J. Service Science & Management, 2010, 3, 369-372
doi:10.4236/jssm.2010.33043 Published Online September 2010 (http://www.SciRP.org/journal/jssm)
369
Study on Comprehensive Evaluation Model of
Commercial Housing Price-Rationalization
Yifei Lai, Yuanxin Wei, Haiyun Luo
School of Economics and Management, Wuhan University, Wuhan, China.
Received July 7th, 2010; revised August 10th, 2010; accepted September 12th, 2010.
ABSTRACT
In recent years, the prices of city commercial housing are soaring, causing wide attention of public and fierce discus-
sion about whether it is reasonable for the housing prices in China. This paper attempts to establish a method to meas-
ure housing price-rationalization. Firstly, the paper establishes rationalization evaluation system of housing price from
commercial housing price formation, residents’ endurance and coordination parity system. Then it selects an appropri-
ate standard ways to build affordable housing product evaluation criteria.
Keywords: Commercial Housing, Rationalization of Price, Comprehensive Evaluation
1. Introduction
Housing Industry is an important industry to promote
economy and social development. In recent years, the
price of commercial housing is soaring. Currently, there
is a fierce controversy about whether the commercial
housing prices are rational. Therefore, this paper attempts
to establish a measurement system to determine the ra-
tionality of housing price.
Most rational studies about commercial housing
mainly focus on two aspects: Firstly, according to bubble
of the real estate, we can judge whether the commercial
housing price is reasonable. Secondly, by choosing single
or multiple indexes, we can study rationality of commer-
cial housing price. Recently, the study about an index
system mainly centers on analysis of single or many in-
dexes. In a multiple criteria system, some indexes are
chose to measure the rationality. There are two kinds:
one results from formation of housing price, establish-
ment, bearing capability of residents, revenue and so
on[1]; another results from aspects of demand and re-
quirement, factors of influencing price, and demand and
requirement [2,3].
This paper is based on generalizing two kind of index
evaluation method to establish an integrated evaluation
model.
2. Index System and Determine the
Weight-AHP
AHP (Analytical Hierarchy Process) is proposed by
American operations researcher Satty. T. L in 1970s. AHP
basic steps are as follows:
2.1. Construction of Analytic Hierarchy
Firstly, we should decompose the complex problem into
single element. These elements should be divided into
several groups to form different levels according to the
relationship between these elements. At the top level
there is usually only one element, which is the general
target of the problem or the desired results. The middle
layer is always the criteria layer, and the lowest layer
includes the decision-making program. The dominant
relationship between the elements in different levels is
not necessarily complete.
According to the relevant information and practical
experience, author has selected some representative and
comprehensive indexes which can reflect each side of the
system, to finalize the evaluation index system of the
commercial housing price rationality.
1) Target layer A
The overall objective is whether the commercial hous-
ing price is rational.
2) Criteria layer B
Criteria layer includes three parts: the formation of
housing price, the affordability of residents and coordi-
nation of parity price.
3) Index layer
It includes: Ratio of commercial housing, Homeown-
ership rate, Housing Vacancy Rate, Ratio of Housing Price

Study on Comprehensive Evaluation Model of Commercial Housing Price-Rationalization 370
to Income, Housing expenditure ratio, Ratio of housing
price growth rate to it of income, Ratio of rent to housing
price, Ratio of housing price growth rate to it of retail
price, Ratio of housing price growth rate to it of GDP.
(Figure 1)
The ideal range of the indexes is shown in Table 1.
2.2. Structure the Judgment Matrix
After the establishment of the hierarchy, the relationships
of the elements between the upper and lower layers were
determined. In this step, decision-makers should repeat-
edly answer: For the guidelines Bk, which element is
more important between Ci and Cj, and gives this a cer-
tain mark. The formula for assignment can be directly
given by the decision-makers, or by analysis through
some kind of received advice. Generally, the expert fa-
miliar with the matter can give the weight according to
the 1-9 scaling law. (Table 2)
Figure 1. Rationality index system of chinese urban commodity housing.
Table 1. The ideal and rational ranges of the indexes in Figure 1.
Index Ideal range Max Min
Ratio of commercial housing 90%～100% 100% 45%
Homeownership rate 60%～70% 100% 30%
Housing Vacancy Rate 15%～30% 45% 7.5%
Ratio of house Price to Income 4～7 10.5 2
Housing expenditure ratio 20%～30% 10% 45%
Ratio of housing price growth rate to it of income 0～1.2 1.8 0
Ratio of rent to housing price 100～200 50 300
Ratio of housing price growth rate to it of retail price 1.2～1.5 2.25 0.6
Ratio of housing price growth rate to it of GDP 0～1.3 2 0
Target layer Reasonable degree of urban commercial housing price A
Coordination of parity
price B3
Ratio of rent to housing price C7
Ratio of housing price growth rate to it of retail price C8
Ratio of housing price growth rate to it of GDP C9
The affordability of
residents B2
Ratio of house Price to Income C4 Housing expenditure ratio C5
Criteria layer
Index layer
The formation of housing
price B1
Ratio of housing price growth rate to it of in- come C6
Ratio of commercial housing C1
Homeownership rate C2
Housing Vacancy Rate C3

Study on Comprehensive Evaluation Model of Commercial Housing Price-Rationalization 371
Table 2. 1-9 scaling law.
Significance level Cij
Concern the previous layer, Ci and Cj are equally important 1
Concern the previous layer, Ci is slightly important than Cj 3
Concern the previous layer, Ci is obviously important than Cj 5
Concern the previous layer, Ci is strongly important than Cj 7
Concern the previous layer, Ci is extremely important than Cj 9
Concern the previous layer, Ci is slightly less important than Cj 1/3
Concern the previous layer, Ci is obviously less important than Cj 1/5
Concern the previous layer, Ci is strongly less important than Cj 1/7
Concern the previous layer, Ci is extremely less important than Cj 1/9
The important scale between the two adjacent judgments 2,4,6,8,1/2,1/4,1/6,1/8
Structure the comparison matrix Cn
×
n:
11 121
21 222
12
n
n
nn
nn nn
CC C
CC C
C
CC C










  

2.3. Single-Level Sorting and Consistency Check
In theory, single-level sorting can come down to the cal-
culation of the characteristic roots and eigenvector of the
judgment matrix C. CW =

maxW, here,

max is the maxi-
mum characteristic root, and W is the corresponding
normalized vector to 
max. Wi is the component of W, it is
the weight.
We choose square-root method to calculate 
max and W.
Steps are as follows:
1) Calculate Mi, the product of each row elements of
matrix;


n
j
iji cM
1
, ni ,,2,1 

2) Calculate i W, the n-th root of Mi;
ni
iMW 
3) Normalization of the vector

T
n
WWWW ,,, 21   ;


n
j
j
i
i
W
W
W
1
Then

T
n
WWWW ,,, 21 
4) Calculate the maximum characteristic root 
max;


n
ii
i
nW
AW
1
max
)(
 ,
here, (AW)i is the i-th component of AW.
Then we calculate the consistency index:
1
max


n
n
CI

. Obviously, when the matrix is of full
consistency, CI = 0. And we also need to determine the
average and random index of the matrix, RI. For 1 × 1 to
10 × 10 matrix, RI is shown in Table 3.
When n > 2, the rate of CI to RI is called random con-
sistency rate of judgment matrix (CR), CR = CI/RI.
When CR < 0.1, the matrix is acceptable and has full
consistency. Or, proper modification is essential.
3. Weighted Comprehensive Evaluation
The linear weighted comprehensive evaluation can be more
comprehensive to evaluate the rationality of urban hous-
ing price, and can identify the priorities and weaknesses.
In addition, it gives a composite index which can reflect
the general information. This can make up the deficiency
of statistical indicator system.
Weighted comprehensive evaluation uses the individual
index standardized to multiply the corresponding weight
and then add to the overall evaluation.
%100
1
 
i
n
i
iAWA
Here, , A: the rationality index of housing price,
Wi: the weight of i-index, Ai: the rationality index of
i-index.
1
1



n
i
i
W
Accordingly, A∈[0,1]. If A = 100%, the commercial
housing prices are entirely reasonable; If A = 0, the hous-
ing prices are completely unreasonable. In this article, we
provides A = 60% as the critical point, that means urban
commercial housing prices is basically rational in China.
Table 3. Average random consistency index RI.
n123 45 6 7 8 9 10
R
I
00 0.580.91.121.26 1.36 1.411.461.49

Study on Comprehensive Evaluation Model of Commercial Housing Price-Rationalization 372
4. Conclusions
This paper establishes the integrated evaluation model of
urban commercial housing. The sorting of indexes are as
follows: Ratio of commercial housing, Homeownership
rate, Housing Vacancy Rate, Ratio of house Price to In-
come, Housing expenditure ratio, Ratio of housing price
growth rate to it of income, Ratio of rent to housing price,
Ratio of housing price growth rate to it of retail price,
Ratio of housing price growth rate to it of GDP. On one
hand, the results reflected the relative importance of the
factors which affect China’s commercial housing. On the
other hand, it reflects we should cut down housing prices,
increase income, and improve the affordability of resi-
dents of purchase currently.
REFERENCES
[1] G. F. Wen, “Observation about Housing Price,” Price
Theory and Practice, Vol. 4, 1998.
[2] Y. L. Zhao and H. Li, “Construction of City Housing
Price System,” Research about Engineering and Higher
Education, Vol. 23, No. 4, 2004, pp. 11-12.
[3] R. Y. Zhu and X. M. Li, “Positive Analysis about Rea-
sonableness of City Housing Price in the East of Our
Country,” China Consumption Price, Vol. 23, No. 4, 2008,
pp. 11-12.
[4] D. Du and Q. H. Pang, “Comprehensive Evaluation Me-
thod and Selective Case,” Tsinghua University Press, Bei-
jing, 2005.
[5] I. Greef and R. Haas, “Housing Prices, Bank Lending,
and Monetary Policy,” Financial Structure, Bank Behav-
ior and Monetary Policy in the EMU Conference, Gron-
ingen, 2000.
[6] J. R. A. Pozdena, “Testing for Bubbles in the U. S. Hous-
ing Market,” University of Oregon, 2006.
[7] J. M. Quigley, “Real Estate and the Asian Crisis,” Jour-
nal of Housing Economics, Vol. 10, No. 2, 2001, pp. 129-
161.