Showing papers on "Dynamic pricing published in 1996"

Optimal pricing and lot-sizing under conditions of perishability and partial backordering

Abstract: We formulate a generalized model of dynamic pricing and lot-sizing by a reseller who sells a perishable good. We assume that when it is economic to backlog demand, the reseller can plan for periods of shortage during which demand can be partially backordered. When the good is highly perishable, the reseller may need to backlog demand in order to market the good at a reasonable price. We present a simple solution procedure for solving the optimization problem. The procedure entails solving first a single nonlinear equation and then, if required, two nonlinear equations.

Dynamic Pricing in Retail Gasoline Markets

Abstract: Supergame models of tacit collusion show that supportable price-cost margins increase with expected future collusive profits, ceteris paribus. As a result, collusive margins will be larger when demand is expected to increase or marginal costs are expected to decline. Using panel data on sales volume and gasoline prices in 43 cities over 72 months, we find behavior consistent with tacit collusion in retail gasoline markets. Controlling for current demand and cost, current margins increase with expected next-month demand and decrease with expected next-month cost. The results are not consistent with intertemporal l inkages due to inventory behavior or customer loyalty.

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 reference price is the current price of the last brand bought---the reference brand. We adapt the individual level RB formulation in Hardie et al., to an aggregate demand specification. For the ES process, we obtain most results analytically; for the RB process we use simulation. Finally, we extend our results to a population with two customer segments: Segment 1 which weighs gains more than losses, and Segment 2 which does the opposite, i.e., is loss averse. When the market consists exclusively of Segment 1 customers and ES is the reference price process, we find that prices are cyclical in all cases analyzed, i.e., for a monopoly, a monopolist retailer managing multiple brands, a duopoly, and an oligopoly. If the RB formulation is the underlying process, a monopolist retailer managing two brands uses cyclical prices, but in a duopoly, the equilibrium solution is for the brands to maintain constant prices. When all customers belong to Segment 2 i.e., they are loss averse constant prices are optimal in all cases for both reference price formulations. When the population consists of both Segment 1 and Segment 2 and the ES process applies, we develop a sufficient condition for cyclical pricing policies to be optimal. The condition is expressed in terms of the proportion of the two segment sizes, the absolute difference between the gain and loss parameters of each segment, and their respective exponential smoothing constants. Interestingly, for reasonable values of the latter two factors, cyclical policies are optimal even when the proportion of Segment 1 is quite small. Similar magnitudes are obtained numerically for the RB case.

Pricing strategies in a dynamic duopoly: a differential game model

Abstract: We formulate a differential game model for dynamic pricing in a duopolistic market. Firms' demand functions are derived from utility maximizing behavior of consumers with the demand for a brand given by the logit model. Preferences for brands are assumed to evolve over time in the market in a manner akin to learning models postulated in the marketing literature. We derive the differential equations governing the equilibrium open-loop price paths over time and show that in steady state, the brand with the higher preference level charges the higher price. The formulation is extended to include the effects of consumer heterogeneity, and equilibrium steady-state prices are compared with those obtained when heterogeneity is ignored. A comparison of steady-state dynamic prices with myopic prices is provided. An empirical example is discussed to show how steady-state model predictions may be obtained from actual longitudinal purchase data.

A simulation study of usage-based pricing strategies for packet-switched networks

Abstract: This paper presents a simulation study of two proposed usage-based pricing strategies (one static, one dynamic) for computer networks. In the static pricing strategy evaluated, a price per packet is assigned and held constant over time. Results from the static strategy simulations show that network utilization decreases as the price per packet increases. Revenue, on the other hand, first increases and then falls as the price per packet increases. In the dynamic pricing strategy simulations, the price varies over time as a result of the user demand for bandwidth. As the number of users on the network increases, the price per unit of bandwidth increases. While the behaviour of the dynamic pricing scheme makes it appear promising as a pricing framework for packet-switched networks, further work is clearly required to better address the tradeoffs between network utilization, revenue, and network efficiency.

Pricing Strategies in a Dynamic Duopoly

Abstract: We formulate a differential game model for dynamic pricing in a duopolistic market. Firms' demand functions are derived from utility maximizing behavior of consumers with the demand for a brand giv...