electronics used the Snapdragon 410 with only a 1.2 GHz Quadcore. Luna’s success and popularity have been attributed to its low production cost, which is due to a collaboration with Taiwanese manufacturing company, Foxconn. Luna’s success also led to the perception that low-priced smartphones could have high quality. Since the seminal work of Nelson (1970, 1974), it has been controversial whether a low or a high price better signals quality.1According to the longstanding economic wisdom, it depends on the comparison between two conflicting effects, the so-called Nelson effect and the Schmalensee effect. The Nelson effect occurs whenever high-quality firms have a stronger incentive to attract consumers than low-quality firms do because high-quality goods succeed at generating repeat purchases. On the other hand, the Schmalensee effect occurs whenever low-quality firms have a stronger incentive to attract consumers than high-quality firms do because doing so yields high profits due to a lower production cost. Therefore, the Schmalensee effect occurs only when the cost of producing high-quality products is greater than the cost of producing low-quality products. The anecdotal example about Luna, however, raises questions about how relevant or realistic this assumption is. In fact, high profit margins would seem to be more valuable to high-quality firms because they can sell larger quantities that bring in more revenue than low-quality firms can. Therefore, a firm producing a high-quality product may have a stronger incentive to lower its marginal cost of production; consequently, the marginal cost of producing high-quality products may counterintuitively be lower than the marginal cost of producing low-quality products. The Schmalensee effect would then disappear or be reversed. 1To name only a few, see Wolinsky (1983), Milgrom & Roberts (1986), Bagwell & Riordan (1991), Judd & Riordan (1994), Daughety & Reinganum (1995), Kaya (2013) and Kim (2016). 2 In this paper, we reexamine the Schmalensee effect by formalizing this insight. Our main approach is to consider an extended model by incorporating the investment decision of the monopolist to lower the marginal cost rather than take the production cost as exogenous.2 The above insight turns out to be correct. We show that under some sorting condition (that the cost-saving effect exceeds the demand-increasing effect), there is a separating equilibrium in which a high-quality monopolist invests more to reduce cost and, as a result, charges a lower price. Note that, in our model, the result that high quality can be signaled by selling at lower prices than the competition’s is not due to the Nelson effect. Although we consider a model of repeat purchase, the Nelson effect does not appear in our model because consumers can make repeat purchases of low-quality products as well. Our result comes from a cost difference that follows from a difference in the monopolist’s investment decision. Although the difference in equilibrium investments to reduce marginal costs is due to a difference in sales in the second period when all uncertainty about quality is resolved, the difference in equilibrium prices does not rely on the assumption of repeat purchases as long as there is a cost difference across qualities. Therefore, the main driving force that separates a highquality product from a low-quality one is the difference in the second-period sales. This difference in a low-quality-typeversus a high-quality-type firms’ second-period sales leads to a difference in their incentives to invest and, therefore, to the crucial difference in marginal costs that drives our main result of low price being used as a signal of high quality. The article is organized as follows. In Section 2, we set up a model of an experience good. In Section 3, as a benchmark case, we consider the complete information case in which consumers are informed about the quality of the experience good. In Section 4, we consider the monopolist’s joint pricing and investment decisions in the case of incomplete information. Concluding remarks follow in Section 5. All the proofs are provided in Appendix. 2None of the articles mentioned above considers the dynamic incentive to reduce the monopolist’s cost of producing experience goods. Kaya (2013) analyzes a dynamic model of experience goods, dynamic in the sense that the monopolist sets prices in a multi-period model. 3 2 Model We consider a monopolist who sells an experience good. The firm possesses private information about the quality of the good, whereas consumers do not. Let the quality of the good be r. Then, ris either Hor Lwith H > L.3 The monopolist makes a cost-saving R&D investment K. Marginal cost is not exogenously given but endogenously determined by K. We will denote the monopolist’s marginal cost by c(K) where c′(K)<0, c′′(K)>0,limK→0c′(K) = −∞ and limK→∞ c′(K) = 0.4 The interaction between the monopolist and consumers proceeds in three stages. At t= 0, the monopolist determines its investment level K, which is not observable to consumers. Then at t= 1, the monopolist chooses its first-period price, which is observable to consumers. Consumers then update their beliefs about the quality of the good and, based on their beliefs, choose either to buy one or not. Uncertainty about the quality of the good is resolved at the end of the period. Then, at t= 2, the firm chooses the second-period price and consumers make purchasing decisions. We use π(p, K;r) to denote the monopolist’s profit net of investment cost when it chooses the investment Kand the price p. It is formally defined by π(p, K;r) = (p−c(K))D(p;r). Here, D(p, r) is the demand function for the good, where D1≡∂D ∂p <0 and D2≡∂D ∂r >0. For simplicity, we assume that D(p) = r−p. The total profit of the monopolist is defined by Π(p1, p2, , K;r) = π(p1, K;r) + π(p2, K :r)−K, where ptis the t-period price for t= 1,2. 3We could have denoted λ∈(0,1) as the prior probability that the quality of the good is H, but this notation will not be used in this paper. 4Inada conditions characterized by these two assumptions on c(K) are technical assumptions to ensure the existence of an interior solution for the optimal K. 4 3 Complete Information In this section, we consider the benchmark case of complete information in which consumers are fully informed about the quality of the good. To analyze this case, we will use backward induction. Because price decisions at t= 1,2 are the same under complete information, we simply consider the one-period price decision. Let K∗(r) and p∗(r) be the optimal investment level and the optimal price, respectively, of the monopolist producing a good of quality r. At t= 1, for any given K, the optimal price of the monopolist is determined from the first order condition for profit maximization, implying that equilibrium price p∗must satisfy πp=D(p∗(r)) + (p∗(r)−c(K))D1(p∗(r); r) = 0.(1) Taking account of the fact that it will choose p∗(r) satisfying (1) in response to its own choice K, the monopolist will make its optimal R&D investment K∗(r) to solve the following problem: max KΠ = 2π−K= 2(p∗(r)−c(K))D(p∗(r); r)−K. (2) Let π∗(K;r) = π(p∗(r), K;r) and Π∗(K;r) = Π(p∗(r), K;r). Then, by the Envelope Theorem, we have dπ∗(r) dK =πK. Thus, dΠ∗(K) dK = 2πK−1 = −2c′(K∗(r))D(p∗(r); r)−1 = 0.(3) Equation (3) has the usual interpretation that an optimal investment must equate the marginal cost of increasing the investment to the marginal benefit from the increase through cost saving. The existence of K∗(r) is guaranteed by the assumptions on c(K) including the Inada conditions. Assuming that the second order condition (i.e., πKK <0) of the monopolist’s optimization problem holds, comparative statics lead to the following proposition. Proposition 1 K∗(r)is increasing in r(i.e., K∗(H)> K∗(L)). This proposition implies that a monopolist producing a high-quality good has an incentive to invest more in cost-saving R&D. Accordingly, the monopolist’s marginal cost of producing a high-quality product could be lower than for a low-quality product (although the fixed R&D 5 cost of producing a high-quality product is greater). The insight behind this result is exactly what is provided in the introduction. From the monopolist’s point of view, the advantage of increasing its investment is to lower its marginal cost of production and thereby increase the mark-up (price over marginal cost) it earns on each unit sold. Because a high-quality monopolist can sell a larger quantity due to higher demand, the firm has a stronger incentive to invest in R&D than it would if it were a low-quality monopolist.5This confirms the insight in this model of complete information. Now, we will examine the comparative statics of the pricing decision. From equation (1), we have D(p∗, r)+(p∗−c(K∗(r)))D1(p∗, r) = 0. To see the effect of quality on equilibrium price, we differentiate the expression above with respect to rto get ∆dp +[D2−c′∂K∗ ∂r D1+ (p∗−c(K(r)))D12]dr = 0,(4) where ∆ = 2D1+(p−c(K(r)))D11 <0 by the second order condition. We cannot determine the sign of the expression inside the square brackets because D2>0, c′<0, ∂K∗ ∂r >0, D1<0, and D12 = 0. Therefore, it is not clear whether p∗(r) is increasing or decreasing in r. Intuitively, there are two conflicting effects. On the one hand, since the demand for a higher-quality product is larger (D2>0),6the equilibrium price rises as quality increases. On the other hand, since the marginal cost of a higher-quality product is lower, choosing higher quality thus lowers the price of high-quality products. Due to the (dynamic) second effect, the equilibrium price of a higher-quality product may be lower than the price of a lower-quality product. Finally, it is clear that profits are increasing in the quality. Let π∗(r) = π∗(K∗(r); r) and Π∗(r) = Π∗(K∗(r); r). Then, Proposition 2 summarizes the result. 5To elaborate, this is because an increase in Kraises the high-quality monopolist’s profit through a reduction in c. The reason is clear. If pis the same for both types of quality, then a high-quality firm is able to increase its demand more. If presponds optimally, then the high-quality firm’s profit will be greater than a low-quality firm’s profit. 6Mathematically, the second term of equation (4) disappears. 6 Proposition 2 (i) π∗(H)> π∗(L), and (ii) Π∗(H)>Π∗(L). The intuition for (i) is quite obvious. The equilibrium profit of a high-quality monopolist is higher because consumer demand is greater and cost is lower due to the monopolist having made a larger investment. The intuition for (ii) is also clear. Although the highquality monopolist incurs greater investment cost, it optimally chooses to make this larger investment because the return is higher. The profit of the high-quality monopolist (after netting out investment costs and the effects of strategic best-responses among consumers) is also greater. This proposition is essential to deriving our main result. 4 Incomplete Information In this section, we will examine whether the result of different R&D investments carries over to the case in which the quality of the product is not known to consumers before they decide whether or not to purchase one. If consumers are not informed of product quality, the monopolist’s choice of price which consumers do observe may nevertheless reveal private information about product quality. Signaling games often involve many equilibria depending on posterior beliefs. It is therefore usual to use a stronger refinement than weak Perfect Bayesian Equilibria as a solution concept. In this section, we will use the C-K Intuitive Criterion developed by Cho and Kreps (1987) as the main solution concept. 4.1 The Second-Stage Pricing Game Since the true quality of the good is revealed right before the second period, the analysis for the second-period price decision is the same as in the case of complete information. Thus, our main interest will be the price decision in the first period. Given the marginal cost which was determined by the investment decision, the monopolist chooses its first-period price. Our main purpose is to investigate how prices can signal high quality. We therefore restrict attention to separating equilibria in which each type of monopolist charges a different price (what we will call “price-separating equilibria”). 7 Let the investments made by a high-type monopolist and a low-type monopolist in the (price)-separating equilibrium be denoted as KHand KL.. For the time being, we will assume that KHand KLare simply given (and satisfy KH> KL) because the pricing decision is the main focus of this subsection. Note that the monopolist’s private information about quality is not revealed at this stage (after the investment decision is made) even if KH> KL, because Kis not observable to consumers. Let the first-period prices of high-type and low-type monopolists be denoted as pHand pLin the separating equilibrium. Also, let π(p, r, re) represent the profit of a firm with the true quality rand perceived quality re. We say that a weak Perfect Bayesian Equilibrium (pH, pL) passes the C-K Intuitive Criterion (IC) if there does not exist a price p(=pH, pL) such that (i)π(pL, L, L)≥π(p, L, re),∀re=L, H, (5) (ii)π(pH, H, H)< π(p, H, H).(6) Roughly speaking, condition (i) implies that an off-the-equilibrium price pis equilibriumdominated for type L. Condition (ii) implies that if consumers believe that the price p came from type Hfor which pis not equilibrium-dominated, the monopolist of type Hwill have an incentive to deviate to such a price pfrom pH. If there exists a price satisfying these two conditions, then (pH, pL) cannot be a reasonable equilibrium that passes the CK Intuitive Criterion because the H-type monopolist has an incentive to deviate from the equilibrium. Note that the second-period profits cancel out so they cannot affect (5) and (6). This is because Kis already determined and is, thus, unalterable—and the revelation of private information makes the monopolist choose p∗(K;r) regardless of the first-period price decision for any r=H, L. The following lemma will be useful in characterizing the separating equilibrium. Lemma 1 In any price-separating equilibrium, we have pL=p∗(L). This is clear because if pL=p∗(L), then the monopolist would profitably deviate to p∗(L). Lemma 1 implies that in any (price)-separating equilibrium, it must be the case that π(p∗(L), L, L) = π∗(L) in the first period. We now demonstrate a separating equilibrium in which a monopolist signals high quality by choosing a low price. To avoid the trivial case, we assume that π(p∗(H), L, H)> 8 [4] Judd, K. and M. Riordan, 1994, Price and Quality in a New Product Monopoly, Review of Economic Studies 61, 773-789 [5] Kaya, A., 2013, Dynamics of Price and Advertising as Quality Signals: Anything Goes, Economics Bulletin 33, 1556-1564 [6] Kim, J.-Y., 2016, Pricing an Experience Composite Good as Coordinated Signals, The Manchester Schoo, doi:10.1111/manc.12141 [7] Milgrom, P. and J. Roberts, 1986, Price and Advertising Signals of Product Quality, Journal of Political Economy 94, 796-821 [8] Nelson, P., 1970, Information and Consumer Behavior, Journal of Political Economy 78, 311-329 [9] Nelson, P., 1974, Advertising as Information, Journal of Political Economy 81, 729-754 [10] Schmalensee, R., 1978, A Model of Advertising and Product Quality, Journal of Political Economy 86, 485-503 [11] Wolinsky, A., 1983, Price as Signals of Product Quality, Review of Economic Studies 50, 647-658. 15 (p;H,H) (p;H,L) (p;L,L) (p;L,H)  p cH cL Figure 1. Downward Price Signal when KH>KL pp*(H)p*(L) p Please note: You are most sincerely encouraged to participate in the open assessment of this discussion paper. You can do so by either recommending the paper or by posting your comments. Please go to: http://www.economics-ejournal.org/economics/discussionpapers/2017-3 The Editor © Author(s) 2017. Licensed under the Creative Commons License - Attribution 4.0 International (CC BY 4.0).