Praveen K. Kopalle

Bio: Praveen K. Kopalle is an academic researcher from Dartmouth College. The author has contributed to research in topics: Limit price & Dynamic pricing. The author has an hindex of 33, co-authored 70 publications receiving 4891 citations. Previous affiliations of Praveen K. Kopalle include University of Arizona.

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.

Disruptiveness of innovations: measurement and an assessment of reliability and validity

Abstract: Strategic management scholars have long explored the broad topic of innovation, a cornerstone in creating competitive advantage. Any attempt at theory construction in this area must encompass reliable and valid measures for key innovation characteristics. Yet, with respect to an important construct, i.e., disruptiveness of innovations, there has been relatively little academic research. Without formalizing the disruptiveness concept with a reliable and valid measure, it is difficult to conduct rigorous research to uncover the causes of the innovator's dilemma and identify mechanisms to help incumbents develop such innovations. In this paper, we develop a scale for the disruptiveness of innovations. We collected data from senior executives (vice president or general manager level) at 199 strategic business units (SBUs) in 38 Fortune 500 corporations and performed a series of analyses to establish the reliability and validity of the disruptiveness scale. The reliability measures, exploratory factor analysis, confirmatory factor analysis, and subsequent statistical tests strongly support our measure. Further, we also present nomological validity of the disruptiveness construct, thus establishing its predictive validity. Thus, this paper distinguishes the disruptiveness concept from other established innovation constructs, such as radicalness and competency destroying. Finally, we discuss the significance of our results and how this study might be useful to other researchers. Copyright © 2006 John Wiley & Sons, Ltd.

Dynamic Pricing on the Internet: Importance and Implications for Consumer Behavior

Abstract: The pricing of products and services sold over the Internet channel is becoming more dynamic. In part this is due to the increasing use of auction models in business and consumer markets to sell commodities, excess inventories, used merchandise, rare items collectibles, and other items. Marketers are resorting to dynamic prices even for goods and services sold at posted prices, spurred partly by the lower menu cost of changing prices on the Internet and partly as a response to consumer use of price-comparison bots. This paper explains the relevance of dynamic pricing in the digital economy by comparing the physical value chain with the virtual-information-based value chain. It explores the implications of certain aspects of dynamic pricing in consumer markets (e.g., dynamic pricing of posted prices, reverse auction pricing of goods and services as used by Priceline) from the perspective of consumer price expectations, the role of information and consumer learning, and their impact on consumer responses to prices across different product categories. Several propositions are developed, and issues for research are identified.

Collinearity: a review of methods to deal with it and a simulation study evaluating their performance

Abstract: Collinearity refers to the non independence of predictor variables, usually in a regression-type analysis. It is a common feature of any descriptive ecological data set and can be a problem for parameter estimation because it inflates the variance of regression parameters and hence potentially leads to the wrong identification of relevant predictors in a statistical model. Collinearity is a severe problem when a model is trained on data from one region or time, and predicted to another with a different or unknown structure of collinearity. To demonstrate the reach of the problem of collinearity in ecology, we show how relationships among predictors differ between biomes, change over spatial scales and through time. Across disciplines, different approaches to addressing collinearity problems have been developed, ranging from clustering of predictors, threshold-based pre-selection, through latent variable methods, to shrinkage and regularisation. Using simulated data with five predictor-response relationships of increasing complexity and eight levels of collinearity we compared ways to address collinearity with standard multiple regression and machine-learning approaches. We assessed the performance of each approach by testing its impact on prediction to new data. In the extreme, we tested whether the methods were able to identify the true underlying relationship in a training dataset with strong collinearity by evaluating its performance on a test dataset without any collinearity. We found that methods specifically designed for collinearity, such as latent variable methods and tree based models, did not outperform the traditional GLM and threshold-based pre-selection. Our results highlight the value of GLM in combination with penalised methods (particularly ridge) and threshold-based pre-selection when omitted variables are considered in the final interpretation. However, all approaches tested yielded degraded predictions under change in collinearity structure and the ‘folk lore’-thresholds of correlation coefficients between predictor variables of |r| >0.7 was an appropriate indicator for when collinearity begins to severely distort model estimation and subsequent prediction. The use of ecological understanding of the system in pre-analysis variable selection and the choice of the least sensitive statistical approaches reduce the problems of collinearity, but cannot ultimately solve them.

Regression Diagnostics: Identifying Influential Data and Sources of Collinearity

Abstract: 1. Introduction and Overview. 2. Detecting Influential Observations and Outliers. 3. Detecting and Assessing Collinearity. 4. Applications and Remedies. 5. Research Issues and Directions for Extensions. Bibliography. Author Index. Subject Index.

Economics of Information

Abstract: The author systematically examines one of the important issues of information — establishing the market price. He introduces the concept of «search» — where a buyer wanting to get a better price, is forced to question sellers. The article deals with various aspects of finding the necessary information.