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Price asymmetry revisited from a marketing perspective
Economic Modelling 49 (2015) 314–319
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Economic Modelling journal homepage: www.elsevier.com/locate/ecmod
Price asymmetry revisited from a marketing perspective☆ Yoonsung Lim a, Jeong-Yoo Kim b,⁎, Nathan Berg c a b c
Dongduk Women's University, Republic of Korea Kyung Hee University, Republic of Korea University of Otago, New Zealand
a r t i c l e
i n f o
Article history: Accepted 20 May 2015 Available online 6 June 2015 Keywords: Asymmetric price adjustment Marketing Promotion Inventory cost
a b s t r a c t Price asymmetry is a longstanding issue in economics that pre-dates Keynes' introduction of the term, “price rigidity.” Many theories provide possible explanations of price asymmetry. This paper demonstrates that asymmetric marketing decisions based on the inherent asymmetry of inventory costs over the business cycle can generate price asymmetries that match at least one important empirical regularity. The theoretical mechanism we propose follows from the observation that firms face inventory costs proportion to excess supply during recessions, which fall to zero in periods of excess demand. This asymmetry of inventory costs gives firms two incentives during recessions. First, a firm facing excess supply has an incentive to reduce price, seeking to sell larger quantities and thereby reduce inventory costs. The firm may increase its intensity of promotional activity, again seeking to sell larger quantities but with the counterintuitive effect of increasing consumers' willingness to pay which pushes prices higher. If the latter effect dominates the former effect, then prices may not fall much during recessions. A similar phenomenon occurs when the macroeconomic business-cycle faces a cost-side shock. The inventory-cost mechanism explains the empirical finding that asymmetry in gasoline prices are more severe in countries with high degrees of market concentration such as Japan and Korea. This new theoretical link tells us which kinds of industrial structures are likely to produce the most severe price asymmetries. © 2015 Elsevier B.V. All rights reserved.
1. Introduction The prices of final goods tend to respond asymmetrically to positive and negative macroeconomic shocks, with upward price adjustments in response to expansionary shocks regularly observed to be larger and faster than downward adjustments in response to contractionary shocks of a similar magnitude. This pattern is referred to as downward price rigidity or, more generally, price adjustment asymmetry. Price adjustment asymmetry is a longstanding empirical puzzle which dates back long before the term “price rigidity” became a central theme in Keynesian macroeconomics (e.g., Mitchell, 1927). Recent interest in the phenomenon, the evidence that supports it, and its economic significance, appears to have, once again, intensified. The empirical evidence for price adjustment asymmetry can be difficult to interpret because empirical studies have focused on a relatively
☆ We would like to acknowledge the Editor, Sushanta Mallick, and three anonymous referees for their helpful comments. ⁎ Corresponding author at: Department of Economics, Kyung Hee University, 1 Hoegidong, Dongdaemunku, Seoul 130-701, Republic of Korea. Tel.: +82 2 961 0986. E-mail address: [email protected] (J.-Y. Kim).
http://dx.doi.org/10.1016/j.econmod.2015.05.008 0264-9993/© 2015 Elsevier B.V. All rights reserved.
broad range of different outcome measures and classes of macroeconomic shocks. For example, some investigations focus on: demandside shocks1; the role of vertical asymmetry2; spatial asymmetry; asymmetries in adjustment speed; asymmetries in adjustment size; and positive asymmetry versus negative asymmetry. Positive asymmetry refers to prices that adjust upward more easily than they adjust downward (i.e., also referred to as downward price rigidity) is perhaps the most common focus among studies of asymmetric price adjustment. But negative asymmetry (also referred to sometimes as reverse asymmetry) is sometimes reported, which describes prices that adjust downward (negatively) more flexibly than they adjust upward. 3 Whereas asymmetric size of price adjustments following demand-side shocks appear to
1 For excellent discussions on price asymmetry due to demand shocks, see Cover (1992) and DeLong and Summers (1988). 2 Vertical asymmetry can be interpreted as a synonym for asymmetric price transmission. Empirical studies explore the relation between prices of a raw inputs and prices of final output in vertical relationships, such as agricultural or manufactural sectors. See Meyer and von Cramon-Taubadel (2004). 3 For general discussions on reverse asymmetry, see Tsiddon (1993) and Ball and Mankiw (1994). There are relatively few theoretical analyses of reverse asymmetry, with the important exceptions of Bennett and La Manna (2001) and Ray et al. (2005).
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have received more attention in previous decades, recent investigation tends to focus on speed of adjustment following supply-side shocks such as the price of raw materials.4 We believe that the former issue of asymmetric size is more fundamental than the latter issue of speed. Asymmetric size of adjustments will affect measurement of speed in studies of frictions or sticky prices. The focus on speed has theoretical appeal, because it hangs onto the possibility that the long-run sizes of price adjustment are symmetric and only asymmetric frictions are needed to account for asymmetric speeds of adjustment. In contrast, our model provides an inventorycost mechanism in which suppliers with market power optimally adjust marketing and promotional expenditures in a manner that generates asymmetric sizes of price adjustments for final goods in response to identically-sized positive and negative shocks, respectively. The large and growing empirical literature shows that asymmetric price adjustment is no longer an exceptional or peripheral phenomenon but is now regarded rather as a widespread (or, according to some observers, a nearly universal) phenomenon, appearing across many industries (e.g., gasoline, agriculture, manufacturing, electricity, and banking) as well as in most countries.5 For instance, for gasoline prices, Bacon (1991) reports evidence of asymmetric price adjustments based on biweekly data for the period 1982–1989, and Borenstein et al. (1997) also find similar relations by using semi-monthly retail prices and weekly crude oil prices from 1986 through 1990. Also, Galeotti et al. (2003) and Meyler (2009) identify similar patterns of price asymmetry based on monthly data among European countries for the period 1985–2000 and on weekly data among European countries for the period 1994–2008 respectively. Recently, McLaren (2013) also confirms price asymmetry in agricultural sectors by using a sample of 161 agricultural products produced in 117 countries over a period of 35 years. Also, Peltzman (2000) shows that prices rise in response to a negative supply-side shock (i.e., increase in cost of production) nearly twice as often as prices fall following an expansionary positive supply-side shock (i.e., decrease in cost of production) by studying the prices of 77 consumer goods and 165 intermediate goods. His finding suggests that the asymmetry arises as a fundamental of the price mechanism and not merely by chance, as Galeotti et al. (2003) point out.6 Following these striking empirical findings, many authors argue that price asymmetry should be regarded more as a rule rather than an exception (e.g., Ellingsen et al., 2005). Peltzman criticized orthodox economic theory's insistence on models that predict price symmetry rather than asymmetry: “In the paradigmatic price theory we teach, input price increases or decreases move marginal costs and then prices up or down symmetrically and reversibly. Usually we embellish these comparative statics results with adjustment cost or search cost stories to motivate lags in response. But there is no general reason for these costs to induce asymmetric lags. … If that finding was shown to be general and not just limited to a few case studies, it would point to a serious gap in a fundamental area of economic theory.” Acknowledging that there are indeed many alternative theories that seek to explain price asymmetry, it is difficult to avoid the conclusion that most of these theories (including menu cost theory, inventory 4 Bacon (1991) refers to asymmetry in price adjustment as “Rockets and Feathers,” based on the speed and magnitude of the upward trajectory of a rising rocket compared to the downward trajectory of a falling feather. 5 See Johnson (2002) and Brown and Yucel (2000) for gasoline prices, Pick et al. (1991) for agricultural product prices, Zachmann and von Hirschhausen (2008) for electricity charges, Boyde and Bronsen (1988) for pork prices, and Neumark and Sharpe (1992) for interest rates. Verbrugge (1998, 2002) reports evidence of price asymmetry in almost all countries. There are some papers on the other side as well. For instance, Karagiannis et al. (2014) test the symmetry of price adjustments in the gasoline markets of four countries (Germany, France, Italy and Spain) and do not find that the retail fuel speed of upward/downward price adjustment is asymmetric in any of the four economies. Berument et al. (2014) find no significant asymmetry for crude oil price increases versus decreases on petroleum product prices. 6 Galeotti et al. (2003) assert that neither menu costs nor search costs can be the mechanism causing price asymmetry.
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management theory, search theory and coordination theory) appear inconsistent with empirical observation (Peltzman, 2000). Ellingsen et al. (2005) argue that we need a more robust theory that can fill the gap between the theory and observation based on a fundamental explanation of asymmetric price adjustment. Our paper attempts to, at least partially, fill that gap. We propose an intuitive mechanism based on the asymmetric costs of excess inventory (which are strictly positive when there is excess supply and zero when there is excess demand) and producers' joint consideration of marketing and promotional expenditures used to optimally manage the costs of excess inventory. In standard economic theory, firms are assumed to be rather passive players that adapt to changes in the market environment by adjusting output and price. In contrast, a Schumpeterian theory of the firm views its action space as including more choice variables that are used to respond to changes in the environment in a variety of ways. One of these is marketing and promotional activity.7 Modern firms consider marketing as one of its essential activities, readily observable in almost all industries market structures. As Ray et al. (2005) point out, it is quite puzzling that there are only a few marketing approaches to price asymmetry in spite of the universality of firms' marketing activity, considering that marketing is a key decision often made jointly with pricing decisions or made in ways that have intended effects on the prices of goods that the firm sells. In this paper, we assume that a firm engages not only in quoting a price but also in a marketing activity including advertising and sales promotion, which we refer to simply as “promotional activity”.8 If there is excess supply caused by a demand- or cost-shock, then additional costs of excess inventory are incurred. To reduce this excess inventory, the firm has a clear incentive to lower its price. If this were the only incentive driving price responses to a contractionary macroeconomic shock, then the inventory cost mechanism would likely generate reverse price asymmetry, because the costs of excess inventory reinforces the incentive to lower price sending it lower by more than it would rise in response to an expansionary shock of identical magnitude. If the firm responds to a contractionary shock by re-optimizing its mix of expenditures in both production and promotions, however, the firm may choose to engage in more intense marketing activity. Increased marketing and promotion, in turn, shifts the demand curve in way that attenuates (or possibly even reverses) the price response that would have followed the same contractionary shock in the absence of optimal increases in promotional effort. The inventory-cost and promotions mechanism is simple. A contractionary shock occurs. The firm increases marketing and promotions expenditure, which moves the demand curve in a way that pushes prices higher, partially offsetting the otherwise symmetric negative price adjustment that would have occurred without having increased marketing. Our model provides a clear representation of these two motives following a contractionary shock: lowering price to clear inventory and thereby save on the costs of excess inventory; and increasing promotional effort to increase demand for goods held in inventory. If the second promotional effect dominates the first motive of discounting to liquidate inventory, then downward price rigidity occurs in our model. Our model provides analytic inequalities describing market environments that guarantee downward price rigidity. We also provide conditions and demonstrate that joint optimization of inventory costs and promotional expenditure can also explain reverse price asymmetry when the liquidationdiscounting motive dominates the promotions-to-increase-demand
7 Schumpeter (1942)'s definition of “creative destruction” includes new ways to organize production, new products, new methods of advertising and marketing, new ways to transport products, etc. 8 In the marketing literature, the concept of promotion includes advertising, sales promotion, and personal sales, although it is sometimes used in a narrower sense referring only to sales promotion.
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motive. If there is an excess demand, however, then neither motive is relevant because there is zero cost of excess inventory. Our model demonstrates that optimal promotional activity among suppliers with at least some degree of market power provides a mechanism that generates price asymmetry and matches an important empirical regularity surrounding the puzzle of price asymmetry: the empirical finding of SERI (2011) that price asymmetry is most severe in countries with high ratios of market concentration such as Japan and Korea, and smallest in countries with low ratios of market concentration such as Belgium, Netherlands and the U.K. Also, our theoretical result is consistent with the empirical finding of Neumark and Sharpe (1992) that banks in concentrated markets respond slowly to market interest rates when they raise interest rates but respond faster when they reducing interest rates, which suggests that market concentration may lead to downward price rigidity and upward price flexibility. The price asymmetry story most closely related to our model is inventory management theory (e.g., the dynamic models of inventory in Zabel, 1972; Phlips, 1980; Reagan, 1982; and Blinder, 1982). The general intuition is that, in a recession, inventory adjustment partially offsets price fluctuation; but in an expansion or boom (above-trend periods within the business cycle), price is more responsive than inventory, because there is little or no stock held in inventory. Although the intuition underlying inventory management theory appears to be similar to ours, the mechanism through which price asymmetry emerges is entirely different. In inventory management theory, the cushioning effect of inventory adjustment drives their result. In contrast, the cause of asymmetry in our model is based on optimally asymmetric decisions regarding marketing and promotional activity. No previous papers in the price asymmetry literature that we are aware of considers the mechanism of optimal promotional activity chosen jointly with price. Another important contrast is that, in our model, the unit cost of excess inventory plays a key role in describing when downward price rigidity occurs, whereas some studies based on inventory management theory assume that inventory costs are negligible (Reagan, 1982). The paper is organized as follows. Section 2 describes the model. A theoretical analysis of price responses to demand-side shocks is presented in Section 3 and to supply-side cost shocks in Section 4. Section 5 presents our conclusion.
renovations of retail space designed to attract customers,10 or marketing campaign that the firm views as a lump-sum expenditure). We consider an economy that faces macroeconomic shocks that are either demand-side (i.e., shifting the demand curve) or supply-side (i.e., shifting firms' cost of production). These shocks can, of course, be either positive or negative. For simplicity, we assume that a positive demand shock shifts the demand curve outward by α for some α N 0 (and a negative demand shock shifts the demand curve inward by α). Similarly, a positive cost shock, which is equivalent to a “negative” supply shock increases the firm's marginal cost upward by γ (and a negative cost shock, i.e., outward shift in the supply curve, shifts the firm's marginal cost downward by γ). Given the definitions and notation introduced above, the demand curve after a positive or a negative demand shock is given by D(p) + β(e) + α or D(p) + β(e) − α, respectively; and the firm's marginal cost after a positive or a negative cost shock is given by c + γ or c − γ, respectively. Next we consider inventory costs. If excess supply occurs following a negative demand shock,11 then the firm incurs inventory costs. In contrast, if there is excess demand, then the firm incurs no inventory cost.12 We assume that inventory costs are proportional to the quantity of unsold output held in inventory and that the cost per unit of inventory is k, (k N 0).
2. Model
Denote the solutions to the first-order conditions above as p0 and e0, and the corresponding profit-maximizing output decision as Q 0, where the subscript 0 denotes initial values of optimal pricing, promotional effort and output in the absence of any demand or cost shocks. If the economy faces a positive demand shock, then the situation does not change significantly, because inventory costs do not come into play when demand increases from an initial point of equilibrium (i.e., no excess supply). In this case, the monopolist's profit is:
This section describes a simple model of price asymmetry that we use as a platform to analyze demand- and supply-side (i.e., cost-ofproduction) shocks in subsequent sections. We abstract from the complexity of strategic interactions among oligopolists by focusing on a market supplied by a monopolist. The monopolist maximizes profit by jointly choosing two variables: the price of the product it sells, p, and its effort in sales promotion, e. The firm faces market demand given by Q = D(p), which is assumed to be strictly increasing, weakly concave, and continuously differentiable: D′(p) b 0 and D′′(p) ≤ 0. The monopolist is assumed to have access to an effective sales promotion technology that effectively shifts the demand curve to the right while incurring promotional costs introduced below. The increase in market demand is denoted β(e), which is measured in output units, so that total demand in the presence of the firm's promotional effort is given by Q N = D(p) + β(e). We assume that the output effect of promotional effort is strictly increasing and strictly concave, β′ N 0 and β′′ b 0.9 We assume that the firm's cost function is linear with constant marginal cost, c, and that expenditures on promotional activity is just lump-sum (e.g., a large advertising buy, 9 Both assumptions on second derivatives introduced in this paragraph (i.e., D′′ ≤ 0 and β′′ b 0) are simplifying technical conditions so that the second-order conditions of the profit-maximization problem are satisfied and the complication of non-unique solutions can be avoided. The phenomenon of price asymmetry can occur in our model using more general functional forms without global concavity of D(p) and β(e).
3. Demand shock In the absence of a demand shock, the monopolist chooses p and e to maximize its profit function as given by the formula: πðp; eÞ ¼ Q N ðp−cÞ−e: The first-order conditions for an interior optimal choice of p and e require: πp ≡
∂π ¼ D0 ðpÞðp−cÞ þ DðpÞ þ βðeÞ ¼ 0; ∂p
ð1Þ
πe ≡
∂π ¼ β0 ðeÞðp−cÞ−1 ¼ 0: ∂e
ð2Þ
πðp; e; α Þ ¼ ðQ N þ α Þðp−cÞ−e: The first-order conditions are almost the same as Eqs. (1) and (2) except that β(e) is replaced by α + β(e). Let the solutions to the firstorder conditions under a demand shock be denoted as p*(α) and 10 Recently the renovation of retail space seems to be a big part of retailers' strategy, e.g., Mcdonald's Mc cafe and many others throughout U.S., Europe, Korea and Japan. 11 Although the supply function is not properly defined in case of monopoly, the monopolist's profit-maximizing condition (at an interior level of optimal production) requires that it choose the output level to equate marginal revenue and marginal cost. We refer to this profit-maximizing output level that the monopolist chooses as supply or quantity supplied. 12 Our claim that inventory cost is zero when excess demand occurs holds after a normalization that subtracts fixed inventory costs that are incurred throughout the business cycle regardless of excess supply or excess demand. The fixed component of warehouse space, insurance and inventory management costs is acknowledged but then, without loss of generality, can be normalized to zero. Therefore, the asymmetric component of inventory costs that are positive whenever excess supply occurs and zero whenever excess demand occurs is the mechanism that our model focuses on.
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e*(α). Total differentiation of p*(α) and e*(α) with respect to α yields the following comparative statics:
πe ¼ β0 ðeÞðp−c þ kÞ−1 ¼ 0:
dp β00 ðp−cÞ ¼− N 0; dα jH α j
ð3Þ
de β0 ¼ N 0; dα jHα j
ð4Þ
We will denote the solutions to the negative-demand-shock firstorder conditions as p⁎⁎(α, k) and e⁎⁎(α, k). In other words, the optimal pricing and promotional effort rules, p⁎⁎(α, k) and e⁎⁎(α, k), are obtained by taking joint account of both the magnitude of the negative demand shock and the inventory cost parameter, k (unlike the corresponding optimal pricing and promotional effort functions in the case of a positive demand shock, p*(α) and e*(α)). If k = 0, it is clear from Eq. (3) that p⁎⁎(α, 0) b p0 b p*(α). Here, p*(α) is the optimal price in case of a positive shock and p⁎⁎(α, 0) is the optimal price in case of a negative shock. Also, from comparing the first-order conditions in the cases of negative versus positive demand shocks, it is clear that the price adjustments are symmetric in the sense that the two first-order conditions differ only in the sign of the shock. To see whether inventory cost generates asymmetry in price adjustment, we now consider the effect of k N 0 on the optimal price. For this purpose, it is sufficient to check the sign of ∂p⁎⁎(α, k)/∂k. Total differentiation of Eqs. (5) and (6) with respect to k yields the following:
where Hα is the Hessian matrix for π(p, e; α) with respect to p and e, and |Hα| N 0 by the second-order condition. The two comparative statics with positive signs are intuitive: during a macroeconomic expansion or following any events that cause a positive demand shock, the monopolistic firm will optimally charge higher price and engage in more costly promotional effort. The effect on the price is obvious. The effect on the promotional effort can be intuitively explained as follows. The profitmaximizing firm chooses promotional efforts at a level where marginal revenue equals marginal cost. If there is a positive demand shock, the firm will raise its price, thereby increasing marginal revenue of promotional efforts. Since the marginal revenue is now larger than marginal cost, the firm will increase its promotional efforts.13 We observe that, in the case of a positive demand shock, there is no inventory despite the price being higher, because demand has increased due to a positive shock and an optimal response of increased promotional expenditures. In contrast to the case of positive demand shocks which do not affect inventory costs, the case of negative demand shocks leads to accumulation of larger inventories and, consequently, greater inventory costs. Taking inventory costs into account, the monopolist chooses p and e to maximize its profit function in the negative-demand-shock environment, which is given by the formula: πðp; e; −α Þ ¼
ðp−cÞQ − −e−kðQ 0 −Q − Þ ðp−cÞQ − −e
if Q − b Q 0 if Q − ≥ Q 0 ;
where Q− = Q N − α. To be realistic about bounds on the effectiveness of promotional effort, and to avoid the technical difficulty arising from non-differentiability of the profit function, we assume that β(e) is bounded above by α. This assumption captures the idea that promotional activities can, at most, only partially offset a negative demand shock. Given that that β(e) is bounded above by α, it suffices to focus exclusively on the case in which Q− b Q0, from which it follows that the negativedemand-shock profit function can be written simply as π(p; − α) = (p − c + k)Q− − e − kQ 0. Note that the unit inventory cost k can now be interpreted as a reduction in marginal cost, because an additional unit of sales decreases the inventory cost by k, and this decrease in inventory cost is equivalent to lowering the marginal cost of production by k. The first-order conditions in the case of a negative demand shock (− α) are given by: πp ¼ D0 ðpÞðp−c þ kÞ þ DðpÞ−α þ βðeÞ ¼ 0;
ð5Þ
13 We are grateful to an anonymous referee who suggested an alternative intuition for this comparative static result based on the threat of entry. Suppose the monopolist faces the threat of entry but that entry is blockaded in the current period. If there is a positive demand shock, then the monopolist, who now faces a more probable threat of entry, tries to deter entry, either by limit pricing or by rationally choosing excessive promotional effort (i.e., advertising), assuming asymmetric information between entrants and the monopolist. See Bagwell and Ramey (1988) for more details motivating such a mechanism. If the monopolist uses limit pricing, then there will be downward distortion in pricing during a boom (i.e., following positive demand shocks) but no price distortion during a recession (i.e., following negative demand shocks) because there is no effective threat of entry during a recession. Hence, reverse price asymmetry may result. If the monopolist uses promotional effort to deter entry, then the implication for price asymmetry is ambiguous because the effect of the (asymmetric) threat of entry works in the opposite direction to the (asymmetric) effect of inventory costs. Introducing both mechanisms (i.e., the threat of entry under incomplete information and asymmetric inventory costs, the latter of which is the focus of our analysis) is left to future research to pursue such a generalization.
ð6Þ
2
∂p β0 −D0 β00 ðp −c þ kÞ ⋛ 0; ¼ H α;k ∂k
ð7Þ
β0 D00 ðp −c þ kÞ þ D0 ∂e N 0: ¼− H α;k ∂k
ð8Þ
Eq. (8) implies that a rise in k unambiguously increases optimally chosen promotional expenditures. The inequality directly above is intuitively obvious, because an increase in inventory costs induces the monopolist to increase its promotional effort to reduce unsold output held as excess inventory. On the other hand, the effect of an increase in k on the monopolist's optimal choice of price is ambiguous because there are two conflicting effects. First, an increase in the inventory cost tends to lower price directly, reflecting the monopolist's incentive to reduce product held in inventory, which is measured by the second term of Eq. (7). Second, an increase in inventory cost increases the monopolist's optimal choice of promotional effort, which boosts demand and, in turn, enables the monopolist to increase price. This indirect effect is measured by the first term in Eq. (7). Therefore, price is increasing in k whenever 2
β0 N D0 β00 ðp −c þ kÞ: ½DAP This inequality, referred to as the Demand-shock Asymmetric Price (DAP) condition, means that, if the monopolist takes inventory cost into account, then it chooses a higher price than it would otherwise: p⁎⁎(α, k) N p⁎⁎(α, 0) under the DAP condition. The DAP condition implies that inventory costs can create an asymmetry in price adjustments (i.e., downward price rigidity). How likely is the DAP condition to hold? If β′ is large, meaning that the promotional effort is sufficiently effective to substantially increase demand, then the indirect promotional effect dominates the direct effect, implying that prices will not decline much in recessions. Also, if β′′ is very small in absolute value (i.e., β(e) is nearly linear), then e⁎⁎ is highly sensitive to the negative demand shock in a demand-side recession, implying that the promotional effect is large relative to the price effect. Therefore, the shape of the promotional technology that the monopolist has available determines when this condition is likely to hold: when the promotional technology has a large first-order effect on demand with very slowly decreasing returns to effort or expenditure. The DAP condition describes precisely when downward price rigidity is predicted to occur. If the DAP condition fails to hold, then the direct effect dominates the indirect effect, and the monopolist will lower prices in recessions to reduce inventory. The DAP condition has a further implication, however, suggesting the possibility of a reverse asymmetry
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in which price reductions observed in a demand-side recession are predicted to be larger than price increases in a demand-side expansion whenever the DAP condition does not hold.14 pffiffiffi For a numerical example, take D(p) = a − bp and βðeÞ ¼ A e, where a, b, A N 0. Then, straightforward calculations yield p ¼
A2 −2b ðc−kÞ−2ða−α Þ A2 −4b
:
2
2
A2 2.
Hence, dpdk ¼ − A2 −2b N 0 if 2b b A2 b 4b or equivalently, A4 b b b A −4b
The possibility of price asymmetry is illustrated in Fig. 1 for parameter values: A = 2, a = 2, c = 1, and α = 1. Intuitively, if b is very small so that demand is very inelastic, then the monopolist must drop the price significantly in order to increase demand. In this case, the price effect is so large that DAP is not be satisfied. On the other hand, if b is so large that demand is highly elastic, then the price effect is indeed very small but, at the same time, the promotional effect is very small because an increase in e has little effect on demand. (Think of an almost horizontal demand curve. Then the new demand curve after a promotional campaign is almost identical to the original demand curve.) Therefore, if b is too high or too low, DAP does not hold. Before closing this section, it is worth considering the possibility that competition would affect the results reported above. It is easy to see that perfectly competitive firms do not engage in any promotional activity, because competitive firms face a free-riding problem in that the effect of promotional activity by an individual firm is shared by all firms. This observation strongly supports the empirical finding of SERI (2011) that countries with high ratios of market concentration such as Japan and Korea exhibit unusually large degrees of price asymmetry. 4. Cost shock In Section 3, we identified two effects of a change in inventory cost: a direct price effect and an indirect (and countervailing) promotional effect. This insight is robust in the sense that it almost obviously extends from the demand-side shocks considered in Section 3 to the cost (i.e., supply-side) shocks considered in this section. For the purpose of completing our argument, an analysis of the case of cost shocks is presented below. If a positive cost shock occurs, then excess demand results, because of the instantaneous decrease in production as an optimal response to increased costs of production and the current output-price level at the prevailing pre-shock price. Thus, the monopolist's profit in the positive cost-shock environment is given by: πðp; e; γÞ ¼ Q N ðp−c−γ Þ−e: The first order conditions imply πp ¼ −D0 ðpÞðp−c−γÞ þ DðpÞ þ βðeÞ ¼ 0;
ð9Þ
πe ¼ β0 ðeÞðp−c−γÞ−1 ¼ 0: Total
differentiation
D0 ðpÞβ0 0 ðeÞðp−c−γÞ−β0 ðeÞ Hγ 2
ð10Þ of
(9)
and
(10)
yields
∂p ∂γ
¼
≷ 0, where Hγ is a Hessian matrix. If we assume
that the second order condition is satisfied, i.e., |Hγ| = 2D′β′′(e)(p −
≷ 0 if and only if D′(p)β′′(e)(p − c − c − γ) − β′2(e) N 0, we have ∂p ∂γ 2
γ) ≷ β′ (e). That is, the effect of a positive cost shock on the price is ambiguous, whereas the effect of a positive demand shock is 14 A symmetry in price adjustments can occur if a negative shock leads to a small decrease in price and a large increase in the promotional activity, so that the resultant demand is higher than after the shock. Then, there will be no inventory in the optimum.
Fig. 1. Possibility of price asymmetry.
unambiguous. Intuitively, if the production cost is higher, it directly 0
moves the price up but it reduces the promotion effort (∂e ¼ ββ0 0ððeeÞÞ b 0) ∂γ
due to a smaller margin, and consequently reducing the demand which indirectly affects the price downward. If the former direct effect dominates the latter indirect effect, the price goes up due to a positive cost shock as we usually expect, but if the latter indirect effect dominates the former, the price may go down as a result of a positive cost shock. If the cost shock is negative, then the monopolist's output will increase instantaneously, thereby generating excess inventory. We continue here analyzing the case of a negative cost shock that generates excess inventory. Let the new output level in the post-negative-costshock environment be denoted as Q′. Then, the inventory is Q′ − QN. Taking the inventory cost into account, the monopolist's profit function can be expressed as: πðp; γÞ ¼
ðp−c þ γ þ kÞQ N −e−kQ 0 ðp−c þ γ ÞQ N −e
if Q N b Q 0 if Q N ≥ Q 0 :
Again, to be realistic about the effectiveness of promotional effort, we focus only on the case in which output levels increase following the cost shock that lowers costs of production: Q N b Q′. In this case, the first-order conditions are given by: πp ¼ D0 ðpÞðp−c þ γ þ kÞ þ DðpÞ þ βðeÞ ¼ 0;
ð11Þ
πe ¼ β0 ðeÞðp−c þ γ þ kÞ−1 ¼ 0:
ð12Þ
Similarly, total differentiation of Eqs. (11) and (12) with respect to unit inventory cost, k, yields: 2
∂p β0 −D0 β00 ðp −c þ γ þ kÞ ⋛ 0; ¼ H γ;k ∂k
ð13Þ
β0 D00 ðp −c þ γ þ kÞ þ D0 ∂e N 0; ¼− H γ;k ∂k
ð14Þ
where Hγ,k is again a Hessian matrix. As in the case of a demand shock, the effect of an increase in k on the monopolist's optimal choice of price is ambiguous. If the inventory cost parameter increases, then the monopolist has a clear incentive to reduce inventory and, as a result, lower price. However, the increase in the inventory cost parameter also increases the monopolist's optimal choice of promotional effort,
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asymmetry, will remain unaffected by relaxing our assumption on the number of firms in the model, as long as the industry is supplied by firms that enjoy an economically significant degree of market power: A negative demand shock creates inventory costs that, in our theory, firms actively seek to avoid by increasing their expenditures on promotional effort. This asymmetric trajectory of inventory costs over the business cycle is a natural description of what faces any firm earning positive profits due to market power. If these promotional efforts lead to a rise in prices by increasing consumer demand, then downward price rigidity is likely to be observed. Of course, we are aware that the result will be sensitive to the nature of the promotion activity, whether a firm's activity is specific or general in the sense that it increases only the demand of its own output or, alternatively, increases demand for competitors' output as well. Such complex issues arising from imperfect competition are beyond the scope of this paper and will be left for future research. Fig. 2. Price asymmetry in case of a cost shock.
References
which exerts a positive effect on its optimal choice of price. Therefore, price is increasing in k if: 2
β0 N D0 β00 ðp −c þ γ þ kÞ: This means that in the case that
∂p ∂γ
N0, asymmetric prices occur
under this condition. We will call this the Cost-shock Asymmetric Price (CAP) condition. Interestingly, even in the case that
∂p ∂γ
b0,
asymmetric prices occur under this condition, but for a different reason. If the indirect effect exceeds the direct effect, the price is higher when the cost goes down than when the cost goes up. However, when the cost goes down, the higher price reduces the demand and some inventory cost is incurred. Since the price is higher as k is larger under [CAP] condition, it means that a positive asymmetry in price adjustment results. On the other hand, if the CAP condition does not hold, a reverse price asymmetry is generated. If we take the same simple function of D(p) = a − bp and βðeÞ ¼ pffiffiffi A e in the case of a cost shock, we have
p ðγÞ ¼
2a− A2 −2b ðc þ γÞ
p ðγ; kÞ ¼
; 2 4b−A 2a− A2 −2b ðc−γ−kÞ 4b−A2
:
Assuming that 2b b A 2 b 4b as before, we have 2a−ðA2 −2bÞðcþγÞ 4b−A2
∂p ∂γ
¼
b 0, i.e., p*(γ) b p ⁎⁎(γ). Fig. 2 illustrates the possibility
of price asymmetry for parameter values of A = 2, a = 2, c = 1, and D′′ ≤ 0 (satisfying [CAP] condition). 5. Conclusion While price asymmetry referred to as “Rockets and Feathers” has been regarded as a robust empirical regularity, virtually no positive theory has yet appeared that can account for the empirical evidence. This paper introduces a promotional effort mechanism (i.e., costly marketing expenditure) into an otherwise standard profit-maximization framework to fill this gap between theory and observation. Although the promotional effort mechanism is intuitive, we acknowledge that our model may be too simple because it focuses on the extreme case of a monopolistic industry. We could consider several firms competing (in quantities or prices) instead of the single monopolist. We strongly believe, however, that our main insight, which identifies market power as a necessary condition for observing price
Bacon, R.W., 1991. Rockets and feathers: the asymmetric speed of adjustment of UK retail gasoline prices to cost changes. Energy Econ. 13, 211–218. Bagwell, K., Ramey, G., 1988. Advertising and limit pricing. Rand J. Econ. 19, 59–71. Ball, L., Mankiw, N.G., 1994. Asymmetric price adjustment and economic fluctuations. Econ. J. 104, 247–261. Bennett, J., La Manna, M., 2001. Reversing the Keynesian asymmetry. Am. Econ. Rev. 91, 1556–1563. Berument, M.H., Sahin, A., Sahin, S., 2014. The relative effects of crude oil price and exchange rate on petroleum product prices: evidence from a set of northern Mediterranean countries. Econ. Model. 42, 243–249. Blinder, A., 1982. Inventories and sticky prices: more on the microfoundations of macroeconomics. Am. Econ. Rev. 72, 334–348. Borenstein, S., Cameron, A.C., Gilbert, R.J., 1997. Do gasoline prices respond asymmetrically to crude oil price changes? Q. J. Econ. 112, 305–339. Boyde, M.S., Bronsen, W.B., 1988. Price asymmetry in the U.S. pork marketing channel. North Cent. J. Agric. Econ. 10, 103–109. Brown, S.P.A., Yucel, M.K., 2000. Gasoline and crude oil prices: why the asymmetry? Federal Reserve Bank of Dallas. Econ. Rev. 23–29. Cover, J.P., 1992. Asymmetric effects of positive and negative money-supply shocks. Q. J. Econ. 107, 1261–1282. DeLong, J.B., Summers, L.H., 1988. How does macroeconomic policy affect output? Brook. Pap. Econ. Act. 19, 433–494. Ellingsen, T., Firberg, R., Hassler, J., 2005. Explaining asymmetric price adjustment available at. http://www.eco.uc3m.es/temp/EFH.pdf. Galeotti, M., Lansa, A., Manera, M., 2003. Rockets and feathers revisited: an international comparison on European gasoline market. Energy Econ. 22, 251–276. Johnson, R.N., 2002. Search cost, lags and prices at the pump. Rev. Ind. Organ. 20, 33–50. Karagiannis, S., Panagopoulos, Y., Vlamis, P., 2014. Are unleaded gasoline and diesel price adjustments symmetric? A comparison of the four larger EU retail fuel markets. Econ. Model. http://dx.doi.org/10.1016/j.econmod.2014.11.003. McLaren, A., 2013. Asymmetry in Price Transmission in Agricultural Markets, WPS 13-102. University of Geneva. Meyer, J., von Cramon-Taubadel, S., 2004. Asymmetric price transmission: a survey. J. Agric. Econ. 55, 581–611. Meyler, A., 2009. The pass through of oil prices into euro area consumer liquid fuel prices in an environment of high and volatile oil prices. Energy Econ. 31, 867–881. Mitchell, W., 1927. Business Cycle. National Bureau of Economic Research, New York. Neumark, D., Sharpe, S.A., 1992. Market structure and the nature of price rigidity: evidence from the market for consumer deposits. Q. J. Econ. 107, 657–680. Peltzman, S., 2000. Prices rise faster than they fall. J. Polit. Econ. 108, 466–502. Phlips, L., 1980. Intertemporal price discrimination and sticky prices. Q. J. Econ. 92, 525–542. Pick, D.H., Karrenbrock, J., Carmen, H.F., 1991. Price asymmetry and marketing margin behavior: an example for California–Arizona citrus. Agribusiness 6, 75–84. Ray, S., Chen, H., Bergen, M.E., Levy, D., 2005. Asymmetric wholesale pricing: theory and evidence. Mark. Sci. 25, 889–902. Reagan, P., 1982. Inventory and price behavior. Rev. Econ. Stud. 49, 137–142. Schumpeter, J., 1942. Capitalism, Socialism and Democracy. Harper and Row, New York. SERI, 2011. The Structure of Korea Consumer Prices and The Task for Price Stabilization. SERI Report 701. Samsung Economic Research Institute. Tsiddon, D., 1993. The (Mis)Behavior of the Aggregate Price Level. Rev. Econ. Stud. 60, 889–902. Verbrugge, R., 1998. A Cross-Country Investigation of Macroeconomic Asymmetries. Working Paper. VPI & SU. Verbrugge, R., 2002. Longitudinal inflation asymmetry. Appl. Econ. Lett. 9, 261–264. Zabel, E., 1972. Multiperiod monopoly under uncertainty. J. Econ. Theory 5, 524–536. Zachmann, G., von Hirschhausen, C., 2008. First evidence of asymmetric cost pass-through of EU emissions allowances: examining wholesale electricity prices in Germany. Econ. Lett. 99, 465–469.
Contents lists available at ScienceDirect
Economic Modelling journal homepage: www.elsevier.com/locate/ecmod
Price asymmetry revisited from a marketing perspective☆ Yoonsung Lim a, Jeong-Yoo Kim b,⁎, Nathan Berg c a b c
Dongduk Women's University, Republic of Korea Kyung Hee University, Republic of Korea University of Otago, New Zealand
a r t i c l e
i n f o
Article history: Accepted 20 May 2015 Available online 6 June 2015 Keywords: Asymmetric price adjustment Marketing Promotion Inventory cost
a b s t r a c t Price asymmetry is a longstanding issue in economics that pre-dates Keynes' introduction of the term, “price rigidity.” Many theories provide possible explanations of price asymmetry. This paper demonstrates that asymmetric marketing decisions based on the inherent asymmetry of inventory costs over the business cycle can generate price asymmetries that match at least one important empirical regularity. The theoretical mechanism we propose follows from the observation that firms face inventory costs proportion to excess supply during recessions, which fall to zero in periods of excess demand. This asymmetry of inventory costs gives firms two incentives during recessions. First, a firm facing excess supply has an incentive to reduce price, seeking to sell larger quantities and thereby reduce inventory costs. The firm may increase its intensity of promotional activity, again seeking to sell larger quantities but with the counterintuitive effect of increasing consumers' willingness to pay which pushes prices higher. If the latter effect dominates the former effect, then prices may not fall much during recessions. A similar phenomenon occurs when the macroeconomic business-cycle faces a cost-side shock. The inventory-cost mechanism explains the empirical finding that asymmetry in gasoline prices are more severe in countries with high degrees of market concentration such as Japan and Korea. This new theoretical link tells us which kinds of industrial structures are likely to produce the most severe price asymmetries. © 2015 Elsevier B.V. All rights reserved.
1. Introduction The prices of final goods tend to respond asymmetrically to positive and negative macroeconomic shocks, with upward price adjustments in response to expansionary shocks regularly observed to be larger and faster than downward adjustments in response to contractionary shocks of a similar magnitude. This pattern is referred to as downward price rigidity or, more generally, price adjustment asymmetry. Price adjustment asymmetry is a longstanding empirical puzzle which dates back long before the term “price rigidity” became a central theme in Keynesian macroeconomics (e.g., Mitchell, 1927). Recent interest in the phenomenon, the evidence that supports it, and its economic significance, appears to have, once again, intensified. The empirical evidence for price adjustment asymmetry can be difficult to interpret because empirical studies have focused on a relatively
☆ We would like to acknowledge the Editor, Sushanta Mallick, and three anonymous referees for their helpful comments. ⁎ Corresponding author at: Department of Economics, Kyung Hee University, 1 Hoegidong, Dongdaemunku, Seoul 130-701, Republic of Korea. Tel.: +82 2 961 0986. E-mail address: [email protected] (J.-Y. Kim).
http://dx.doi.org/10.1016/j.econmod.2015.05.008 0264-9993/© 2015 Elsevier B.V. All rights reserved.
broad range of different outcome measures and classes of macroeconomic shocks. For example, some investigations focus on: demandside shocks1; the role of vertical asymmetry2; spatial asymmetry; asymmetries in adjustment speed; asymmetries in adjustment size; and positive asymmetry versus negative asymmetry. Positive asymmetry refers to prices that adjust upward more easily than they adjust downward (i.e., also referred to as downward price rigidity) is perhaps the most common focus among studies of asymmetric price adjustment. But negative asymmetry (also referred to sometimes as reverse asymmetry) is sometimes reported, which describes prices that adjust downward (negatively) more flexibly than they adjust upward. 3 Whereas asymmetric size of price adjustments following demand-side shocks appear to
1 For excellent discussions on price asymmetry due to demand shocks, see Cover (1992) and DeLong and Summers (1988). 2 Vertical asymmetry can be interpreted as a synonym for asymmetric price transmission. Empirical studies explore the relation between prices of a raw inputs and prices of final output in vertical relationships, such as agricultural or manufactural sectors. See Meyer and von Cramon-Taubadel (2004). 3 For general discussions on reverse asymmetry, see Tsiddon (1993) and Ball and Mankiw (1994). There are relatively few theoretical analyses of reverse asymmetry, with the important exceptions of Bennett and La Manna (2001) and Ray et al. (2005).
Y. Lim et al. / Economic Modelling 49 (2015) 314–319
have received more attention in previous decades, recent investigation tends to focus on speed of adjustment following supply-side shocks such as the price of raw materials.4 We believe that the former issue of asymmetric size is more fundamental than the latter issue of speed. Asymmetric size of adjustments will affect measurement of speed in studies of frictions or sticky prices. The focus on speed has theoretical appeal, because it hangs onto the possibility that the long-run sizes of price adjustment are symmetric and only asymmetric frictions are needed to account for asymmetric speeds of adjustment. In contrast, our model provides an inventorycost mechanism in which suppliers with market power optimally adjust marketing and promotional expenditures in a manner that generates asymmetric sizes of price adjustments for final goods in response to identically-sized positive and negative shocks, respectively. The large and growing empirical literature shows that asymmetric price adjustment is no longer an exceptional or peripheral phenomenon but is now regarded rather as a widespread (or, according to some observers, a nearly universal) phenomenon, appearing across many industries (e.g., gasoline, agriculture, manufacturing, electricity, and banking) as well as in most countries.5 For instance, for gasoline prices, Bacon (1991) reports evidence of asymmetric price adjustments based on biweekly data for the period 1982–1989, and Borenstein et al. (1997) also find similar relations by using semi-monthly retail prices and weekly crude oil prices from 1986 through 1990. Also, Galeotti et al. (2003) and Meyler (2009) identify similar patterns of price asymmetry based on monthly data among European countries for the period 1985–2000 and on weekly data among European countries for the period 1994–2008 respectively. Recently, McLaren (2013) also confirms price asymmetry in agricultural sectors by using a sample of 161 agricultural products produced in 117 countries over a period of 35 years. Also, Peltzman (2000) shows that prices rise in response to a negative supply-side shock (i.e., increase in cost of production) nearly twice as often as prices fall following an expansionary positive supply-side shock (i.e., decrease in cost of production) by studying the prices of 77 consumer goods and 165 intermediate goods. His finding suggests that the asymmetry arises as a fundamental of the price mechanism and not merely by chance, as Galeotti et al. (2003) point out.6 Following these striking empirical findings, many authors argue that price asymmetry should be regarded more as a rule rather than an exception (e.g., Ellingsen et al., 2005). Peltzman criticized orthodox economic theory's insistence on models that predict price symmetry rather than asymmetry: “In the paradigmatic price theory we teach, input price increases or decreases move marginal costs and then prices up or down symmetrically and reversibly. Usually we embellish these comparative statics results with adjustment cost or search cost stories to motivate lags in response. But there is no general reason for these costs to induce asymmetric lags. … If that finding was shown to be general and not just limited to a few case studies, it would point to a serious gap in a fundamental area of economic theory.” Acknowledging that there are indeed many alternative theories that seek to explain price asymmetry, it is difficult to avoid the conclusion that most of these theories (including menu cost theory, inventory 4 Bacon (1991) refers to asymmetry in price adjustment as “Rockets and Feathers,” based on the speed and magnitude of the upward trajectory of a rising rocket compared to the downward trajectory of a falling feather. 5 See Johnson (2002) and Brown and Yucel (2000) for gasoline prices, Pick et al. (1991) for agricultural product prices, Zachmann and von Hirschhausen (2008) for electricity charges, Boyde and Bronsen (1988) for pork prices, and Neumark and Sharpe (1992) for interest rates. Verbrugge (1998, 2002) reports evidence of price asymmetry in almost all countries. There are some papers on the other side as well. For instance, Karagiannis et al. (2014) test the symmetry of price adjustments in the gasoline markets of four countries (Germany, France, Italy and Spain) and do not find that the retail fuel speed of upward/downward price adjustment is asymmetric in any of the four economies. Berument et al. (2014) find no significant asymmetry for crude oil price increases versus decreases on petroleum product prices. 6 Galeotti et al. (2003) assert that neither menu costs nor search costs can be the mechanism causing price asymmetry.
315
management theory, search theory and coordination theory) appear inconsistent with empirical observation (Peltzman, 2000). Ellingsen et al. (2005) argue that we need a more robust theory that can fill the gap between the theory and observation based on a fundamental explanation of asymmetric price adjustment. Our paper attempts to, at least partially, fill that gap. We propose an intuitive mechanism based on the asymmetric costs of excess inventory (which are strictly positive when there is excess supply and zero when there is excess demand) and producers' joint consideration of marketing and promotional expenditures used to optimally manage the costs of excess inventory. In standard economic theory, firms are assumed to be rather passive players that adapt to changes in the market environment by adjusting output and price. In contrast, a Schumpeterian theory of the firm views its action space as including more choice variables that are used to respond to changes in the environment in a variety of ways. One of these is marketing and promotional activity.7 Modern firms consider marketing as one of its essential activities, readily observable in almost all industries market structures. As Ray et al. (2005) point out, it is quite puzzling that there are only a few marketing approaches to price asymmetry in spite of the universality of firms' marketing activity, considering that marketing is a key decision often made jointly with pricing decisions or made in ways that have intended effects on the prices of goods that the firm sells. In this paper, we assume that a firm engages not only in quoting a price but also in a marketing activity including advertising and sales promotion, which we refer to simply as “promotional activity”.8 If there is excess supply caused by a demand- or cost-shock, then additional costs of excess inventory are incurred. To reduce this excess inventory, the firm has a clear incentive to lower its price. If this were the only incentive driving price responses to a contractionary macroeconomic shock, then the inventory cost mechanism would likely generate reverse price asymmetry, because the costs of excess inventory reinforces the incentive to lower price sending it lower by more than it would rise in response to an expansionary shock of identical magnitude. If the firm responds to a contractionary shock by re-optimizing its mix of expenditures in both production and promotions, however, the firm may choose to engage in more intense marketing activity. Increased marketing and promotion, in turn, shifts the demand curve in way that attenuates (or possibly even reverses) the price response that would have followed the same contractionary shock in the absence of optimal increases in promotional effort. The inventory-cost and promotions mechanism is simple. A contractionary shock occurs. The firm increases marketing and promotions expenditure, which moves the demand curve in a way that pushes prices higher, partially offsetting the otherwise symmetric negative price adjustment that would have occurred without having increased marketing. Our model provides a clear representation of these two motives following a contractionary shock: lowering price to clear inventory and thereby save on the costs of excess inventory; and increasing promotional effort to increase demand for goods held in inventory. If the second promotional effect dominates the first motive of discounting to liquidate inventory, then downward price rigidity occurs in our model. Our model provides analytic inequalities describing market environments that guarantee downward price rigidity. We also provide conditions and demonstrate that joint optimization of inventory costs and promotional expenditure can also explain reverse price asymmetry when the liquidationdiscounting motive dominates the promotions-to-increase-demand
7 Schumpeter (1942)'s definition of “creative destruction” includes new ways to organize production, new products, new methods of advertising and marketing, new ways to transport products, etc. 8 In the marketing literature, the concept of promotion includes advertising, sales promotion, and personal sales, although it is sometimes used in a narrower sense referring only to sales promotion.
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motive. If there is an excess demand, however, then neither motive is relevant because there is zero cost of excess inventory. Our model demonstrates that optimal promotional activity among suppliers with at least some degree of market power provides a mechanism that generates price asymmetry and matches an important empirical regularity surrounding the puzzle of price asymmetry: the empirical finding of SERI (2011) that price asymmetry is most severe in countries with high ratios of market concentration such as Japan and Korea, and smallest in countries with low ratios of market concentration such as Belgium, Netherlands and the U.K. Also, our theoretical result is consistent with the empirical finding of Neumark and Sharpe (1992) that banks in concentrated markets respond slowly to market interest rates when they raise interest rates but respond faster when they reducing interest rates, which suggests that market concentration may lead to downward price rigidity and upward price flexibility. The price asymmetry story most closely related to our model is inventory management theory (e.g., the dynamic models of inventory in Zabel, 1972; Phlips, 1980; Reagan, 1982; and Blinder, 1982). The general intuition is that, in a recession, inventory adjustment partially offsets price fluctuation; but in an expansion or boom (above-trend periods within the business cycle), price is more responsive than inventory, because there is little or no stock held in inventory. Although the intuition underlying inventory management theory appears to be similar to ours, the mechanism through which price asymmetry emerges is entirely different. In inventory management theory, the cushioning effect of inventory adjustment drives their result. In contrast, the cause of asymmetry in our model is based on optimally asymmetric decisions regarding marketing and promotional activity. No previous papers in the price asymmetry literature that we are aware of considers the mechanism of optimal promotional activity chosen jointly with price. Another important contrast is that, in our model, the unit cost of excess inventory plays a key role in describing when downward price rigidity occurs, whereas some studies based on inventory management theory assume that inventory costs are negligible (Reagan, 1982). The paper is organized as follows. Section 2 describes the model. A theoretical analysis of price responses to demand-side shocks is presented in Section 3 and to supply-side cost shocks in Section 4. Section 5 presents our conclusion.
renovations of retail space designed to attract customers,10 or marketing campaign that the firm views as a lump-sum expenditure). We consider an economy that faces macroeconomic shocks that are either demand-side (i.e., shifting the demand curve) or supply-side (i.e., shifting firms' cost of production). These shocks can, of course, be either positive or negative. For simplicity, we assume that a positive demand shock shifts the demand curve outward by α for some α N 0 (and a negative demand shock shifts the demand curve inward by α). Similarly, a positive cost shock, which is equivalent to a “negative” supply shock increases the firm's marginal cost upward by γ (and a negative cost shock, i.e., outward shift in the supply curve, shifts the firm's marginal cost downward by γ). Given the definitions and notation introduced above, the demand curve after a positive or a negative demand shock is given by D(p) + β(e) + α or D(p) + β(e) − α, respectively; and the firm's marginal cost after a positive or a negative cost shock is given by c + γ or c − γ, respectively. Next we consider inventory costs. If excess supply occurs following a negative demand shock,11 then the firm incurs inventory costs. In contrast, if there is excess demand, then the firm incurs no inventory cost.12 We assume that inventory costs are proportional to the quantity of unsold output held in inventory and that the cost per unit of inventory is k, (k N 0).
2. Model
Denote the solutions to the first-order conditions above as p0 and e0, and the corresponding profit-maximizing output decision as Q 0, where the subscript 0 denotes initial values of optimal pricing, promotional effort and output in the absence of any demand or cost shocks. If the economy faces a positive demand shock, then the situation does not change significantly, because inventory costs do not come into play when demand increases from an initial point of equilibrium (i.e., no excess supply). In this case, the monopolist's profit is:
This section describes a simple model of price asymmetry that we use as a platform to analyze demand- and supply-side (i.e., cost-ofproduction) shocks in subsequent sections. We abstract from the complexity of strategic interactions among oligopolists by focusing on a market supplied by a monopolist. The monopolist maximizes profit by jointly choosing two variables: the price of the product it sells, p, and its effort in sales promotion, e. The firm faces market demand given by Q = D(p), which is assumed to be strictly increasing, weakly concave, and continuously differentiable: D′(p) b 0 and D′′(p) ≤ 0. The monopolist is assumed to have access to an effective sales promotion technology that effectively shifts the demand curve to the right while incurring promotional costs introduced below. The increase in market demand is denoted β(e), which is measured in output units, so that total demand in the presence of the firm's promotional effort is given by Q N = D(p) + β(e). We assume that the output effect of promotional effort is strictly increasing and strictly concave, β′ N 0 and β′′ b 0.9 We assume that the firm's cost function is linear with constant marginal cost, c, and that expenditures on promotional activity is just lump-sum (e.g., a large advertising buy, 9 Both assumptions on second derivatives introduced in this paragraph (i.e., D′′ ≤ 0 and β′′ b 0) are simplifying technical conditions so that the second-order conditions of the profit-maximization problem are satisfied and the complication of non-unique solutions can be avoided. The phenomenon of price asymmetry can occur in our model using more general functional forms without global concavity of D(p) and β(e).
3. Demand shock In the absence of a demand shock, the monopolist chooses p and e to maximize its profit function as given by the formula: πðp; eÞ ¼ Q N ðp−cÞ−e: The first-order conditions for an interior optimal choice of p and e require: πp ≡
∂π ¼ D0 ðpÞðp−cÞ þ DðpÞ þ βðeÞ ¼ 0; ∂p
ð1Þ
πe ≡
∂π ¼ β0 ðeÞðp−cÞ−1 ¼ 0: ∂e
ð2Þ
πðp; e; α Þ ¼ ðQ N þ α Þðp−cÞ−e: The first-order conditions are almost the same as Eqs. (1) and (2) except that β(e) is replaced by α + β(e). Let the solutions to the firstorder conditions under a demand shock be denoted as p*(α) and 10 Recently the renovation of retail space seems to be a big part of retailers' strategy, e.g., Mcdonald's Mc cafe and many others throughout U.S., Europe, Korea and Japan. 11 Although the supply function is not properly defined in case of monopoly, the monopolist's profit-maximizing condition (at an interior level of optimal production) requires that it choose the output level to equate marginal revenue and marginal cost. We refer to this profit-maximizing output level that the monopolist chooses as supply or quantity supplied. 12 Our claim that inventory cost is zero when excess demand occurs holds after a normalization that subtracts fixed inventory costs that are incurred throughout the business cycle regardless of excess supply or excess demand. The fixed component of warehouse space, insurance and inventory management costs is acknowledged but then, without loss of generality, can be normalized to zero. Therefore, the asymmetric component of inventory costs that are positive whenever excess supply occurs and zero whenever excess demand occurs is the mechanism that our model focuses on.
Y. Lim et al. / Economic Modelling 49 (2015) 314–319
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e*(α). Total differentiation of p*(α) and e*(α) with respect to α yields the following comparative statics:
πe ¼ β0 ðeÞðp−c þ kÞ−1 ¼ 0:
dp β00 ðp−cÞ ¼− N 0; dα jH α j
ð3Þ
de β0 ¼ N 0; dα jHα j
ð4Þ
We will denote the solutions to the negative-demand-shock firstorder conditions as p⁎⁎(α, k) and e⁎⁎(α, k). In other words, the optimal pricing and promotional effort rules, p⁎⁎(α, k) and e⁎⁎(α, k), are obtained by taking joint account of both the magnitude of the negative demand shock and the inventory cost parameter, k (unlike the corresponding optimal pricing and promotional effort functions in the case of a positive demand shock, p*(α) and e*(α)). If k = 0, it is clear from Eq. (3) that p⁎⁎(α, 0) b p0 b p*(α). Here, p*(α) is the optimal price in case of a positive shock and p⁎⁎(α, 0) is the optimal price in case of a negative shock. Also, from comparing the first-order conditions in the cases of negative versus positive demand shocks, it is clear that the price adjustments are symmetric in the sense that the two first-order conditions differ only in the sign of the shock. To see whether inventory cost generates asymmetry in price adjustment, we now consider the effect of k N 0 on the optimal price. For this purpose, it is sufficient to check the sign of ∂p⁎⁎(α, k)/∂k. Total differentiation of Eqs. (5) and (6) with respect to k yields the following:
where Hα is the Hessian matrix for π(p, e; α) with respect to p and e, and |Hα| N 0 by the second-order condition. The two comparative statics with positive signs are intuitive: during a macroeconomic expansion or following any events that cause a positive demand shock, the monopolistic firm will optimally charge higher price and engage in more costly promotional effort. The effect on the price is obvious. The effect on the promotional effort can be intuitively explained as follows. The profitmaximizing firm chooses promotional efforts at a level where marginal revenue equals marginal cost. If there is a positive demand shock, the firm will raise its price, thereby increasing marginal revenue of promotional efforts. Since the marginal revenue is now larger than marginal cost, the firm will increase its promotional efforts.13 We observe that, in the case of a positive demand shock, there is no inventory despite the price being higher, because demand has increased due to a positive shock and an optimal response of increased promotional expenditures. In contrast to the case of positive demand shocks which do not affect inventory costs, the case of negative demand shocks leads to accumulation of larger inventories and, consequently, greater inventory costs. Taking inventory costs into account, the monopolist chooses p and e to maximize its profit function in the negative-demand-shock environment, which is given by the formula: πðp; e; −α Þ ¼
ðp−cÞQ − −e−kðQ 0 −Q − Þ ðp−cÞQ − −e
if Q − b Q 0 if Q − ≥ Q 0 ;
where Q− = Q N − α. To be realistic about bounds on the effectiveness of promotional effort, and to avoid the technical difficulty arising from non-differentiability of the profit function, we assume that β(e) is bounded above by α. This assumption captures the idea that promotional activities can, at most, only partially offset a negative demand shock. Given that that β(e) is bounded above by α, it suffices to focus exclusively on the case in which Q− b Q0, from which it follows that the negativedemand-shock profit function can be written simply as π(p; − α) = (p − c + k)Q− − e − kQ 0. Note that the unit inventory cost k can now be interpreted as a reduction in marginal cost, because an additional unit of sales decreases the inventory cost by k, and this decrease in inventory cost is equivalent to lowering the marginal cost of production by k. The first-order conditions in the case of a negative demand shock (− α) are given by: πp ¼ D0 ðpÞðp−c þ kÞ þ DðpÞ−α þ βðeÞ ¼ 0;
ð5Þ
13 We are grateful to an anonymous referee who suggested an alternative intuition for this comparative static result based on the threat of entry. Suppose the monopolist faces the threat of entry but that entry is blockaded in the current period. If there is a positive demand shock, then the monopolist, who now faces a more probable threat of entry, tries to deter entry, either by limit pricing or by rationally choosing excessive promotional effort (i.e., advertising), assuming asymmetric information between entrants and the monopolist. See Bagwell and Ramey (1988) for more details motivating such a mechanism. If the monopolist uses limit pricing, then there will be downward distortion in pricing during a boom (i.e., following positive demand shocks) but no price distortion during a recession (i.e., following negative demand shocks) because there is no effective threat of entry during a recession. Hence, reverse price asymmetry may result. If the monopolist uses promotional effort to deter entry, then the implication for price asymmetry is ambiguous because the effect of the (asymmetric) threat of entry works in the opposite direction to the (asymmetric) effect of inventory costs. Introducing both mechanisms (i.e., the threat of entry under incomplete information and asymmetric inventory costs, the latter of which is the focus of our analysis) is left to future research to pursue such a generalization.
ð6Þ
2
∂p β0 −D0 β00 ðp −c þ kÞ ⋛ 0; ¼ H α;k ∂k
ð7Þ
β0 D00 ðp −c þ kÞ þ D0 ∂e N 0: ¼− H α;k ∂k
ð8Þ
Eq. (8) implies that a rise in k unambiguously increases optimally chosen promotional expenditures. The inequality directly above is intuitively obvious, because an increase in inventory costs induces the monopolist to increase its promotional effort to reduce unsold output held as excess inventory. On the other hand, the effect of an increase in k on the monopolist's optimal choice of price is ambiguous because there are two conflicting effects. First, an increase in the inventory cost tends to lower price directly, reflecting the monopolist's incentive to reduce product held in inventory, which is measured by the second term of Eq. (7). Second, an increase in inventory cost increases the monopolist's optimal choice of promotional effort, which boosts demand and, in turn, enables the monopolist to increase price. This indirect effect is measured by the first term in Eq. (7). Therefore, price is increasing in k whenever 2
β0 N D0 β00 ðp −c þ kÞ: ½DAP This inequality, referred to as the Demand-shock Asymmetric Price (DAP) condition, means that, if the monopolist takes inventory cost into account, then it chooses a higher price than it would otherwise: p⁎⁎(α, k) N p⁎⁎(α, 0) under the DAP condition. The DAP condition implies that inventory costs can create an asymmetry in price adjustments (i.e., downward price rigidity). How likely is the DAP condition to hold? If β′ is large, meaning that the promotional effort is sufficiently effective to substantially increase demand, then the indirect promotional effect dominates the direct effect, implying that prices will not decline much in recessions. Also, if β′′ is very small in absolute value (i.e., β(e) is nearly linear), then e⁎⁎ is highly sensitive to the negative demand shock in a demand-side recession, implying that the promotional effect is large relative to the price effect. Therefore, the shape of the promotional technology that the monopolist has available determines when this condition is likely to hold: when the promotional technology has a large first-order effect on demand with very slowly decreasing returns to effort or expenditure. The DAP condition describes precisely when downward price rigidity is predicted to occur. If the DAP condition fails to hold, then the direct effect dominates the indirect effect, and the monopolist will lower prices in recessions to reduce inventory. The DAP condition has a further implication, however, suggesting the possibility of a reverse asymmetry
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in which price reductions observed in a demand-side recession are predicted to be larger than price increases in a demand-side expansion whenever the DAP condition does not hold.14 pffiffiffi For a numerical example, take D(p) = a − bp and βðeÞ ¼ A e, where a, b, A N 0. Then, straightforward calculations yield p ¼
A2 −2b ðc−kÞ−2ða−α Þ A2 −4b
:
2
2
A2 2.
Hence, dpdk ¼ − A2 −2b N 0 if 2b b A2 b 4b or equivalently, A4 b b b A −4b
The possibility of price asymmetry is illustrated in Fig. 1 for parameter values: A = 2, a = 2, c = 1, and α = 1. Intuitively, if b is very small so that demand is very inelastic, then the monopolist must drop the price significantly in order to increase demand. In this case, the price effect is so large that DAP is not be satisfied. On the other hand, if b is so large that demand is highly elastic, then the price effect is indeed very small but, at the same time, the promotional effect is very small because an increase in e has little effect on demand. (Think of an almost horizontal demand curve. Then the new demand curve after a promotional campaign is almost identical to the original demand curve.) Therefore, if b is too high or too low, DAP does not hold. Before closing this section, it is worth considering the possibility that competition would affect the results reported above. It is easy to see that perfectly competitive firms do not engage in any promotional activity, because competitive firms face a free-riding problem in that the effect of promotional activity by an individual firm is shared by all firms. This observation strongly supports the empirical finding of SERI (2011) that countries with high ratios of market concentration such as Japan and Korea exhibit unusually large degrees of price asymmetry. 4. Cost shock In Section 3, we identified two effects of a change in inventory cost: a direct price effect and an indirect (and countervailing) promotional effect. This insight is robust in the sense that it almost obviously extends from the demand-side shocks considered in Section 3 to the cost (i.e., supply-side) shocks considered in this section. For the purpose of completing our argument, an analysis of the case of cost shocks is presented below. If a positive cost shock occurs, then excess demand results, because of the instantaneous decrease in production as an optimal response to increased costs of production and the current output-price level at the prevailing pre-shock price. Thus, the monopolist's profit in the positive cost-shock environment is given by: πðp; e; γÞ ¼ Q N ðp−c−γ Þ−e: The first order conditions imply πp ¼ −D0 ðpÞðp−c−γÞ þ DðpÞ þ βðeÞ ¼ 0;
ð9Þ
πe ¼ β0 ðeÞðp−c−γÞ−1 ¼ 0: Total
differentiation
D0 ðpÞβ0 0 ðeÞðp−c−γÞ−β0 ðeÞ Hγ 2
ð10Þ of
(9)
and
(10)
yields
∂p ∂γ
¼
≷ 0, where Hγ is a Hessian matrix. If we assume
that the second order condition is satisfied, i.e., |Hγ| = 2D′β′′(e)(p −
≷ 0 if and only if D′(p)β′′(e)(p − c − c − γ) − β′2(e) N 0, we have ∂p ∂γ 2
γ) ≷ β′ (e). That is, the effect of a positive cost shock on the price is ambiguous, whereas the effect of a positive demand shock is 14 A symmetry in price adjustments can occur if a negative shock leads to a small decrease in price and a large increase in the promotional activity, so that the resultant demand is higher than after the shock. Then, there will be no inventory in the optimum.
Fig. 1. Possibility of price asymmetry.
unambiguous. Intuitively, if the production cost is higher, it directly 0
moves the price up but it reduces the promotion effort (∂e ¼ ββ0 0ððeeÞÞ b 0) ∂γ
due to a smaller margin, and consequently reducing the demand which indirectly affects the price downward. If the former direct effect dominates the latter indirect effect, the price goes up due to a positive cost shock as we usually expect, but if the latter indirect effect dominates the former, the price may go down as a result of a positive cost shock. If the cost shock is negative, then the monopolist's output will increase instantaneously, thereby generating excess inventory. We continue here analyzing the case of a negative cost shock that generates excess inventory. Let the new output level in the post-negative-costshock environment be denoted as Q′. Then, the inventory is Q′ − QN. Taking the inventory cost into account, the monopolist's profit function can be expressed as: πðp; γÞ ¼
ðp−c þ γ þ kÞQ N −e−kQ 0 ðp−c þ γ ÞQ N −e
if Q N b Q 0 if Q N ≥ Q 0 :
Again, to be realistic about the effectiveness of promotional effort, we focus only on the case in which output levels increase following the cost shock that lowers costs of production: Q N b Q′. In this case, the first-order conditions are given by: πp ¼ D0 ðpÞðp−c þ γ þ kÞ þ DðpÞ þ βðeÞ ¼ 0;
ð11Þ
πe ¼ β0 ðeÞðp−c þ γ þ kÞ−1 ¼ 0:
ð12Þ
Similarly, total differentiation of Eqs. (11) and (12) with respect to unit inventory cost, k, yields: 2
∂p β0 −D0 β00 ðp −c þ γ þ kÞ ⋛ 0; ¼ H γ;k ∂k
ð13Þ
β0 D00 ðp −c þ γ þ kÞ þ D0 ∂e N 0; ¼− H γ;k ∂k
ð14Þ
where Hγ,k is again a Hessian matrix. As in the case of a demand shock, the effect of an increase in k on the monopolist's optimal choice of price is ambiguous. If the inventory cost parameter increases, then the monopolist has a clear incentive to reduce inventory and, as a result, lower price. However, the increase in the inventory cost parameter also increases the monopolist's optimal choice of promotional effort,
Y. Lim et al. / Economic Modelling 49 (2015) 314–319
319
asymmetry, will remain unaffected by relaxing our assumption on the number of firms in the model, as long as the industry is supplied by firms that enjoy an economically significant degree of market power: A negative demand shock creates inventory costs that, in our theory, firms actively seek to avoid by increasing their expenditures on promotional effort. This asymmetric trajectory of inventory costs over the business cycle is a natural description of what faces any firm earning positive profits due to market power. If these promotional efforts lead to a rise in prices by increasing consumer demand, then downward price rigidity is likely to be observed. Of course, we are aware that the result will be sensitive to the nature of the promotion activity, whether a firm's activity is specific or general in the sense that it increases only the demand of its own output or, alternatively, increases demand for competitors' output as well. Such complex issues arising from imperfect competition are beyond the scope of this paper and will be left for future research. Fig. 2. Price asymmetry in case of a cost shock.
References
which exerts a positive effect on its optimal choice of price. Therefore, price is increasing in k if: 2
β0 N D0 β00 ðp −c þ γ þ kÞ: This means that in the case that
∂p ∂γ
N0, asymmetric prices occur
under this condition. We will call this the Cost-shock Asymmetric Price (CAP) condition. Interestingly, even in the case that
∂p ∂γ
b0,
asymmetric prices occur under this condition, but for a different reason. If the indirect effect exceeds the direct effect, the price is higher when the cost goes down than when the cost goes up. However, when the cost goes down, the higher price reduces the demand and some inventory cost is incurred. Since the price is higher as k is larger under [CAP] condition, it means that a positive asymmetry in price adjustment results. On the other hand, if the CAP condition does not hold, a reverse price asymmetry is generated. If we take the same simple function of D(p) = a − bp and βðeÞ ¼ pffiffiffi A e in the case of a cost shock, we have
p ðγÞ ¼
2a− A2 −2b ðc þ γÞ
p ðγ; kÞ ¼
; 2 4b−A 2a− A2 −2b ðc−γ−kÞ 4b−A2
:
Assuming that 2b b A 2 b 4b as before, we have 2a−ðA2 −2bÞðcþγÞ 4b−A2
∂p ∂γ
¼
b 0, i.e., p*(γ) b p ⁎⁎(γ). Fig. 2 illustrates the possibility
of price asymmetry for parameter values of A = 2, a = 2, c = 1, and D′′ ≤ 0 (satisfying [CAP] condition). 5. Conclusion While price asymmetry referred to as “Rockets and Feathers” has been regarded as a robust empirical regularity, virtually no positive theory has yet appeared that can account for the empirical evidence. This paper introduces a promotional effort mechanism (i.e., costly marketing expenditure) into an otherwise standard profit-maximization framework to fill this gap between theory and observation. Although the promotional effort mechanism is intuitive, we acknowledge that our model may be too simple because it focuses on the extreme case of a monopolistic industry. We could consider several firms competing (in quantities or prices) instead of the single monopolist. We strongly believe, however, that our main insight, which identifies market power as a necessary condition for observing price
Bacon, R.W., 1991. Rockets and feathers: the asymmetric speed of adjustment of UK retail gasoline prices to cost changes. Energy Econ. 13, 211–218. Bagwell, K., Ramey, G., 1988. Advertising and limit pricing. Rand J. Econ. 19, 59–71. Ball, L., Mankiw, N.G., 1994. Asymmetric price adjustment and economic fluctuations. Econ. J. 104, 247–261. Bennett, J., La Manna, M., 2001. Reversing the Keynesian asymmetry. Am. Econ. Rev. 91, 1556–1563. Berument, M.H., Sahin, A., Sahin, S., 2014. The relative effects of crude oil price and exchange rate on petroleum product prices: evidence from a set of northern Mediterranean countries. Econ. Model. 42, 243–249. Blinder, A., 1982. Inventories and sticky prices: more on the microfoundations of macroeconomics. Am. Econ. Rev. 72, 334–348. Borenstein, S., Cameron, A.C., Gilbert, R.J., 1997. Do gasoline prices respond asymmetrically to crude oil price changes? Q. J. Econ. 112, 305–339. Boyde, M.S., Bronsen, W.B., 1988. Price asymmetry in the U.S. pork marketing channel. North Cent. J. Agric. Econ. 10, 103–109. Brown, S.P.A., Yucel, M.K., 2000. Gasoline and crude oil prices: why the asymmetry? Federal Reserve Bank of Dallas. Econ. Rev. 23–29. Cover, J.P., 1992. Asymmetric effects of positive and negative money-supply shocks. Q. J. Econ. 107, 1261–1282. DeLong, J.B., Summers, L.H., 1988. How does macroeconomic policy affect output? Brook. Pap. Econ. Act. 19, 433–494. Ellingsen, T., Firberg, R., Hassler, J., 2005. Explaining asymmetric price adjustment available at. http://www.eco.uc3m.es/temp/EFH.pdf. Galeotti, M., Lansa, A., Manera, M., 2003. Rockets and feathers revisited: an international comparison on European gasoline market. Energy Econ. 22, 251–276. Johnson, R.N., 2002. Search cost, lags and prices at the pump. Rev. Ind. Organ. 20, 33–50. Karagiannis, S., Panagopoulos, Y., Vlamis, P., 2014. Are unleaded gasoline and diesel price adjustments symmetric? A comparison of the four larger EU retail fuel markets. Econ. Model. http://dx.doi.org/10.1016/j.econmod.2014.11.003. McLaren, A., 2013. Asymmetry in Price Transmission in Agricultural Markets, WPS 13-102. University of Geneva. Meyer, J., von Cramon-Taubadel, S., 2004. Asymmetric price transmission: a survey. J. Agric. Econ. 55, 581–611. Meyler, A., 2009. The pass through of oil prices into euro area consumer liquid fuel prices in an environment of high and volatile oil prices. Energy Econ. 31, 867–881. Mitchell, W., 1927. Business Cycle. National Bureau of Economic Research, New York. Neumark, D., Sharpe, S.A., 1992. Market structure and the nature of price rigidity: evidence from the market for consumer deposits. Q. J. Econ. 107, 657–680. Peltzman, S., 2000. Prices rise faster than they fall. J. Polit. Econ. 108, 466–502. Phlips, L., 1980. Intertemporal price discrimination and sticky prices. Q. J. Econ. 92, 525–542. Pick, D.H., Karrenbrock, J., Carmen, H.F., 1991. Price asymmetry and marketing margin behavior: an example for California–Arizona citrus. Agribusiness 6, 75–84. Ray, S., Chen, H., Bergen, M.E., Levy, D., 2005. Asymmetric wholesale pricing: theory and evidence. Mark. Sci. 25, 889–902. Reagan, P., 1982. Inventory and price behavior. Rev. Econ. Stud. 49, 137–142. Schumpeter, J., 1942. Capitalism, Socialism and Democracy. Harper and Row, New York. SERI, 2011. The Structure of Korea Consumer Prices and The Task for Price Stabilization. SERI Report 701. Samsung Economic Research Institute. Tsiddon, D., 1993. The (Mis)Behavior of the Aggregate Price Level. Rev. Econ. Stud. 60, 889–902. Verbrugge, R., 1998. A Cross-Country Investigation of Macroeconomic Asymmetries. Working Paper. VPI & SU. Verbrugge, R., 2002. Longitudinal inflation asymmetry. Appl. Econ. Lett. 9, 261–264. Zabel, E., 1972. Multiperiod monopoly under uncertainty. J. Econ. Theory 5, 524–536. Zachmann, G., von Hirschhausen, C., 2008. First evidence of asymmetric cost pass-through of EU emissions allowances: examining wholesale electricity prices in Germany. Econ. Lett. 99, 465–469.