Spatial equilibrium analysis is well known as a quantitative method to analyze the structure of interregional competition of agricultural products. And the uniqueness of equilibrium solution is essential to the application of this analysis. Usually researchers take it for granted that the uniqueness holds. But, if the uniqueness does not hold, conclusion of the application is meaningless or it must be corrected. In this paper, we show theoretically that some spatial equilibrium models, which have been thought to have unique equilibrium solution respectively, have not unique but infinitely many equilibrium solutions respectively and that it is very important to carefully check the uniqueness of equilibrium solution. In Section Ⅰ: Introduction, we make clear the subject in this paper. In Section Ⅱ: On the Uniqueness of Equilibrium Solution as Optimal Solution of Nonlinear Programming, we show the point mentioned above in most general form. In Section Ⅲ: An Algorithm for-Solving Quadratic Programming Problems and the Uniqueness of Equilibrium Solution, we show an efficient algorithm to parametrically solve quadratic programming problems based on Dantzig-Panne and Whinston's method, and show the point mentioned above more concretely based on this algorithm for the case of spatial equilibrium models specified as quadratic programming problems. In Section Ⅳ: Conclusion, we summarize the point mentioned above briefly. In another paper, we will make a case study to show the importance and correctness of the conclusion of this paper.