eThesis - Kauppakorkeakoulun sähköiset gradut

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Objectives: The objective of this thesis is to build models where the demand of a product has an explicit, recognizable trend effect. With the models we seek to infer the properties of a trend based on observable firm behavior.

Methods: I construct in total three different models: a monopoly model, a Stackelberg duopoly model and a simultaneous-choice duopoly model. Moreover, I study three different trend types in each of the models: a nonexistent trend, a linear trend and a parabel trend. The demand in each of the models is determined through initial value problems that incorporate the trends into the probabilities for buying a product. All presented initial value problems are modified versions of the initial value problems of the Susceptible-Infective-Susceptible epidemiological model. I am unable to find analytical solutions for the initial value problems, and so I use numerical methods for solving them. The numerical solutions are done with MATLAB. The use of numerical solutions for the initial value problems means that also the firm behavior is solved numerically. The firms seek to maximize their profits by choosing the price, quality and free samples of their products. I limit the firms' choices to finite choice sets in order to be able to optimize using simple brute force. Brute force is used to calculate the firms' profits for every possible choice combination from the finite choice sets. This allows us to describe firm behavior either directly (the monopoly model and the Stackelberg duopoly model) or by studying the subgame-perfect Nash equilibrium of an interaction game that the firms play (the simultaneous-choice duopoly model).

Results: We are not able to deduce the properties of a trend solely by observing firm behavior. In each model the values for exogenous variables may be chosen such that firm behavior is the same for different trend types. We may, however, formulate an existence result for trends: If we observe at least one firm giving out free products, we may infer the existence of a trend. The result does not run in the other direction, i.e. we may not infer the nonexistence of a trend if we observe no firm giving out free products.