Pass-Through along the Supply Chain

Transcription

1 Pass-Through along the Supply Chain Germain Gaudin March 3, 2015 PRELIMINARY DRAFT COMMENTS ARE WELCOME Abstract This paper analyzes the determinants of channel pass-through specific to vertical relationships between manufacturers and retailers. Pass-through depends on the firms relative bargaining power and on the type of agreement they contract upon. Pass-through rates at the upstream and downstream levels generally differ, although common modelling assumptions imply a constant pass-through between the different levels of the supply chain. Manufacturers may alleviate the problem of incomplete pass-through of trade promotions by giving more bargaining power to retailers. Keywords: Pass-through; Bargaining; Vertical contracting; Trade promotions. JEL Codes: L11; L81; M30. Düsseldorf Institute for Competition Economics, Heinrich Heine University ( germain.gaudin@dice.hhu.de).

2 1 Introduction Trade promotions represent the main promotional activity for manufacturers. 1 However, the extent to which these promotions reach final consumers depends on the pass-through rate at the retail level. An issue commonly faced by manufacturers is that this rate is typically lower than 100%, so that promotions do not benefit consumers but are instead pocketed by retailers. 2 In this context, it is important to understand the determinants of pass-through. Particular attention has been given to the role of horizontal market structure and functional forms of demand and supply in affecting the pass-through rate of costs to prices, as pioneered by Bulow and Pfleiderer (1983) in the case of a monopolist facing linear costs, and recently generalized by Weyl and Fabinger (2013) to various market structures and demand and cost forms. In their papers, they have emphasized, in particular, that pass-through typically depends on demand curvature. 3 There is, however, little theoretical work on the impact of vertical market structures on pass-through. The theory seems thus lagging as the empirical literature has investigated the link between pass-through rates and vertical relationships by inferring, for instance, ratios of firms margins (Bresnahan and Reiss (1985)), vertical structure and contractual agreements (Villas-Boas (2007)), bargaining power (Draganska, Klapper and Villas-Boas (2010)) or the use of non-linear pricing contracts and vertical restraints (Bonnet et al. (2013)). Finally, in related work, Hong and Li (2014) empirically analyze the interaction between vertical and horizontal structure to explain incomplete pass-through. This paper proposes to fill this gap in the literature, by analyzing the impact of specific features of manufacturer-retailer relationships on pass-through. In particular, we show that firms relative bargaining power, as well as the agreement they contract upon, are important determinants of pass-through. 4 1 According to Kantar Retail (2012), US manufacturers spend the majority of their marketing budget in trade promotions. This represented 59% of their total marketing expenses in For instance, Ailawadi and Harlam (2009) find that retail pass-through rates are generally lower for trade promotions than for retailers own private-label branches promotions. 3 On this point, see also Tyagi (1999). 4 Our focus is solely on the impact on pass-through of contractual agreements and relative bargaining power between vertically-related firms, not between consumers and retailers. See, e.g., Busse, Silva-Risso and Zettelmeyer (2006) for an empirical analysis of pass-through of trade promotions when consumers bargain with retailers. 1

3 In addition, we derive pass-through rates at both the upstream and downstream levels. This allows us to bring some theoretical arguments to explain empirical observations of large differences between pass-through at various stages of the supply chain (see, e.g., Nijs et al. (2010)). In particular, we show that, in a manufacturer- Stackelberg setting, the assumption of iso-elastic or linear demand that is often used in the empirical literature implies that the pass-through rate of input price to retail price equals that from upstream cost to input price. Finally, we consider the classic manufacturer s problem of incomplete retail pass-through. We highlight the conditions on the demand form and the type of contract firms negotiate upon which allow the manufacturer to alleviate the incomplete pass-through problem, and therefore to target consumers more easily through trade promotions. Related literature. The marketing literature has already put forward several determinants of pass-through in addition to the well-known impact of demand curvature, functional form of the supply function and horizontal market structure. For instance, imperfect information and consumer search (Kumar, Rajiv and Jeuland (2001)) or seasonality of demand (Meza and Sudhir (2006)) can have a significant effect on pass-through. However, the literature on vertical determinants of pass-through is scarce. In a paper mixing theory and empirics, Bresnahan and Reiss (1985) show that when a manufacturer sets linear prices the ratio of the retailer s margin to that of the manufacturer is equal to the retail pass-through rate, i.e., the rate at which wholesale prices affect retail prices. Weyl and Fabinger (2013) extend this result to a chain of imperfectly competitive markets as an application of their main findings to vertically-related markets. In a related work, Peitz and Reisinger (2014) study the effects of indirect taxation in two-tier oligopoly markets. They compare the effects of upstream and downstream cost shocks on retail prices and show that passthrough of downstream cost shocks typically depends on the upstream market structure. Note that, however, none of the aforementioned papers investigates the relationship between retail, wholesale and total chain pass-through rates nor do they consider firms bargaining power or different contractual agreements. Two exceptions are the papers by Adachi and Ebina (2014a) and Hong and Li (2014). Adachi 2

4 and Ebina (2014a) show that the total chain pass-through rate is greater than the wholesale one if and only if demand is log-concave, 5 while Hong and Li (2014) investigate the relationship between retail and total pass-through assuming that the elasticity of demand always increases in price. Both analyses are however limited to the simple case of Stackelberg-manufacturer setting with linear input pricing and assume away the impact of bargaining power and different contractual agreements. In addition, they do not investigate how the retail pass-through rate compares to the wholesale one. The remainder of the paper is as follows. Our baseline model with linear input pricing is presented in Section 2 and solved in Section 3, provided with an extensive analysis of the results. Section 4 presents the robustness of our result to various contractual agreements commonly used between manufacturers and retailers. The impact of bargaining power on pass-through of trade promotions is investigated in Section 5. Finally, Section 6 concludes. 2 Model and pass-through rates 2.1 The model A manufacturer, M, produces an input at a constant marginal cost, c, and sells it to a retailer, R, at a linear wholesale price, w. 6 The retailer then sells at a linear price p to price-taking consumers. 7 Firms bargain over the linear wholesale price. 8 The manufacturer has an exogenous bargaining power θ [0, 1], and the retailer has the remaining bargaining power 1 θ. We assume that firms can only bargain over the input price, and retail pricing is not contractible at this stage of the game (e.g., firms cannot agree 5 In follow-up work, Adachi and Ebina (2014b) derive similar results in the case of two-tier Cournot oligopoly markets. 6 In Sections 4 and 5 we allow for wholesale pricing agreements other than the linear one. 7 The retail price is thus set after the wholesale one, a common assumption in the literature. We acknowledge, however, that the timing of the game can have an impact on the pass-through of trade promotions. See for instance the paper by Sudhir (2001) who considers both manufacturer- Stackelberg and vertical-nash settings. 8 We assume that firms engage in Nash-bargaining, a commonly used bargaining setting; see, e.g., Iyer and Villas-Boas (2003). This setting of vertical bilateral bargaining was introduced by Horn and Wolinsky (1988), and builds on the findings of Binmore, Rubinstein and Wolinsky (1986) which present foundations of the Nash-bargaining setting as a non-cooperative game. 3

5 on Resale Price Maintenance clauses). 9 The canonical Stackelberg-manufacturer setting proposed by Spengler (1950) thus corresponds to the case where θ = 1. Finally, firms face no outside option to sell or buy the input, therefore both have a disagreement payoff of zero. 10 We only consider upstream costs in order to focus on how these costs are passed through the entire supply chain to final consumers. 11 At the upstream level, our results are robust to considering additional (constant marginal) costs, as the analysis is always marginal. Retail demand at price p is given by q ( p ). We assume that demand is well defined for any price, is three times differentiable and decreasing in price everywhere over the relevant range where it is positive, i.e., q ( p ) < 0. In the analysis, we will often refer to the elasticity of demand, ε ( p ) q ( p ) p/q ( p ), as well as the curvature of demand, E ( p ) q ( p ) q ( p ) /q ( p )2. Formally, the demand curvature is the elasticity of the slope of inverse demand. 12 It takes wellidentified values for common demand forms. For instance, E = 0 when demand is linear, E = 1 when it is of the negative exponential form, and E = 1 + 1/ε when it displays a constant elasticity. In addition, a negative curvature is equivalent to the demand form being concave, and a curvature lower than unity to the demand being log-concave (see, e.g., Bulow and Pfleiderer (1983), Tyagi (1999), and Amir, Maret and Troege (2004)). 2.2 Pass-through rates Our focus is on the determinants of three pass-through rates. The first one is the retail pass-through rate, dp/dw, which corresponds to the variation in retail price following a change in the input price. This rate matters to manufacturers which set trade promotions, as these promotions are not fully transferred to final consumers 9 This implies (some) double marginalization under linear input pricing. However, the additional contracts considered in Sections 4 and 5 allow for supply chain coordination and industry-profit maximization. 10 Because our aim is to demonstrate that pass-through may depend on firms relative bargaining power, it would be out of the scope of this paper to consider nonzero disagreement payoffs. 11 See Peitz and Reisinger (2014) for an analysis of the impact of vertical structure on pass-through of exogenous downstream cost shocks. 12 When expressed as a function of the inverse demand, P ( ), it gives E ( q ) = qp ( q ) /P ( q ). Note also that the demand curvature is related to the derivative of the elasticity of demand, as ε/ p = (1 + 1/ε E) ( ε 2 /p ). 4

6 by retailers whenever the retail pass-through is too low, i.e., dp/dw < 1. The two other rates are the wholesale pass-through rate, dw/dc, and the total pass-through rate, dp/dc, which represent the impacts of a cost shock for the manufacturer on the wholesale and retail prices, respectively. Comparing both retail and wholesale pass-through rates is particularly interesting because this indicates whether incomplete pass-through occurs at the upstream or at the retail level (see, e.g., Nijs et al. (2010)). Finally, note that our analysis, which aims at deriving results on pass-through, can be performed either by using pass-through rates or elasticities. To this end, we provide a summary of our pass-through calculations by using elasticities in the appendix. 3 Analysis Retail pricing. In the last stage of the game, the retailer takes the wholesale price, w, as given, and sets the retail price, p. Its profit is thus given by π R = ( p w ) q(p). The retailer s profit maximization problem gives the following first-order condition: q(p) + (p w)q (p) = 0. (1) The second-order condition is equivalent to 2 E > 0, and is assumed to be satisfied everywhere over the relevant interval. Solving for the equilibrium price leads to: p = w q q. (2) Implicitly differentiating the above equilibrium result with respect to the wholesale price gives the retail pass-through rate, i.e., the rate at which an increase in the wholesale price is passed-through to consumers. Lemma 1 (Bulow and Pfleiderer (1983)). The retail pass-through rate is dp dw = 1 2 E. This pass-through rate thus depends on demand curvature only. The relative bargaining power does not directly enter the expression of retail pass-through, even though it plays a role in defining the equilibrium quantity at which demand 5

7 curvature is evaluated, as demonstrated below. This result holds due to our assumptions about the supply side (i.e., constant marginal costs) and the horizontal structure of the retail market (i.e., monopoly). 13 The retail pass-through rate is strictly positive due to the second-order condition and lies below unity if and only if demand is log-concave, i.e., E < 1 (Tyagi (1999), Amir, Maret and Troege (2004)). A pass-through lower than unity corresponds to a less than 100% transmission of input price changes (due to trade promotions, for instance) to final consumers. Note that the retail pass-through takes on properly defined values for commonly used demand forms, as it equals 1/2 for linear demands, 1 for negative exponential demands, and 1/ (1 1/ε) for constant-elasticity ones. Since the retail pass-through rate only depends on demand curvature and that the chain rule implies that the total pass-through rate is the product of the retail and wholesale ones, we can easily compare both wholesale and total pass-through rates. Proposition 1. For any given level of bargaining power, the total pass-through rate is smaller (respectively, larger) than the wholesale one if and only if demand is log-concave (resp., log-convex). Both rates equal unity if and only if demand curvature equals unity. Indeed, log-concavity of demand is equivalent to the retail pass-through being lower than unity. This directly provides a ranking of both total and wholesale passthrough rates, because dp/dc = dp/dw dw/dc. This result was first documented by Adachi and Ebina (2014a) in the case where the manufacturer has all bargaining power. We thus show that it is robust to any split of bargaining power between firms. Wholesale pricing. When firms engage in Nash bargaining, the first-stage equilibrium is determined by solving the following maximization problem: { argmax π θ M w } π1 θ R where π M = (w c) q(p) and π R = ( p w ) q(p) are the manufacturer s and retailer s profits, respectively. Using the second-stage retail equilibrium from equation (2), this maximization 13 Weyl and Fabinger (2013) provide an extensive analysis relaxing these assumptions. (3) 6

8 problem can be re-written as: Solving for w gives: argmax w ( [ ] (w θ c) q q2 q ) 1 θ. (4) w = c q q θ (2 E) [1 + (1 E) (1 θ)]. (5) Comparing the results for the retail and wholesale equilibria given by equations (2) and (5), respectively, we can state the following result. Proposition 2. Demand curvature and bargaining power determine the ratio of retail to wholesale margins: p w w c = [1 + (1 E) (1 θ)] 1 dp θ dw. This result shows that the ratio of both margins only depends on demand curvature and the relative bargaining power between firms. In the Stackelbergmanufacturer framework, i.e., when θ = 1, this ratio simply equals the retail pass-through, as first demonstrated by Bresnahan and Reiss (1985). The second-order condition of the wholesale maximization problem is equivalent to (2 E) 2 [1 + (1 E) (1 θ)] θ 2 qe /q > 0 and is assumed to be satisfied everywhere over the relevant interval. This means that the curvature of demand should not decrease too rapidly (i.e., E should not be too negative). Note that the derivative of the demand curvature, E, is formally given by: E E p = q qq (1 2E) +. (6) q q 2 Having obtained the equilibrium wholesale price, we can derive the wholesale pass-through rate by implicitly differentiating w with respect to c. Lemma 2. When firms bargain over the linear input price, the wholesale pass-through rate is dw dc = (2 E) [1 + (1 E) (1 θ)] 2 (2 E) 2 [1 + (1 E) (1 θ)] θ q. 2 q E Therefore, as emphasized by Weyl and Fabinger (2013), the wholesale passthrough rate depends on demand curvature and the third derivative of demand, 7

9 q. More specifically, it depends on the rate at which the curvature of demand changes with price. The wholesale pass-through also directly depends on the relative bargaining power, even when demand curvature is constant. When the retailer has all bargaining power, so that θ = 0, the input is sold at cost and the wholesale pass-through rate equals unity. Bulow and Pfleiderer (1983) have identified the set of demand forms which lead to a constant retail pass-through, i.e., which have a constant curvature. 14 Linear and iso-elastic demand forms are included in this set. By comparing both retail and wholesale pass-through rates in the Stackelberg-manufacturer case, where θ = 1, we see that a constant demand curvature is a necessary and sufficient condition for both retail and wholesale pass-through rates to be equal. This allows us to state the following result. Proposition 3. In the Stackelberg-manufacturer case, the wholesale pass-through is larger (respectively, smaller) than the retail one if and only if the demand curvature decreases (resp., increases) in price. Also, both wholesale and retail pass-through rates are equal if and only if demand curvature is constant. This result, albeit relatively simple, does not appear in the literature as far as we know. 15 It is important because it allows to easily compare pass-through between different levels of the supply chain. In addition, it sheds light on implications of models that use a linear or constant-elasticity demand, which have constant demand curvatures, equal to 0 and 1 + 1/ε, respectively. This relationship between pass-through rates occurs in addition to the restrictions on their range implied by the selected model (see the discussion in Besanko, Dubé and Gupta (2005)). There is no reason though to assume this equality between pass-through rates should generally hold. For instance, Nijs et al. (2010) measure both wholesale and retail pass-through rates for a major consumer packaged goods category and find that they differ significantly. Finally, we can also compute the equilibrium retail price by plugging the equilibrium wholesale price given by equation (5) into the retail equilibrium given by 14 A demand with constant curvature takes one of the following (inverse) forms: (i) a bq δ, with a, b, δ > 0, (ii) bq 1/ε, with b > 0 and ε > 1, or (iii) a b log(q), with a, b > 0 and e a/b > q > Weyl and Fabinger (2013) provide a method to derive pass-through rates at different levels of the supply chain but do not directly compare them (see their Section VI, B). 8

10 equation (2). We obtain: p = c q q [1 + ] θ (2 E). (7) [1 + (1 E) (1 θ)] The total pass-through rate, dp/dc, is obtained either by differentiating p with respect to c in the equation above or via the chain rule, where dp/dc = dp/dw dw/dc. Lemma 3. When firms bargain over the linear input price, the total pass-through rate is dp dc = [1 + (1 E) (1 θ)] 2 (2 E) 2 [1 + (1 E) (1 θ)] θ q. 2 q E Overall, firms relative bargaining power impacts the total pass-through via two effects. The first one is a classic indirect effect on the equilibrium price which ultimately depends on θ. The second effect, illustrated by Lemma 3 above, shows that firms bargaining power directly impacts the total price-cost pass-through, even when demand displays a constant curvature. When the manufacturer is a price taker, i.e., θ = 0, we find the classic pass-through of a single firm facing linear costs studied by Bulow and Pfleiderer (1983), dp/dc = dp/dw = 1/ (2 E). Also, if the curvature is constant and known, estimates of the total pass-through rate are sufficient in order to identify firms relative bargaining power. In the special case of constant curvature, additional insights can be derived on how pass-through rates compare, including the retail one. Proposition 4. When the demand curvature is constant, pass-through rates rank as follows for any given level of bargaining power: dp dc dp dw dw dc 1 if and only if demand is log-concave; dp dc dp dw dw 1 if and only if demand is log-convex. dc Proposition 4 provides a simple tool to rank wholesale and retail pass-through under a constant demand curvature. It also implies that a variable demand curvature in price is a necessary condition to obtain wholesale and retail pass-through rates which are greater and smaller than unity, respectively. This occurs for instance for some of the estimations by Nijs et al. (2010), who found median pass-through rates of 1.13 and 0.67 for dw/dc and dp/dw, respectively. 9

11 4 Other contractual agreements We now allow firms to contract according to agreements other than the linear wholesale pricing. Of particular interest are agreements which coordinate the supply chain, i.e., which allow firms to maximize industry profits and avoid distortions due to double-marginalization. The relative bargaining power between firms then determines how they split joint profits. More specifically, our focus is on two types of agreements which coordinate the supply chain: two-part tariffs and revenue-sharing agreements. When these agreements are used to maximize industry profits in combination with linear retail pricing, the equilibrium retail price corresponds to the market monopoly price. Therefore, the total pass-through rate, dp/dc, always equals 1/ (2 E) in equilibrium under these contracts, that is, the total pass-through rate of an integrated monopolist. 16 Nevertheless, as demonstrated below, wholesale and retail pass-through rates vary according to different contracts. 4.1 Two-part tariffs When firms use two-part tariffs, the manufacturer first sets a wholesale price, w, which the retailer has to incur for every unit bought. In addition, firms agree on a fixed-fee the retailer transfers to the manufacturer, F. It is well-known that this contractual agreement, which is widely used in manufacturer-retailer relationships (see, e.g., the empirical analyses by Villas-Boas (2007) or Bonnet and Dubois (2010)), coordinates the supply-chain when the variable wholesale price equals the wholesale marginal cost. Firms share the (maximized) industry profits through the fixed fee according to their relative bargaining power, denoted λ [0, 1] for the manufacturer. In the joint-profit maximizing equilibrium, the input is sold at marginal cost and the retail price equals the monopoly price: p = w q/q = c q/q. Pass-through rates are therefore as follows. 16 See Tyagi (1999) for a detailed demonstration in the case of two-part tariffs. 10

12 Lemma 4. Under two-part tariffs, wholesale and retail pass-through rates are given by dw dc = 1, dp dw = 1 2 E. The relative bargaining power of firms plays no role in how changes in upstream cost or input are transmitted to final consumers. Besides, note that this system of rates equals the one under linear wholesale pricing which occurs when the retailer has all bargaining power, i.e., θ = 0. Therefore, as emphasized by Villas-Boas (2007), one cannot distinguish between the two types of contract by estimating pass-through rates when the bargaining power lies with the retailer. 4.2 Revenue-sharing agreements When firms use revenue-sharing agreements, the retailer buys input at a linear price, w, and transfers a share α [0, 1] of its total revenue to the manufacturer. This contract also helps firms to coordinate on maximizing industry profits by setting w = (1 α) c (see Cachon and Larivière (2005)). Firms can then share these profits through the revenue-share α which corresponds to the manufacturer s bargaining power. This type of contract is for instance widely used in the videorental industry. 17 In the joint-profit maximizing equilibrium, the wholesale price is thus w = (1 α) c, while the retailer sets p = w/ (1 α) q/q = c q/q in the second stage. Wholesale and retail pass-through rates are thus as follows. Lemma 5. Under revenue-sharing, wholesale and retail pass-through rates are given by dw dc = 1 α, dp dw = 1 (1 α) (2 E). Under revenue-sharing agreements, firms bargaining power has a direct impact 17 See Mortimer (2008) for a welfare analysis of the 1998 wide adoption of such contracts in the video-rental industry. 11

13 on both the retail and wholesale pass-through rates. This is in striking contrast with the case of two-part tariffs. Therefore, in addition to the distribution of bargaining power between the manufacturer and its retailer, the type of agreement they contract upon is an important determinant of the pass-through rates at both upstream and downstream levels. 5 Bargaining and pass-through of trade promotions One of the most important questions when considering manufacturer-retailer relationships is that of incomplete pass-through, where dp/dw < 1 (see, e.g., Tyagi (1999), Moorthy (2005), Besanko, Dubé and Gupta (2005) or Nijs et al. (2010)). When a manufacturer sets promotional discounts at the upstream level, the degree to which the retailer passes on these promotions to consumers depends on the retail pass-through. Some external factors such as promotion advertising can help a manufacturer to (partially) solve the problem induced by an incomplete retail pass-through (see Kumar, Rajiv and Jeuland (2001)). However, both manufacturers and retailers generally have some bargaining power in negotiating the input prices, and it is thus relevant to consider the impact of bargaining power on retail pass-through. In this section, we investigate whether the manufacturer can alleviate the incomplete pass-through problem by giving more bargaining power to its retailer. 5.1 Linear wholesale price When firms bargain over a linear input price w, the retail pass-through is given by Lemma 1 and does not directly depend on bargaining power. However, it is implicitly defined at the equilibrium quantity, which varies with this bargaining power. In order to determine the impact of a change in bargaining power on the retail pass-through, we need to compute d 2 p/dθdw. Differentiating dp/dw gives: d 2 p dθdw = E (2 E) 2 dp dθ. (8) The variable dp/dθ, which indicates how the retail price reacts to bargaining power changes, is given by differentiating equation (7) with respect to the bargaining 12

14 power parameter: dp dθ = q (2 E)2 q (2 E) 2 [1 + (1 E) (1 θ)] θ q > 0. (9) 2 q E Because the retail price always increases with the manufacturer s bargaining power, the direction of a change in bargaining power on pass-through of trade promotions is solely driven by the derivative of demand curvature. When demand curvature is not constant, i.e., E 0, a manufacturer can modify the rate at which the retailer passes its manufacturing promotions to consumers by giving it more bargaining power. Proposition 5. The retail pass-through rate increases (respectively, decreases) when the manufacturer s bargaining power decreases if and only if the slope of the demand curvature is negative (resp., positive). Moreover, the retail pass-through rate is independent of the bargaining power if and only if the demand curvature is constant. Proposition 5 shows that the manufacturer can (partially) alleviate the problem of incomplete pass-through of trade promotions if demand satisfies the right property, i.e., a decreasing curvature in price. This is equivalent to a retail pass-through decreasing in price. This condition is satisfied for several demand systems, such as a large subset of the Almost Ideal Demand System (AIDS) forms or demand forms resulting from a CARA utility. 18 Moreover, commonly used demand forms in structural empirical analyses, such as linear and iso-elastic demands, have a constant curvature, and therefore eliminate any impact of a change in bargaining power on retail pass-through. In case it can increase the retail pass-through, the manufacturer would face a direct and negative impact on profits from reduced bargaining power. Therefore, there is a trade-off between this direct impact and that from enhanced pass-through of trade promotions. A fully characterized model that explains the mechanisms driving promotions seems thus necessary to tackle this issue in greater detail. 18 The single-firm AIDS demand can be written as q(p) = ( a + b log(p) ) /p and has a decreasing curvature in price when b < 0 (see Fabinger and Weyl (2014)). The single-firm demand from a CARA utility takes the form q(p) = a log(p)/b (see Behrens and Murata (2007)) and always has a downward sloping curvature, with the only condition that marginal revenue is decreasing, i.e., q(p) < 2/b. 13

15 5.2 Two-part tariffs and revenue-sharing agreements When firms use contractual agreements based on two-part tariffs or revenuesharing agreements in order to maximize industry profits, the retail price remains constant for any level of bargaining power. The joint profit does not depend on the relative bargaining power between the manufacturer and its retailer. We thus have dp/dλ = 0 and dp/dα = 0 under two-part tariffs and revenue-sharing agreements, respectively. When firms use two-part tariffs, differentiating the retail pass-through rate from Lemma 4 with respect to bargaining power gives us: d 2 p dλdw This result can be expressed by the following proposition. = 0. (10) Proposition 6. Under two-part tariffs, the retailer s pass-through rate is independent of the bargaining power. Therefore, the manufacturer cannot change the retail pass-through by giving away some of its bargaining power to its retailer. By contrast, in the case of revenue-sharing agreements, we can determine the impact of a change in bargaining power on the retail pass-through rate from Lemma 5: d 2 p dαdw = 1 (1 α) 2 (2 E). (11) Hence, the retail pass-through changes when the manufacturer reduces its bargaining power. However, since the expression in equation (11) is strictly positive, the change in pass-through of trade promotions always has the same sign as the change in bargaining power. The manufacturer is thus unable to increase passthrough by decreasing its bargaining power. The following proposition states this result. Proposition 7. Under revenue-sharing agreements, the retailer s pass-through rate decreases when the manufacturer s bargaining power decreases. The linear pricing contract is therefore the only one among the three analyzed contracts for which the manufacturer can alleviate the incomplete pass-through problem by lowering its bargaining power relatively to that of its retailer. When 14

16 firms use two-part tariffs or revenue-sharing agreements and maximize industry profits, retail pass-through cannot be unilaterally increased by the manufacturer. 6 Conclusion We have investigated the determinants of pass-through in manufacturer-retailer relationships. Pass-through depends on firms relative bargaining power and on the type of agreement they contract upon. When firms bargain over a linear price for the input, the manufacturer can increase pass-through of trade promotions by lowering its relative bargaining power if demand displays a decreasing curvature in price. In this case, the manufacturer faces a trade-off between a reduction of direct profit and an increase of retail pass-through. A fully fledged model which endogenizes the incentives to set temporary promotions could help solving this trade-off. Our focus on the simple bilateral monopoly setting is sufficient to demonstrate that pass-through depends on contractual and bargaining parameters. A more sophisticated model could consider competition at one or both levels. One approach is to consider homogeneous competition at the upstream level, as Peitz and Reisinger (2014) or Adachi and Ebina (2014b). Another, more realistic approach would be to consider that firms engage in bilateral negotiations and that products can be differentiated. However, as demonstrated by Iozzi and Valletti (2014), this type of analysis hinges heavily on the model choice of firms disagreement payoffs and could necessitate the introduction of a specific demand form. Another extension could be to consider multi-product retailers, which can buy differentiated products from multiple manufacturers or produce their own private labels. Such an analysis should consider the impact of a cost shock for one product on pricing of the other products, i.e., cross-brand pass-through, as analyzed by Moorthy (2005) or Besanko, Dubé and Gupta (2005). 19 Various multi-product pricing strategies such as loss-leading (see, e.g., Pancras, Gauri and Talukdar (2013)) could also be investigated. 19 See also the discussions and following work by McAlister (2007), Dubé and Gupta (2008), and Duan, McAlister and Sinha (2011). 15

17 Appendix: Pass-through elasticities It can be useful for empirical applications to estimate the retail pass-through as an elasticity instead of a rate. When the retailer and manufacturer use linear pricing agreements, the retail pass-through elasticity, η, is given by: η dp w dw p = ε 1 ε (2 E). (12) It is always positive, thanks to the second-order conditions, and equals unity for iso-elastic demands. The pass-through elasticity is lower than unity for demand forms that are less-convex than the iso-elastic ones. Note that the pass-through elasticity is constant if and only if: (2 E) (1 + 1 ) } {{ } ε E > 0 + (p + qq ) } {{ } > 0 E = 0 (13) where the derivative of the demand curvature, E, is given by equation (6). Therefore, among the set of demand forms with constant curvature, only iso-elastic demands (for which 1 + 1/ε E = 0) satisfy a constant retail pass-through elasticity. by: Through a similar construction, the wholesale pass-through elasticity, β, is given β dw dc c w = (2 E) [1 + (1 E) (1 θ)] ε 1 (ε 1) [1 + (1 E) (1 θ)] θ (2 E) (2 E) 2 [1 + (1 E) (1 θ)] θ 2 q q E. (14) Finally, the total pass-through elasticity is simply the product of the retail and wholesale pass-through elasticities. 16

18 References Adachi, Takanori, and Takeshi Ebina. 2014a. Double marginalization and cost pass-through: Weyl-Fabinger and Cowan meet Spengler and Bresnahan-Reiss. Economics Letters, 122(2): Adachi, Takanori, and Takeshi Ebina. 2014b. Cost pass-through and inverse demand curvature in vertical relationships with upstream and downstream competition. Economics Letters, 124(3): Ailawadi, Kusum L., and Bari A. Harlam Retailer Promotion Pass-Through: A Measure, Its Magnitude, and Its Determinants. Marketing Science, 28(4): Amir, Rabah, Isabelle Maret, and Michael Troege On Taxation Pass- Through for a Monopoly Firm. Annales d Economie et de Statistique, 75-76: Behrens, Kristian, and Yasusada Murata General equilibrium models of monopolistic competition: A new approach. Journal of Economic Theory, 136: Besanko, David, Jean-Pierre Dubé, and Sachin Gupta Own-Brand and Cross-Brand Retail Pass-Through. Marketing Science, 24(1): Binmore, Ken, Ariel Rubinstein, and Asher Wolinsky The Nash Bargaining Solution in Economic Modelling. RAND Journal of Economics, 17(2): Bonnet, Céline, and Pierre Dubois Inference on vertical contracts between manufacturers and retailers allowing for nonlinear pricing and resale price maintenance. RAND Journal of Economics, 41(1): Bonnet, Céline, Pierre Dubois, Sofia B. Villas Boas, and Daniel Klapper Empirical Evidence on the Role of Nonlinear Wholesale Pricing and Vertical Restraints on Cost Pass-Through. Review of Economics and Statistics, 95(2): Bresnahan, Timothy F., and Peter C. Reiss Dealer and Manufacturer Margins. RAND Journal of Economics, 16(2): Bulow, Jeremy I., and Paul Pfleiderer A Note on the Effect of Cost Changes on Prices. Journal of Political Economy, 91(1): Busse, Meghan, Jorge Silva-Risso, and Florian Zettelmeyer $1, 000 Cash Back: The Pass-Through of Auto Manufacturer Promotions. American Economic Review, 96(4):

19 Cachon, Gérard P., and Martin A. Larivière Supply Chain Coordination with Revenue-Sharing Contracts: Strengths and Limitations. Management Science, 51(1): Draganska, Michaela, Daniel Klapper, and Sofia B. Villas-Boas A Larger Slice or a Larger Pie? An Empirical Investigation of Bargaining Power in the Distribution Channel. Marketing Science, 29(1): Duan, Jason A., Leigh McAlister, and Shameek Sinha Reexamining Bayesian Model-Comparison Evidence of Cross-Brand Pass-Through. Marketing Science, 30(3): Dubé, Jean-Pierre, and Sachin Gupta Cross-Brand Pass-Through in Supermarket Pricing. Marketing Science, 27(3): Fabinger, Michal, and E. Glen Weyl A Tractable Approach to Pass-Through Patterns. Mimeo. Available at Hong, Gee Hee, and Nicholas Li Market Structure and Cost Pass-Through in Retail. Mimeo. Horn, Henrick, and Asher Wolinsky Bilateral Monopolies and Incentives for Merger. RAND Journal of Economics, 19(3): Iozzi, Alberto, and Tommaso Valletti Vertical Bargaining and Countervailing Power. American Economic Journal: Microeconomics, 6(3): Iyer, Ganesh, and J. Miguel Villas-Boas A Bargaining Theory of Distribution Channels. Journal of Marketing Research, 40(1): Kantar Retail Trade Promotion Industry Benchmarking Study. Kumar, Nanda, Surendra Rajiv, and Abel Jeuland Effectiveness of Trade Promotions: Analyzing the Determinants of Retail Pass Through. Marketing Science, 20(4): McAlister, Leigh Cross-Brand Pass-Through: Fact or Artifact? Marketing Science, 26(6): Meza, Sergio, and K. Sudhir Pass-through timing. Quantitative Marketing and Economics, 4(4): Moorthy, Sridhar A General Theory of Pass-Through in Channels with Category Management and Retail Competition. Marketing Science, 24(1): Mortimer, Julie H Vertical Contracts in the Video Rental Industry. Review of Economic Studies, 75(1):

20 Nijs, Vincent, Kanishka Misra, Eric T. Anderson, Karsten Hansen, and Lakshman Krishnamurthi Channel Pass-Through of Trade Promotions. Marketing Science, 29(2): Pancras, Joseph, Dinesh K. Gauri, and Debabrata Talukdar Loss leaders and cross-category retailer pass-through: A Bayesian multilevel analysis. Journal of Retailing, 89(2): Peitz, Martin, and Markus Reisinger Indirect Taxation in Vertical Oligopoly. Journal of Industrial Economics, 62(4): Spengler, Joseph J Vertical Integration and Antitrust Policy. Journal of Political Economy, 58(4): Sudhir, K Structural Analysis of Manufacturer Pricing in the Presence of a Strategic Retailer. Marketing Science, 20(3): Tyagi, Rajeev K A Characterization of Retailer Response to Manufacturer Trade Deals. Journal of Marketing Research, 36(4): Villas-Boas, Sofia Berto Vertical Relationships between Manufacturers and Retailers: Inference with Limited Data. Review of Economic Studies, 74(2): Weyl, E. Glen, and Michal Fabinger Pass-Through as an Economic Tool: Principles of Incidence under Imperfect Competition. Journal of Political Economy, 121(3):