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We specify and analyze the conditions under which the MNL market share models are appropriate for equilibrium analysis. Our results show that a linear price response func
tion as is often used in empirical research, in conjunction with the typical concavity assumed in a large range of marketing response functions, would yield an interior equilibrium solution. We then consider the optimal reactions on pricing and marketing spending to entry and potential market expansion. In the context of the MNL models, we demonstrate that the entry of a new brand evokes a decrease in the equilibrium prices of the existing brands as a defensive reaction. This is true in both an expanding market as well as a fixed market. However, while new entry into a fixed market would trigger the incumbents to lower the marketing expenditure, we show that firms tend to raise marketing activities as they experience market expansion. Consequently, there exist distinct possibilities that marketing efforts for the existing brands increase in view of entry in an expanding market. Further managerial and marketing implications for endogeneity of the number of firms are explored.
(MNL Market Attraction Models; Equilibrium Analysis; Entry and Market Expansion; Competitive Pricing and Advertising; Free-Entry Equilibrium)
1. Introduction The large literature on market-share analysis as exemplified in Cooper and Nakanishi s well-known book (1988) has concentrated on justifying and estimating various specifications of market share models such as the linear, the multiplicative, the exponential and in particular, the Multiplicative Competitive Interaction Model (MCI), and the Multinomial Logit Model (MNL). Their book also addresses certain theoretical relations among these models and their estimation implications. The basic justification for some of these specifications is rooted in what has been known as Kotler's fundamental theorem (on market share) and the axiomatic approach in the Bell-Keeney-Little market share theorem (Bell, Keeney, and Little 1975). Since the MCI and the MNL models imply immediately that each brand's market share is nonnegative and the sum of market shares of all brands is unity, both specifications satisfy the so-called logical-consistency requirements (Naert and Bultez 1973). While these two models have not always resulted in superior performance in terms of predictive accuracy in comparison to the other models, it has been argued that they nevertheless yield more...