The existence, uniqueness and stability of steady state for a class of first-order difference equations with application to the housing market dynamic

IF 1.4 Q2 MATHEMATICS, APPLIED
Lu Bai , Sizhong Sun
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Abstract

We study the existence, uniqueness and stability of the steady state for the dynamic described by a class of first-order difference equations. We then apply the result to analyse a housing market where the supply is linear and demand is a bounded and monotone decreasing function of price, derived from households’ optimization behaivour. Under two linear price adjustment mechanisms, we prove the existence and uniqueness of an equilibrium, which is independent of the mechanisms. That is, the house price converges to a same steady state where it clears the market under both mechanisms. The result is general in the sense that we do not need to specify a particular form of demand function. Besides, the same approach can be utilized to analyse the dynamics of other markets.

一类一阶差分方程稳态的存在性、唯一性和稳定性及其在住房市场动态中的应用
我们研究了一类一阶差分方程所描述的动态稳态的存在性、唯一性和稳定性。然后,我们将这一结果应用于分析一个住房市场,在该市场中,供给是线性的,需求是价格的有界单调递减函数,该函数来源于家庭的优化行为。在两种线性价格调整机制下,我们证明了均衡的存在性和唯一性,而均衡与机制无关。也就是说,在两种机制下,房价都会收敛到一个相同的稳定状态,在该状态下,房价会清算市场。这一结果具有普遍性,因为我们无需指定需求函数的特定形式。此外,同样的方法也可用于分析其他市场的动态。
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来源期刊
Results in Applied Mathematics
Results in Applied Mathematics Mathematics-Applied Mathematics
CiteScore
3.20
自引率
10.00%
发文量
50
审稿时长
23 days
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