房地产外文及翻译

Three-Dimensional Nonlinear Dynamic Model and Macro
Control of Real Estate
Dan Ma1, Shengwu Zhou1*, Haojin Lv2
1School of Science, China University of Mining & Technology, Xuzhou, China
2School of Information & Electrical Engineering, China University of Mining & Technology, Xuzhou, China
Abstract
In this paper, according to economics of real estate and macro-control theory, combine with the characteristics of the real estate market, macro-control of the real estate market is studied. After giving the dynamic model of three-dimensional nonlinear differential equations based on the total number of houses on the real estate business, the government’s averages housing investment funds and the standard price, systematically established the stability conditions of equilibrium point for this model. What’s more, through the use of extreme value analysis model, government funds have been invested in real estate business building devotion principles and the construction base of the real estate businessmen has also been estimated successfully. This provides the corresponding theoretical basis for government macro control policy-making.
Keywords: Real Estate, Macro Control, Three-Dimensional Dynamic Model, Extreme Value Analysis
1. Introduction
Having a high correlation and a strong driving force, the real estate industry has become one of the pillar industries of the national economy. As the basic industry of society, the development of the real estate industry is not only directly related to the virtual economy and the bubble economy, but also closely related to the financial crisis. As a result of the failure of the real estate market, the real estate market itself isn’t able to guarantee the efficient allocation of resources. In order to achieve the needs of effective function of the economy, the government must carry out macroeconomic regulation to control the real estate market.
The so-called macro-control is that the government takes a series of economic measures including regulating and controlling the process of the Macroeconomic mainly through fiscal and monetary policy basing on the overall interests of the national economy, in order to achieve the macroeconomic objectives of the basic balance between the social demand and supply in total and so on.
A survey carried out by Sirmans and Worzala [1] underlines the emphasis given to the asset treatment of the housing investment. In the broader context of diversification of mixed asset portfolios, investment in real estate would try to offset the negative consequences of excessive concentration in equities, especially considering the relative correlation of equities’ prices in international financial markets. Modigliani [2] pointed out that although the credit merit plays an indirect role on the construction of the real estate in the mortgage market, but the conduction of monetary policy is mainly through the consumption of capital investment. Kling
and McCue [3] studied on the seasonal impact of macroscopically economic to office buildings and industrial constructions, and founded out that the output; the nominal interest rate and money supply shocks have a strong impact on the office buildings. Aoki et al. [4] founded that housing provides housing services to consumers and at the same time it also plays an indirect role in reducing the cost of borrowing, which magnifies the effect of impact on monetary policy of housing investment and housing prices via the research of the real estate market in the United Kingdom. As a result, it has a theoretical basis when studying how the monetary policy responding to the real estate price bubble basing on the conductive effect. Matteo [5] pointed out that the reverse of the currency has obvious negative effects on housing prices, what’s more, monetary policy and the impact on the demand of housing has played a significant role in bringing on the shortterm fluctuations in housing prices.
At present, China’s real estate market has long-term and stable relations [6], to the money supply, and monetary policy can affect real estate investment and real estate prices. Thus we can carry out macroeconomic regulation and control [7] by the means of the implementation of monetary policy to affect the real estate market. However, some academicians have put forward a different view, pointing out that the long-term money supply amount has limited ability to regulate and control [8] the real estate market. In this paper, according to economics of real estate and macro-control theory, combine with the characteristics of the real estate market and [9], macrocontrol of the real estate market is studied. Systematically established the model which is given by dynamic model of three-dimensional non-linear differential equations based on the total number of houses on the real estate business, the government's average housing investment funds and the standard price, which providing the corresponding theoretical basis for government macrocontrol policy-making.
2. Three-Dimensional Nonlinear Dynamic Model
The total number of real estate business building N(t) is a function of time t. D, T, C > 0 are respectively representing the average housing funds for the government’s investment, the standard of consumer prices and construction costs of the average housing of real estate businessmen; γ > 0 is the purchase value-added cost coefficient of customers, which is inversely proportional to value-added rate.
Assumptions:
1) Rate of the change of time of the N(t) has a positive linear relationship with government have invested funds and consumers purchase expenditures, while has a negative linear correlation with the real estate business costs.
2) If the total building number of real estate is more (or less), then the housing price standard should be lowered (or increased).
3) If the price standard is higher (or lower), then the government needs to fully consider the afford ability of housing consumers. At the same time, government should increase (or decrease) funds for housing construction to carry out reasonable regulation and control.
Government set a housing base Nm of the real estate business and also recent prices have a standard TM, with the foregoing assumptions, we have the following three
dimensional dynamic models of coupled nonlinear differential Equations about the total number of houses on the real estate business, the government’s average housing investment funds and the standard price.
where, δ, k > 0 are the proportional coefficient.
To model (1), through the application of Routh-Hurwitz criterion, the stability criteria [10], as well as value analysis, we can wait until the following conclusions occur. Theorem 1: When Nm > k/γ, the three-dimensional dynamic model of coupled differential Equation (1) has a stable equilibrium point
Fatherly, the government gives the building base which is the number of building of recent price standard to achieve maximum value (the largest consumer affordability) to the real estate businessmen. And also the expanding number of housing can be estimated as follows:
where, Dm > D* is the consumption level of moment tm.
Prove: due to the right side of Equation (1) equals to zero, easy to get the equilibrium point of Equation (1) as follows:
whose characteristic equation:
Due to γNm > 0, δkNm > 0, therefore, when Nm > k/γ, coefficients of Equation (5) need to be satisfied as follows:
Thus, according to Routh-Hurwitz criterion [10], all the characteristic roots of Equation (5) have a negative real part; then basing on the stability decision theory of differential equations’ equilibrium point[10], from which we get to know that the equilibrium point (5) is stable.
To prove the second conclusion, we use extreme discrimination of functions. Diction
of the real estate businessmen to expand the housing scale is
thus
Therefore, housing price standard in the base that the government gives is the number of housing when reaching the maximum number of standard input price. Finally, by
the first equation of the model (3) we can know:
Also by we can know, therefore
D(t) is monotonous reduced function. So we get, put it into
Equation (7) we will get the estimate total number of real estate after expanding housing, that is Equation (3).
Finally, due to the stability of the results, check on the limits of , then we
obtain the results that .
According to Theorem 1, the principle of government regulation and control of the building base of real estate is as follows: As long as the government determine the building base of real estate businessmen by reference to the great value of recent price standard (the maximum tolerance of consumers), then the size of buildings of the real estate businessmen will be stabilized at the base to expand the buildings, it is necessary to consider all aspects
about the government's housing investment, consumers’ hous ing afford ability and the price situation in the value-added.
If the tuition fee is higher (or lower), the government carry out macro-control by reducing (or increasing) in the construction funds of average, then the third Equation of model1 should be altered as follows:
Then, we get the corresponding three-dimensional dynamic model Equations as follows:
According to reference [10] which gives all the necessary conditions that the roots of all the algebraic equations have negative real part, we can prove that:
Theorem 2: The equilibrium point of model (9) is unstable.
According to Theorem 2, our evaluations of the actions of the government are as follows: in reality, there are some local government’s implementations of policies [11] that raising prices to replace part of the government’s investment in real estate investment funds because of lacking real estate investment funds. This is precisely the assumption conditions (7) of model (9). Therefore, under such conditions, the number of the building houses of real estate
is bound to be unstable. It will lead to bad housing order of real estate business, which is not conducive to the stability of the coordinated development of the real estate industry. Obviously it is undesirable.
3. Model Improvement
In order to avoid the uncertainty of the equilibrium point of model (5), we alter the absolute rate of change dT/dt and dD/dt with the relative rate of change 1 /dT* T/ dt and
1 /D * Dd / dt in the second and third Equation of model (1).Then, we can obtain the improved three-dimensional dynamic model of differential equations among the establishment
of the total number of houses on the real estate businessmen, the government's invested housing funds, and the housing standard as follows:
where, δ, k > 0 are the proportion coefficients. Through the application of Routh-Hurwitz criterion, the stability criteria [10], as well as value analysis, we can wait until the following conclusions occur.
Theorem 3: Three-dimensional dynamic model of coupled differential Equations (10) has the equilibrium point:
A necessary condition for the equilibrium point for Equation (10) stability is:
Fatherly, GDP to be expanded is estimated:
Prove: Because of the right side of Equation (11) is zero, we can obtain results easily that Equation (13) is the equilibrium point of Equation (12). The matrix for liberalized system of model (12) in Equation (13) is as follow:
According to [10], it gives a necessary condition that the roots of all the algebraic equations have a negative real part, thus a necessary condition for that the roots of all negative real part of algebraic Equation (13) is that all the coefficients of Equation (13) need to be positive, that
is,
From the above we can get conditions Equation (11), and then basing on the stability
equilibrium of equilibrium point [10]. We get to know that the Equation (11) to be set up is a necessary condition for equilibrium point Equation (8) to be stable. We can get estimates of GDP for the expansion of Equation (10) via the use of extreme value analysis of model function (5). End of proof.
Theorem 3 is of great significance in guiding the government macro-control. In fact, to achieve the scale of housing buildings of the real estate businessmen’s demand, house price standard and the stable equilibrium of government funds for each house, which must be requested that the government’s funding for each house is more than the house price standard (D* > TM); Moreover, when the increase in the cost of the purchase price is low (γ→∞. Hi gh rate of value-added), Real estate required by the Government to build the base can be controlled
within the framework of a larger range (It corresponds to the second condition of estimation Equation (13)).
Finally, we would also like to point out that, by Routh-Hurwitz criteria we can also obtain all the sufficient conditions for the department of negative real roots of Equation (14), but the conditions are very complicated and it’s inconvenient to take practical application of. Therefore, we will no longer to discuss it in detail in this paper. In addition, estimation Equation (13) is weaker than Equation (3).
4. Conclusions
In this paper, the main results are as follows:
1) The three-dimensional dynamic model of differential equations among the establishment of the total number of houses on the real estate business, the government’s housing funds are invested, the housing standard.
2) The stabilities of equilibrium conditions of each model are given.
3) Government determines the building base of real estate principles and the estimation of real estate businessmen’s building size.
4) These conclusions were used to analyze the government’s macro-control, which can provide references for the government departments of management decision- making.
For future research, we will take some numeric simulations to proof our theory.
5. Acknowledgements
This research was supported by the NUIEPC (Grant 081029018). The first author would like to thank the guidance of the second author Professor Shengwu Zhou at China University of Mining & Technology.
6. References
[1] C. F. Sirmans and E. Worzala, “International Direct Real Estate Investment: A Review of the Literature,” Urban Studies, Vol. 40, No. 5-6, 2003, pp. 1081-1114. [2] F. Modigliani, “The Channels of Monetary Pol icy in the Federal Reserve—MIT University of Pennsylvania Econometric model of the United States,” In: G. A. Renton, Ed., Modeling the Economy, Heinemann Educational Books, London, 1995, pp. 240-267.
[3] J. L. Kling and T. E. McCue, “Stylized Facts about I ndustrial Property Construction,” Journal of Real Estate Research, Vol. 6, No. 3, 1991, pp. 293-304. [4] K. Aoki, J. Proudman and G. Vlieghe, “House Prices, Consumption, and
Monetary Policy: A Financial Accelerator Approach,” Journal of Financial Intermediation, Vol.13, No. 4, October 2004, pp. 414-435.
[5] M. M. Iacoviello, “House Prices and the Macro Economy in Europe: Results from
a Structural VAR Analysis,” European Central Bank Working Paper No. 18, April 2000.
[6] J. Xu and X. Xiao, “Game Analysis on the Government and Developer Behaviors in the Process of Macro Control of Real Estate,” Journal of Chongqing Institute of Technology, Vol. 21, No. 8, 2007, pp. 34-36.
[7] X. F. Nie and C. Z. Liu. “A Practical Analysis on the Impact of Monetary Policy upon Real Estate,” Journal of Henan Institute of Financial Management, Vol. 23, No. 4, 2005, pp. 63-65.
[8] Y. J. Li and Y. Yang, “The Effect of Interest Rate and Money Supply Impose on Real Estate Investment: In China an Empirical Analysis,” Journal of Xi’an Institute of Finance and Economics, Vol. 18, No. 5, 2005, pp. 47-51.
[9] C. Hua, “Three Dimensional Dynamical Models for the Scale of Recruiting Students of universities, Government’s Devotion of Outlays and Standard of Tuitions with Applications to Governm ent’s Macroscopically Controls,” Journal of Chengdu University of Technology (Science & Technology Edition), Vol. 34, No. 6, 2007, pp. 657-660.
[10] Q. Lu, “Qualitative Methods and Bifurcation of Ordinary Differential Equations,” Beijing University of Aero nautics and Astronautics Press, Beijing, 1989.
[11] C. Hua, “Mathematical Models of Dynamical Prices for Sale of Commodity when the Prices Wave: Stability of Prices with Analysis of Macroscopic Adjustment and Control,” Chinese Journal of Engineering Mathematics, Vol. 24, No. 3, 2007, pp. 446-450.
三维非线性动态模型房地产宏观调控
作者：1.马丹、周胜武（中国，徐州，中国矿业大学，理学院）
2.吕浩金（中国，徐州，中国矿业大学，信息与电气工程学院）
文章来源：Scientific Research数据库
摘要
在本文中，根据房地产宏观调控的经济理论，结合房地产市场的特点，对房地产市场的宏观调控研究。

在给出三维非线性微分方程的动态模型的基础上的房屋总数的房地产企业，政府的平均住房投资基金和价格标准，系统地建立了该模型平衡点的稳定性条件。

更重要的是，通过极值分析模型的使用，政府已经投入的资金在房地产企业的建设投入原则和房地产商人建设基地也已成功估计。

这为政府宏观调控政策的制定提供相应的理论依据。

关键词：房地产，宏观调控，三维动态模型，极值分析
1.简介
具有高相关性和强大的驱动力，房地产行业已经成为国民经济的支柱产业。

作为社会的基础产业，房地产业的发展不仅是虚拟经济与泡沫经济直接相关，但也与金融危机密切相关。

由于房地产市场的失败，房地产市场本身不能够保证资源的有效分配。

为了实现经济的有效运行的需要，必须实行政府宏观调控对房地产市场调控。

所谓的宏观调控是政府采取一系列措施，包括经济调控宏观经济的过程主要是通过财政和货币政策对国民经济的整体利益为基础的政策，以实现社会的需求和供给总量等之间的基本平衡的宏观经济目标。

进行了一项调查，[ 1 ]强调了房地产投资的资产治理的重点。

在混合资产组合多样化的大背景下，房地产投资将试图抵消过度的消极后果集中在股市，尤其是考虑到在国际金融市场上的股票价格的相关性。

莫迪利亚尼[ 2 ]指出，尽管信贷的优点在抵押贷款市场的房地产建设起着间接的作用，但货币政策的传导主要是通过资本投资消费。

Kling和麦库[ 3 ]研究了宏观经济对写字楼和工业结构的季节性的影响，并建立了其输出；名义利率和货币供给冲击对写字楼的强烈影响。

青木等人。

[ 4 ]建立住房提供的住房服务的消费者，它在降低借贷成本也起到了间接的作用的同时，放大的住房投资和住房价格的货币政策效果的影响，通过对美国房地产市场的研究王国。

作为一个结果，它有一个在研究货币政策如何应对基于导电影响房地产价格泡沫的理论基础。

利玛窦[ 5 ]指出，货币的反对房屋价格明显的负面影响，更重要的是，货币政策对住房需求的影响也将对住房价格的短期波动起到了重要的作用。

目前，中国的房地产市场长期稳定的关系[ 6 ]，以货币供给，货币政策可以影响房地产投资和房地产价格。

因此，我们可以进行宏观调控[ 7 ]利用货币政策实施的手段来影响房地产市场。

然而，一些学者提出了不同的看法，指出长期的货币供应量有限的能力来调节和控制[ 8 ]的房地产市场。

在本文中，根据房地产宏观调控的经济理论，结合房地产市场
和[ 9 ]的特征，宏观调控房地产市场的研究。

系统模型采用基于房屋总数对房地产企业的三维非线性微分方程的动态模型，政府的住房的平均投资资金和价格标准，为政府宏观调控政策的制定提供相应的理论基础。

2.三维非线性动态模型
商业房地产建筑总数N（t）是一个时间T，D，T，C＞0分别代表政府投资的平均住房基金，对房地产的平均住房消费价格及建设成本标准商人；γ> 0是购房客户增值成本系数，即增值率成反比
假设：
1）的N的时间变化率（T）与政府之间存在着一种积极的线性关系已经投入资金和消费者的购房支出，而与房地产企业成本成负线性相关。

2）如果房地产建筑总数量更多（或更少），那么房价标准应该降低（或增加）。

3）如果价格水平越高（或低），那么政府需要充分考虑到负担得起的住房消费者的能力。

同时，政府应增加（或减少）的住房建设资金进行合理的管理和控制。

政府设立的房地产开发企业nm的房基地和最近的价格有一个标准的TM，与先前的假设，我们有以下的耦合非线性微分方程对房地产企业的房屋总数的三的三维动态模型，政府的投资基金和住房平均价格标准。

在这，δ，K＞0的比例系数模型（1），通过Routh-Hurwitz判据的应用，稳定的标准[ 10 ]，以及价值分析，我们可以等到以下结论发生。

定理1：当纳米＞K /γ，耦合微分方程的三维动态模型（1）有一个稳定的平衡
在此基础上，政府给基地建设是实现价值最大化，近期价格标准建筑的数量（最大的消费承受力）对房地产商人。

同时不断增加的住房可以估算如下：
在那里，DM＞D *是时刻TM消费水平。

证明：由于方程的右边（1）等于零，很容易得到方程的平衡点（1）如下：
其特征方程：
由于γnm＞0，δkNm＞0，因此，当纳米＞K / γ系数的方程（5）需要满足如下：
因此，根据Routh-Hurwitz判据[ 10 ]，所有方程的特征根（5）有一个负真正的部分；然后基于决策理论的稳定性微分方程的平衡点[ 10 ]，从我们知道，平衡点（5）是稳定的。

证明了第二个结论，我们使用极端歧视功能。

的房地产商人用语扩大住房规模，因此，在住房价格标准基地，政府给经济适用房的数量当达到最大数量的标准输入价格。

最后，通过对模型的第一个方程（3）我们可以知道：
的T（T）/TM我们可以知道DT/0DT，因此D（T）是单调的功能降低。

所以我们得到的把它放进方程（7）我们将得到的估计总人数的房地产扩大后的住房，这是方程（3）。

最后，由于结果的稳定性，检查（M）M D T D T D对T极限，那么我们获得的结果，M *。

D D根据定理1，政府的原则调控房地产的建筑基础控制如下：
只要政府确定参照房地产商建基地最近的价格标准的巨大价值（最大宽容的，那么消费者）建筑物的大小房地产商人将稳定在基地扩大的建筑，这是需要考虑的所有方面“政府的住房投资，消费者住房负担能力和价格情况增值。

如果学费高（或低），政府进行宏观调控的减少（或增加）在平均的建设资金，然后第三方程的模型应该修改如下：
然后，我们得到了相应的三维动态模型方程如下：
根据参考文献[ 10 ]提供了所有必要的所有的代数方程根的条件具有负实部，我们可以证明：定理2：模型的平衡点是不稳定的（9）。

根据定理2，我们的行为评价政府的如下：在现实中，有一些地方政府实施的政策[ 11 ]提高价格来代替政府的投资部分房地产投资基金由于缺乏房地产投资基金。

这正是假设条件（7）模型（9）。

因此，在这样的的条件下，房地产的建筑房屋的数量肯定是不稳定的。

这将导致不良的住房房地产经营秩序，这是不利于房地产业的协调发展的稳定性工业。

显然，这是不可取的。

3.模型的改进
为了避免平衡点的不确定性模型（5），我们改变改变DT的绝对速率DT与DD/DT随着改变1 DT的相对速率T/DT和1/DD，D/DT模型在第二次和第三次方程（1）。

然后，我们可以得到改进的三维微分方程在建立动态模型房子的总数房房地产商人，政府投资房地产基金，
和住房标准如下：
在这，δ，K＞0的比例系数。

通劳斯-赫尔维茨判据的应用，稳定性
标准[ 10 ]，以及价值分析，我们可以等到以下结论发生。

定理3：三维动态模型耦合差分方程（10）的平衡点：
一个必要条件，平衡点方程（10）的稳定性：
GDP是扩展的估计
证明：因为公式右侧（11）是零，我们可以得到结果，方程（13）是很容易的方程的平衡点（12）。

矩阵开放的系统模型（12）在方程（13）是遵循：
根据[ 10 ]，它给出了一个必要条件所有的代数方程的根具有负实部，从而一个必要条件，根代数方程的负实部（13）是所有方程的系数（13）要积分是
从以上我们可以得到状态方程（11），然后基于平衡稳定平衡点[ 10 ]。

我们知道，方程（11）到应设置的平衡点的一个必要条件方程（8）是稳定的。

我们可以得到的估计对方程的扩展（10）通过极端的使用模型的功能价值分析（5）。

最后的证明。

定理3政府指导具有重要意义宏观调控。

事实上，实现规模房屋的房地产商的需求，房子的价格标准和稳定的平衡点每一家的政府资金，必须要求政府的资助，每个房子以上房价标准（D * > TM）；此外，在购买价格成本的增加是低（γ→∞。

增值率高），房地产的要政府建立的基础是可以控制的在一个大范围的框架（它对应于估计方程的第二个条件（13））。

最后，我们还想指出，通过Routh-Hurwitz准则也可以得到所有的足够对于负实根部条件方程（14），但条件是很复杂的它不采取实际应用。

因此，我们将不再讨论它了纸类。

此外，估计方程（13）是弱方程（3）比。

4.结论
在本文中，主要研究结果如下：
1）差异的三维动态模型的总人数在方程的建立房屋上的房地产企业，政府住房基金投资，住房标准。

2）的每个平衡状态的稳定性给出了模型。

3）政府决定房基地建设地产原则和房地产商的估计建设规模。

4）这些结论被用于政府的分析宏观调控，可提供参考对管理决策的政府部门—制作。

未来的研究，我们将采取一些数值模拟为了证明我们的理论。

5.致谢
这项研究是由NUIEPC支持（批准081029018）。

第一作者要感谢第二作者中国矿业大学武周指导教授。

6.工具书类
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[ 2 ]莫迪利亚尼，“在货币政策的渠道美联储的麻省理工学院宾夕法尼亚大学计量经济模型的美国，”：G.A.兰顿，主编，建模的经济，心理教育书，伦敦，1995，pp. 240-267。

[ 3 ] J. L. Kling和T. E. McCue，“程式化事实的工业房地产建设，“房地产杂志研究，6卷，3号，1991，pp. 293-304。

[ 4 ] k.青木，J.曼和G. vlieghe，“房价，消费，与货币政策：金融加速器的方法，”金融杂志，十月13，4号，2004，pp. 414-435。

[ 5 ] M. M.亚科维耶洛，“房价与宏观经济在欧洲：从结构VAR分析结果，”欧洲中央银行工作了18号，四月2000。

[ 6 ] J.徐和X.肖，“政府的博弈分析在宏观调控的过程中，开发商的行为房地产，”重庆工学院学报，卷21，8号，2007，pp. 34-36。

[ 7 ]范聂和C. Z. Liu。

“在一个实际的分析货币政策对房地产的影响，”杂志河南金融管理学院，Vol. 23，No. 4，2005，pp. 63-65.。

[ 8 ] Y.J.李杨和Y，“加息的效果对房地产投资对货币供应：在中国的实证分析，《西安财经学院学报经济学，卷18，5号，2005，pp. 47-51。

[ 9 ] C.华，“三维动力学模型高校的招生规模，政府和学费标准的奉献
政府的宏观上的应用控制，”成都理工大学学报（自然科学版），34卷，6号，2007，pp.657-660。

[ 10 ]问：路，“定性分析方法和分支的普通微分方程，”北京大学航空航天出版社，北京，1989。

[ 11 ] C.华，“动态价格的数学模型销售商品的价格波动时，稳定性价格与宏观调控分析控制，“中国化学工程学报，卷24，3号，2007，pp. 446-450。