某些常微分方程在若干经济领域的应用
毕业论文关键词：常微分方程；物价供需模型；库存的物价供需模型；定性和稳定性理论
Some Application of Ordinary Differential Equations in Some Areas of the Economy
Abstract: From the perspective of ordinary differential equations, we examine relationship between the prices of supply and demand. Different from previous research, this paper emphasize the important of establishment of different supply and demand model in studying the stability of market. In what follow, we want discuss the stability of the different market. There are three parts in this paper. We start with a brief introduction of some relevant knowledge of economics, leading to one of the most basic model of demand-supply model. The second chapter mainly study simple demand-supply model, analyzing from two aspects of whether demand function linear, which need the related knowledge of first-order differential equations. The third chapter mainly examined the demand-supply model with inventory, also analyzing from two aspects of whether demand function linear, mainly involving two order constant coefficient differential equation, the qualitative and stability theory of ordinary differential equations and related knowledge. At last, we simulate the stability of the models by MATLAB，making the article more readable.
Key words: ordinary differential equations; simple demand-supply model; demand-supply model with inventory; the qualitative and stability theory of ordinary differential equations;
目录
第一章 需求-供给模型简介 1
第二章 需求-供给模型 3
2.1线性需求模型 3
2.2非线性需求模型 5
情况2.2.1： 6
情况2.2.2： 9
情况2.2.3： 11
第三章 带库存的需求-供给模型 13
3.1 线性需求库存模型 13
情况3.1.1 14
情况3.1.2 15
情况3.1.3 16
3.2非线性需求库存模型 17
情况3.2.1 18
情况3.2.2： 27
情况3.2.3： 27
附录：（MATLAB命令） 29
致谢 30
第一章 需求-供给模型简介
在日常生活中，或许你没有学过微观经济学，或许你没有受过高等教育，但你总会认可一个经济规律：供大于需，价格下降；供小于需，价格上升。当经济调整稳定时，此时价格趋于稳定，供给量等于需求量。
在微观经济学中，通过供给和需求曲线来研究市场。需求-供给模型是研究市场重要工具，其中包含两个重要的概念：需求曲线和供给曲线。需求曲线是指，在其他影响某商品需求的因素（像消费者收入、消费者预期）不变的情况下，对应于每一给定价格，消费者愿意购买的某种商品的数量[1]。一般来说，随着商品价格的上升，消费者对商品的需求量会下降，如图1-1所示，随着价格从 上升到 ，消费者对产品的需求量从 下降到 。一般需求曲线可以用如下方程表示：