تجزیه و تحلیل حساسیت برای مسئله تعادل قیمت فضایی وابسته زمان

We present some sensitivity results for the spatial price equilibrium problem in the case of quantity formulation model and in presence of excess supply and excess demand. The equilibrium conditions that describe the above model are expressed in terms of a time dependent variational inequality. The variational inequality formulation plays a fundamental role in order to achieve the sensitivity results.

This paper is concerned with the sensitivity analysis of the equilibrium solution of the time dependent spatial price problem. The interest of this study resides in the fact that it is necessary to know how the solution changes under suitable variation of the data, for example, of the supply prices, the demand prices and the transportation costs. In order to perform this analysis it is useful to formulate this problem in terms of a time dependent variational inequality. In the static case the spatial price equilibrium problem has been formulated in terms of such a variational inequality by Nagurney and Zhao [7] and by Nagurney [6]. Subsequently Daniele [2] has considered the spatial price equilibrium problem in the case of the quantity formulation model under the assumption that the data evolve with the time. She proved that the time dependent equilibrium conditions can be directly incorporated into a time dependent variational inequality. In [5] the authors extended this result of [2] considering a model with excess supply and demand and with capacity constraints on prices and on transportation costs. In Section 2 we present the spatial price equilibrium problem in the case of the time dependent quantity formulation model and some existence theorems. In Section 3 we show how Lagrangean and duality theory can be applied to our problem and finally in Section 4 we give the sensitivity analysis results.