Dynamics of market models with inventory
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Date
2004
Authors
Ratnayake, R. M. T.
Journal Title
Journal ISSN
Volume Title
Publisher
University of Peradeniya
Abstract
Dynamics of three types of market models with inventory are considered. These models are categorized into Quasi-Periodic, Lagged - Inventory and Pseudo - Quadratic according to the mathematical nature of the assumptions of the model. The governing mechanism of these models can be stated commonly in the functional form <mathematical formular>, is the excess supply function (inventory function) and θ(≥ 0) is.a time independent parameter.
In the three models the dynamic stability of time paths of the price function P (unit price at time f) are investigated by providing possible ranges of values for the stock — t + 7 st induced- price- adjustment (SIPA) coefficient <mathematical formular> in terms of the exogenous model parameters.
In this direction the following main results are established:
1, In the Quasi-Periodic model, P, is asymptotically stable if, and only if <Mathematical formular>
2. Unlagged Inventory model (UIM) is a deductive sub - model of the Lagged - Inventory (LIM) model.
3 . In the Pseudo — Quadratic model, equilibrium price <mathematical formular> is attainable but it is unstable for all θ > 0.
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Mathematics