Asymmetric Reference Price Effects and Dynamic Pricing Policies

Abstract

We consider a group of frequently purchased consumer brands which are partial substitutes and examine two situations; the first where the group of brands is managed by a retailer, and second where the brands compete in an oligopoly. We assume that demand is a function of actual prices and reference prices, and develop optimal dynamic pricing policies for each situation. In addition to researchers studying pricing strategy, our results may interest retailers choosing between hi-lo pricing and an everyday low price, and manufacturers assessing whether to follow Procter & Gamble's lead and replace a policy of funding consumer price reductions through trade deals with a constant wholesale price. A reference price is an anchoring level formed by customers based on the pricing environment. The literature suggests that demand for a brand depends not only on the brand price, but also whether the brand price is greater than the reference price (a perceived loss) or is less than it (a perceived gain). The responses to gains and losses are asymmetric. Broadly speaking, we find that when enough consumers weigh gains more than losses, the optimal pricing policy is cyclical. Likewise, when they weigh losses more than gains, a constant price is optimal. Thus, we provide a rationale for dynamic pricing which is quite distinct from the three explanations previously offered: (1) decreasing unit variable costs due to learning effects, (2) the transfer of inventory to consumers who face lower inventory holding costs than do retailers, and (3) competitive effects. Our explanations apply even when the other explanations do not, i.e., in mature product categories where learning effects are minimal, when retailer inventories are minimized through the use of just-in-time policies and when competitive effects do not exist, as in a monopoly. Greenleaf (1995) has shown numerically that in the presence of reference price effects, the optimal pricing policy for a monopolist can be cyclical. We first analytically extend Greenleaf's result to a monopolist with a constant cost of goods, facing a homogeneous market where all customers either weigh gains more than losses or vice versa. Using this building block we examine a monopolist retailer managing multiple brands. We assume that demand is a linear function of prices of multiple brands, and together with an expression which reflects the reference price effect. Further, we assume that the retailer maximizes average profit per period. Next, we analyze a duopoly and extend the results to an oligopoly. We assume that the manufacturers are able to set the retail prices, as in an integrated channel. Here, we retain the same demand function as for the retailer and derive Markov Perfect Nash equilibria. We use two alternative processes of reference price formation: the exponential smoothed (ES) past price process which is frequently used in the literature, and for the multi-brand situations, the recently proposed reference brand (RB) process (Hardie, Johnson, and Fader 1993). In the latter, the refere...

The Role of Big Data and Predictive Analytics in Retailing

“…The demand model we use is also modified to include basic psychological aspects of pricing. The key psychological aspect of pricing that we use in our estimation is that of reference price effects (Greenleaf 1995;Kopalle, Rao, and Assunção 1996;. Reference prices are modeled as an exponential smoothed average of past prices.…”

“…Accordingly, we estimate the corresponding gain and loss parameters. In other words, our model captures the reference prices as an exponentially smoothed average of past price (Kopalle, Rao, and Assunção 1996) and takes into consideration what the unit sales (reference sales) would be when the price is at parity with the reference price. The model parameters are estimated using maximum likelihood estimation.…”

Why the Dynamics of Competition Matter for Category Profitability

“…Based on prior literature in marketing which suggests that High-low pricing policies are generally more profitable relative to a constant price strategy (e.g., Hoch, Dreze and Purk 1994;Mazumdar et al 2005;Kopalle et al 1996), ex ante, our category profit expectations would be higher from a hi-lo pricing path than from an EDLP one.…”

Die Bewährung von Ankerpreismodellen bei der Erklärung der Markenwahl

“…F ur diese Konstellation haben Kopalle et al (1996) mit Hilfe eines dynamischen Optimierungsmodells (allerdings f ur aggregierte Preisabsatzfunktionen) gezeigt, dass im Monopol konstante und nicht etwa zyklische Preise optimal sind. Liegt der Ausgangswert des Ankerpreises unter ( uber) dem entsprechenden konstanten optimalen Preis, so steigt (f allt) der optimale Preispfad im Zeitablauf, bis Ankerpreis und optimaler Preis ubereinstimmen.…”

“…Auch M a r k o {Nash{Gleichgewichte f ur das Duopol zeichnen sich d u r c h k onstante Preise aus. Als Zielfunktion haben Kopalle et al (1996) Barwerte von Deckungsbeitr agen verwendet. Nach dem aufgrund der vorliegenden Untersuchungsergebnisse gew ahlten extrapolativen Ankerpreismodell setzt sich d e r Ankerpreis im wesentlichen aus gewichteten Preisen der drei vorhergehenden Perioden zusammen.…”