Preliminary Research on Urban Land Supply Control Model QIAO Rong-feng ， GAO Jin-yun ， and ZHANG An-lu College of Land Management ， Huazhong Agricultural University ， Wuhan ， P.R.China December 14,2007,HK Tel:

1.Introduction  Economy in China now is developing rapidly and the urbanization is increasing remarkably. In 1978, the level of the urbanization in China was about 18%, while in 2003 it nearly got to 41%.  Going with the rapid urbanization, the scale of city was also keeping expanding. In 2003, the area of cities had been reached km2, about 3 times than in 1978.

Fig.1 Urbanization and Build-up Area in China

 For a long time, the urban land supply in China showed that the land demand catered for its supply and its control was out of order.  Apparently research on the urban land supply mechanism will be helpful to establish reasonable urban land supply policy, and provide available references for promoting urban land efficient utilization.

 Simultaneously, controlling urban land supply has been one of the most important means by which our government controls the macro-economy.  Generally speaking, properly increasing the supply of the urban land first-grade market will promote the development of the real estate.

2.Reletive Research Review  Two main resources in urban land supply, the urban stocking land and the expropriation land(Lu,2004)  The urban land supply should keep a reasonable proportion to promote the forming of city ideal space based on the need of city development (Liu, 2002).  Established a mathematic model aiming at the city development fee and the confirmation of urban boundary on the urban land supply (Geoffrey K. Turnbull ， 2004).  However, few discussions to the urban land supply mechanism about China land market.

 At present, the urban land supply model is still a discussible issue with dispute. Through constructing control model, combining stability and controllability analysis, this paper makes preliminary discussion to the urban land supply mechanism in China.

3.The control model  3.1 simulation the land supply in China Collective land expropriation Available volume of urban land supply Urban stock land Directly Transferable land Redemptory land Land banking Assignment Actual volume of urban and supply Fig.2 Systematic Simulation Diagram of Urban Land Supply X1(k) X2(k) U(k) Y(k)Prop.α Prop.β Prop.θ

 3.2 control model According to the former simulation on land supply,at the time k,the control model can be written as follows, X1 (k ),X2 (k ) : State variable U(k) : Control variable α: directly transferred proportion of the total available supply land β: assignment proportion of banking land θ: redemptory proportion among the actual supply volume

transform this model,

Written as normal form for matrix, In the equations, I is the unit matrix.

4.Model analysis  4.1 model stability System stability At the beginning the system is in the balance state, then has been deviated from this state by external disturbance. If the disturbance removed, the system can get back to the initial balance state automatically. Control model stability When we remove the disturbance to the input, the output of the control model will converge to the initial stable state. Research on the land supply control model stability is very helpful for the land market supply control. 2 1

Model stability analysis Setting. 3 According to the cybernetics, the necessary and sufficient condition of gradually stability is that,all the absolute value of eigenvalues are not greater than 1.So, if the land supply system would reach the stability, the eigenvalue of systematic matrix should be smaller than 1. therefore, the matrix A eigenvalue of this model should meet the following equality, as the eigenvalue of the characteristic matrix A

We can get, Thereinto, <1-1 < Then we can conclude that, when the control model can reach the stable state.

On second thoughts we can reckon X(K) and Y(k), In the equation (4),we can find that X(K) consists of two parts,the first is the system response of its initial state;the second part is the response of the input. 21

So,based on We can get that when k is increased, the influence of initial state on the output of the system is smaller and smaller. When the urban land control model is satisfied with <1, the volume of the banking land and stock land under the initial state will have lesser influence on the urban actual supply land,which mostly influenced by expropriation land. a.the absolute value of matrix eigenvalues is less than 1 b.eqation (4)and(5)

controllability Output controllability analysis 4 Model controllability means that we can get the reasonable solutions if we let the output at time N equal to some certain value,for example,Y(N),then We can control the α,β,andθ,then equation(6) will have solutions.That is to say,we can predict the actual market land supply.

5.Conclusions Control land supply is the key to adjust the balance between land demand and supply ． Firstly ， the most important way to control the urban land supply in China is that government should rationally frame the amount of directly transferred land ， the banking land and the redemptory land ． If the urban land supply need to increase in the short period ， the amount of directly transferred land and the banking land should be enhanced appropriately ， which is equal to augment the parameter α and β ； contrarily ， the adjustment should be reverse ．

 Secondly ， the key of the urban land supply control lies on the land expropriation control which happens on the rural-urban fringe ． In response to the land output formula quantities of the urban land supply mainly rests with the land expropriation on the urban-rural fringe ．  Consequently ， in order to control city expansion ， government should strictly restrain land expropriation now ．