Geometrical analysis of utility functions underlying product differentiation models

Abstract

In this thesis, the reactions of different utility functions and their derived demand functions to product differentiation are examined. I examine the commonly used utility functions and parameters, which have important places in the literature, with graphs. I show the effects of the values of the parameters in the utility functions on the utility functions. In a way, I examine the meanings of these parameters in terms of utility functions before reaching the demand form in which the parameters are contained. In most models, the meanings of the parameters that have the effect of product differentiation are explained at certain intervals. Although linear demand is intensely preferred in the literature and a quadratic utility function is preferred to obtain this demand, I also discuss the preference of different types of utility functions. Most models prefer to use two different parameters in the utility function, but many are based on the assumption that one parameter is exogenous while the other parameter is endogeneous. In this study, I present the effect of these parameters, which can be exogenous and endogenous and have the effect of product differentiation, on demand with graphics. While product differentiation is found in models that can be considered vertical product differentiation such as quality improvement in some studies, horizontal product differentiation in some models has been examined and the use of parameters and the form of utility functions have been chosen in this way. In this study, I discuss how researchers can make different utility models to describe the same type of product differentiation and how their outputs vary in terms of results. Optimum price, quantity, and product differentiation are commonly determined using Cournot and Bertrand type demand functions and some game theory tools. In this study, I describe these research techniques and the results of the studies using these techniques and analyze them with graphics. In some models, although it is not specified how the expenditures of the firm that provides product differentiation will change on the relevant utility parameter, in some models, assumptions are made about how the expenditures made for product differentiation affect the utility parameters. In order to understand the effects of the parameters of the models with and without these assumptions on the utility, I present the paths that the utility can follow with the increase of product differentiation in the graphs.