The existence, uniqueness and stability of steady state for a class of first-order difference equations with application to the housing market dynamic
Bai, Lu, and Sun, Sizhong (2024) The existence, uniqueness and stability of steady state for a class of first-order difference equations with application to the housing market dynamic. Results in Applied Mathematics, 21. 100433.
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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.
| Item ID: | 82017 |
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| Item Type: | Article (Research - C1) |
| ISSN: | 2590-0374 |
| Keywords: | First-order difference equation, Housing market dynamic, Non-linear dynamic, Steady state |
| Copyright Information: | © 2024 The Authors. Published by Elsevier B.V. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). |
| Date Deposited: | 31 Mar 2025 06:44 |
| FoR Codes: | 49 MATHEMATICAL SCIENCES > 4901 Applied mathematics > 490106 Financial mathematics @ 100% |
| SEO Codes: | 15 ECONOMIC FRAMEWORK > 1505 Microeconomics > 150506 Market-based mechanisms @ 100% |
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