Advances in Mathematical Models in Marketing

This dissertation comprises a series of three essays that relate advances made to both theoretical and empirical issues in marketing. The first essay discusses the issue of endogeneity of market share and price in logit models and provides a theoretical procedure to solve this problem. The inseparability of demand and price make the possibility of drawing definite conclusions about either almost impossible. We employ a recently rediscovered mathematical function called the 'LambertW' to solve this problem of endogeneity and in turn yield logit models more conducive to theoretical study. We also employ this methodology to the problem studied by Basuroy and Nguyen (1998). The second essay deals with the issue of pricing implicit bundling. Implicit bundles are products that are sold separately but provide an enhanced level of satisfaction if purchased together. We develop a model that would account for the possible relationships of the products across the different product lines. We show that accounting for these relationships would decrease the amount of price competition in the market and also allow the Firm to enjoy higher profits. We also account for the endogeneity of price and market share when deriving the optimal solutions. We show that optimal prices first increase as the relationship between the firm's two products become stronger and then decrease as the two products become more exclusive to each other. Finally, we also find that a firm's prices increase as the competitor's contingent valuations increase. The third essay helps improve the efficacy of CRM interventions by analyzing the latent psychological loyalty states of the customer. We use state space models to predict these latent loyalty states using observed data. We then use the predicted values of loyalty to derive the probability of repurchase of the customer. We also identify the types of CRM interventions that play a role in improving the loyalty of the customer to the firm and those interventions that have no effect. We compare our model's predictions to those derived from two other estimation methods. We find that our predictions are better than those computed from the other methods discussed.