Calculate and Forecast Shadow Price of Water Resources in China and Its Nine Major River Basins
Calculate and Forecast Shadow Price of Water Resources in China and Its Nine
Major River Basins*
Xiuli Liu1, Xikang Chen1，Jinghua Li2 ，Hongxia Zhang3
1.Institute of System Science, Academy of Mathematics and System Science, Chinese Academy of
Sciences, Zhongguancun East Road No.55, Beijing, 100080, China
2.Business School, China University of Political Science and Law, No.27 Fuxue Road, Changping
District, Beijing, 102249, China
3. School of Economics, Renmin University of China, Zhongguancun Street NO.59, Beijing, 100872,
China
Abstract Shadow price of water resources is an important reference to set water resources
price. In virtue of the extended input-output table on water conservancy for Chinese nine
major river basins, the shadow prices of industrial water and productive water in Chinese
nine river basins in 1999 are calculated for the first time on the academic meaning. Then
two nonlinear models that can be used easily to calculate the shadow prices of industrial
water and productive water are presented. Finally, the shadow prices of industrial water and
productive water in 2000 year price in China and its nine major river basins in 2020 and
2030 are forecasted.
Keywords Extended Input-Output Table on Water Conservancy; Shadow Price of Industrial
Water; Shadow Price of Productive Water; Nonlinear Model; Forecast
1. Introduction
China sustains 21 percent of world population with only 7 percent of world fresh water.
*
This research is funded by the president research fund of Academy of Mathematics and System
Science, Chinese Academy of Sciences, fund Number: K7500612F1 and National Natural Science
Foundation of China (Project No. 60474063)
Corresponding author：Xiuli Liu, Tel.:+86-13683244624; Fax:+86-010-62541823;E-mail address:
xiuli.liu@amss.ac.cn.
Calculate and Forecast Shadow Price of Water Resources in China 2
Per capita amount of water in China is only 2,185 cubic meters, which is less than one third
of the world even level. The space and time distribution of water resources in China is
extremely disequilibrium. Per capita amount of water in most of inshore cities is less than
500 cubic meters.
Contrast with water scarce, water is used in unreasonable structure and in low efficiency.
Water resources have been being badly polluted and wasted in China, which makes water
resources in more scarce state.
With the progress of industrialization, the population increase and more people pour
from rural area to urban area, the demand of water resources would increase greatly. The
conflict between water supply and demand become more and more conspicuous, which has
extremely restricted China even world economy and society development. The even loss of
industrial production value in China yearly is about 2000 hundred millions (Liu Ch. M.,
2000) .Some research revealed that the scarce of water in China would impact the security
of world grain (Brown, Lester R., 1994). So water along with grain and petroleum are
confirmed as strategic resources in China Eleventh Five-Year Plan.
The main factor that leads directly to this serious situation is unreasonable water
price. For a long time, the water price in China only includes water disposal cost which
account for small percent in water price. Water resource value, sewage disposal cost and
water zoology cost aren’t included (Zhao, J. H., 2006).
Water price should reflect water resource value. Then how to calculate water resource
value? Shadow price is a good index to scale it, which not only reflects the value of water
Calculate and Forecast Shadow Price of Water Resources in China 3
resource but also reveals the demand and supply situation of water resource. Many scholars
have tried to obtain the shadow price of water by solving a linear program (Huang, Y. X.,
1987; Jiang, W. L., 1998; Wang, D. X., Wang H. & Yin, M. W., 1999; Zhang, Q. SH., 1990).
Because it was difficult for them to decide the quantitative relationship between the water
resource and other kinds of resources, these authors obtained no rigorous shadow price for
water. There has been no shadow price of water on academic meaning.
In this paper, we combine extended input-output model on water conservancy with
linear programming to calculate shadow prices for industrial water and productive water in
Chinese nine major river basins in 1999. This is the first time to calculate water shadow
price on the academic meaning.
Here we define all the water used in industry as industrial water, all the water used in
productive activities included agriculture, industry and commerce as productive water.
Then we calculate the shadow price for industrial water ( IP ) and productive water ( PP ).
Under the support of the Ministry of Water Resources of the People’s Republic of
China, Academy of Mathematics and Systems Science constructed the extended
input-output tables with assets on water conservancy for the nine major river basins of
China in 1999 (Chen X., Yang C.,& Xu J., 2002). One of the important characteristics of
the table is that it vertically included two parts, input part and asset occupancy part
(holding and using of assets part). The asset occupancy part includes fixed asset, circulating
capital (inventory and financial assets), employee and water resource, including fresh water,
surface water, groundwater, recycled water, and total used water (in physical units). The
Calculate and Forecast Shadow Price of Water Resources in China 4
amount of water used by each sector is listed in the table, from which we can deduce the
quantitative relationship among water resources and all other resources in the national
economy system.
River basins in China are usually divided into nine, which are Southeast Rivers
basin(SE); Zhujiang River basin(ZH); Yangtze River basin(YT); Southwest Rivers
basin(SW); Huaihe River basin(HA); Songhuajiang and Liaohe Rivers basin(SL); Inland
Rivers basin(IL); Yellow River basin(YE) and Haihe and Luanhe Rivers basin
(HL)(http://www.webmap.cn/basicmap/index.php?&embeded=&map=shuixi_liuyu1).
There has previously been no extended input-output table on water conservancy for Chinese
nine major river basins in the world. The tables have 51 sectors, including 12 water
conservancy sectors (Appendix 1). Using these tables, we can research not only water use
and water pollution, but also water-conservancy and water-protection measures.
In the following contents, part 2 gives the linear programming and its dual programming
to obtain the industrial water shadow price ( IP ) and productive water shadow price ( PP )
of nine major river basins. Part 3 gives the results of the dual programming and makes
some explanations and analysis to the results. Part 4 is factor analysis. Part 5 presents a
kind of nonlinear model to calculate PP and IP . Part 6 forecasts the shadow prices of
industrial water and productive water in China and its nine major river basins in 2020 and
2030.
2. Linear Programming Model
The objective function is:
Calculate and Forecast Shadow Price of Water Resources in China 5
n
max(  a vj X j )
(1)
j 1
subject to：
AX  Y  U  V  X
(2)
Xl  X  Xh
n
a
j 1
wj
(3)
Xj w
(4)
Uh U 0
(5)
V h V  0
(6)
Y Yl
(7)
U  V
i
i
C
(8)
where: X is column vector of total output； a vj is the value added coefficient of sector j；
A is the direct input coefficient matrix； Y is column vector of final demand； U is
column vector of exports；V is column vector of imports； X l and X h is the lower bound
and upper bound of X ； a wj is the water-used coefficient of sector j; w is the total
amount of water that can be used in the period; U h is the upper bound of U ; U i is the
export of sector i; Vi is the import of sector i; C is the lower bound of the net export.
In above model w is different with the total amount of water resource which is the sum
of surface water resource and ground water resource without overlap of them. Generally
the total amount of water that can be used in a period ( w ) is only a small part of the total
amount of water resource (it is about18% in 1999), because the most water resource cannot
be used for the natural and ecological cause. The above (1)-(8) equations are the primal for
Calculate and Forecast Shadow Price of Water Resources in China 6
costs, but the shadow price is calculated from the following dual equations:
Min (  S 3 X l  S 4 X h  S 5 w  S 6 Y l  S 7 U h  S 8V h  S 9 C )
(9)
subject to：
S 1 (A  I)  S 2 (I  A)  S 3  S 4  AwT S 5   AvT
(10)
S1  S2  S6  0
(11)
S 1  S 2  S7  I T S 9  0
(12)
 S1  S2  S8  IT S9  0
(13)
S 1  0,S 2  0,S 3  0,S 4  0,S 6  0,S 7  0,S 8  0,S 9  0
In equation (10), AwT  ( a w1 , a w 2 , , a wn ) , AvT  ( a v1 ,a v 2 , ,a vn ) , I T  ( 1,1,1 )T ， S
is the shadow price of corresponding factor, and S 5 represents the shadow price of water.
The linear programming model constrains the input-output analysis by the upper and
lower bounds of total output, the total amount of water that can be used in the period, the
upper bounds of exports and imports, the lower bounds of final demand, the lower bounds
of net exports, and the maximum added value from sector 1 to sector n.
3. Results of the Dual Model
IP and PP for each river basin can be got from the dual solution. For example, in
order to obtain the shadow price of productive water for southeast river basin in
China PPSE , we include all production sectors 1-51 (Appendix 1) in the extended
input-output tables on water conservancy for the southeast river basins in above model. To
calculate the shadow price of industrial water for southeast river basin in China IPSE , we
include only industrial sectors 2-25, and 47-49 (Appendix 1) in the extended input-output
Calculate and Forecast Shadow Price of Water Resources in China 7
table on water conservancy for the southeast river basins in China in above model. Put the
associated data in the extended input-output table on water conservancy to (9)-(13)
equations, use Matlab software and we will get PPSE and IPSE . In the same way, the
shadow
price
of
water
for
the
other
river
basins
can
be
PP  ( PPSE , PPZH , PPYT , PPSW , PPHA , PPSL , PPIL , PPYE , PPHL )T
got.
Thus
and
IP  ( IPSE , IPZH , IPYT , IPSW , IPHA , IPSL , IPIL , IPYE , IPHL )T are obtained. The calculated
results of IP and PP are listed in Table 1. The ratio of the amount of water used to the
total amount of water resource RW is also included in Table 1.
This is the pioneer research in calculating the water shadow price for Chinese nine major
river basins on the academic meaning. There has no industrial and productive water price
for nine major river basins in China. Based on the data of 1999 industrial tap water price,
1999 industrial non-tap water price and the ratio of amount of industrial tap water on the
total amount of industrial water, the actual 1999 industrial water price of nine river basins
is estimated (in Table 1).
Table 1 reveals that, first, IP is higher than PP in each river basin, because the most of
productive water is agricultural water which price is free or very low. In the last decades,
about 70 percent of Chinese water resources were used in agriculture. The statistics reveal
the even price of water set for agriculture is only 1.98 fens every cubic meter.
Second, IP is much greater than the actual industrial water price in each river basin.
For example, the IPHL is 5.13 RMB per ton, but the actual industrial water price of the
basin is only 1.50 RMB per ton. This suggests the actual industrial water price in China
Calculate and Forecast Shadow Price of Water Resources in China 8
should be increased.
Final, the rank order of the river basins according to PP , IP and RW are similar.
PPSE and IPSE are both the lowest; PPHL and IPHL are both the highest. This can be
seen clearly in Figure 1.
4. Factor Analysis
Using the ratio of the amount of water used to the total amount of water resource ( RW )
as an index, the source that leads to the differences in PP and IP is analyzed. As is to be
expected, the correlative coefficient between RW and IP in Table 1 is 0.9306, between
RW and PP is 0.8568. The high correlation of RW with PP and IP reveals that
RW is a potential candidate to explain the phenomenon that PP and IP are different in the
nine river basins.
5. A Kind of Nonlinear Model to Calculate PP and IP
The extended input-output table on water conservancy in China is rare. To construct the
table is a labor-consuming work. The applied extend of model (1)-(13) is very limited. We
need to find other kind of model to calculate water shadow price conveniently. Using a
Gauss-Newton nonlinear simulation on the basis of the data in Table 1, letting RW be an
independent variable, the quantitative relationship between PP and RW , IP and RW can
be obtained. The nonlinear function of PP is as follows,
PPj

0.7962
(5.1294)

R 2  0.8841, F  25.0538
2.2113 * ln( RW j
(5.0054)

0.6023)
(3.4678)
(14)
Calculate and Forecast Shadow Price of Water Resources in China 9
The nonlinear function of IP is:
IPj

 0.7592
( 3.0364)

6.2605 * ln( RW j
(7.4981)

1.0581)
( 4.6879)
(15)
R 2  0.9430, F  56.22
From functions (14) and (15) we know that PP and IP increase as RW increases,
but IP increases more quickly than PP . Given RW , using (14) and (15) we can obtain
PP and IP easily.
6. Forecast Shadow Price of Water Resources in China and its Nine River Basins in
2020 and 2030
In the Eleventh Five-Year Plan of China, the GDP of 2020 year will be quadruple to that
of 2000, which will need much more water than before to realize the goal. In the ‘Strategic
Research on China Water Resources Continual Development in 21 century’ (2002) presided
by Qian Zhengying and Zhang Guangdou academicians, attended by 43 academicians and
almost 300 experts, it is forecasted that water used pinnacle will appear before or after year
2030 in which China population will be 1600 million, the amount of water yearly used will
be 70000 to 80000 million cubic meter. It is necessary and urgent to forecast PP and
IP in 2020 and 2030 of the whole country and nine river basins to ensure water supply in
accordance with society and economy development.
With the amount of water used and the total amount of water resources data from year
1998 to 2004 published by China Water Resources Bulletin, yearly data of RW for the
whole nation and nine river basins from 1998 to 2004 can be got by division method easily
Calculate and Forecast Shadow Price of Water Resources in China 10
(See Table 2).
Based on the time serial data of RW in Table 2, referred to some results of Water
Resources for China’s Sustainable Development Item Group of Chinese Academy of
Engineering (2002) and Song, J.J., ZHANG, Q.J. and Liu, X.Q.(2004), RW of the Whole
Nation and nine River Basins in Year 2020 and 2030 are forecasted. Use model (14) and
(15), IP and PP in 1999 year price for the Whole Nation and nine River Basins in Year
2020 and 2030 can be calculated, then transferred them in 2000 year price, finally adjusted
results with expert method (Results see Table 3).
All IP and PP of nine river basins in 2020 and 2030 in Table 3 is bigger than those of
1999. IP and PP of Haihe and Luanhe Rivers Basin are both the highest in those of nine
river basins, which is the same as the results of 1999. IP and PP of Huaihe River Basin is
the second highest in those of nine river basins in 2020 and 2030, which was the third
highest in 1999.
This reveals, first water scarce situation will be more serious in the near future. Second,
the Haihe and Luanhe Rivers Basin will still be the scarcest of water. Third, China should
strengthen water resource management in Huaihe River Basin. Forth, China government
should take actions to set reasonable water price based on water shadow price, by which to
lead water used efficiently, economically and adjust water resource distribution in the
whole country indirectly.
7. Conclusions
Calculate and Forecast Shadow Price of Water Resources in China 11
The paper calculates water resources shadow price on academic meaning for the first
time. Further more provides two nonlinear models which can be used to calculate shadow
price of industrial water and productive water easily. Then the paper forecasts the shadow
price of industrial water and productive water in 2000 year price for the whole China and
its nine river basins in 2020 and 2030. These are very important tools and references for
setting reasonable water price in China.
Acknowledgements
The authors thank the anonymous referees for comments and valuable suggestions on an
earlier version of this paper.
References
Brown, Lester R.(1994).2030 ,Who Will Feed China? World Watch, September /October.
Chen X., Yang C., Xu J. (2002). Water conservancy economy input-occupancy-output table
of China and its application. International Journal of Development Planning Literature,
17, pp.19–28.
Huang, Y. X. (1987) Expense-Benefit Analysis. Shanghai: Tongji University Press.
Jiang, W. L. (1998). Theory of Water Value. Beijing: Science Publishing House.
Liu Ch. M.( 2000-8-16), China sustainable development and water resources reasonable
use, China Water Resources News , the 3rd Version.
Song, J.J., Zhang, Q.J.,& Liu, X.Q.(2004). Analysis of Safety Factors of Water Resources
in China in 2020 and Strategic Suggestions. China Water Resources, 9, pp.14-17.
Calculate and Forecast Shadow Price of Water Resources in China 12
Wang, D. X., Wang, H. & Yin, M. W. (1999). Water resource, water resource value, water
resource shadow price. Water Resource Evolution, 10, pp.195-200.
Water Resources for China’s Sustainable Development Item Group of Chinese Academy of
Engineering (2002). Comprehensive Report of Strategy on Water Resources for
China’s Sustainable Development. China Water Conservancy and Hydroelectric Power
Press.
Zhang, Q. SH. (1990). The economic meaning of shadow price and its application. Jilin
University Social Science Transaction, 10, pp.14–18.
Zhao, J. H.(2006-8-22). China water price market make some progress, water used amount
decreased continually, China News Net.
Appendix 1: Sector Classification of the Extended Input-Output Tables on Water
Conservancy for the Nine Major River Basins in China. There are 39 non-water
Conservancy Sectors:
1 Agriculture (excluding freshwater fish farming and ecological forest)
2 Coal mining and processing
3 Crude petroleum and natural gas products
4 Metal ore mining
5 Non-ferrous mineral mining
6 Manufacture of food products and tobacco processing
7 Textiles
8 Clothing, leather, furs, down and related products
Calculate and Forecast Shadow Price of Water Resources in China 13
9 Sawmills and furniture
10 Paper and products, printing and recording medium production
11 Petroleum processing and coking
12 Chemicals
13 Nonmetal mineral products
14 Metal smelting and pressing
15 Metal products
16 Machinery and equipment
17 Transport equipment
18 Electric equipment and machinery
19 Electronic and telecommunications equipment
20 Instruments, meters, cultural and office machinery
21 Maintenance and repair of machine and equipment
22 Other manufacturing products
23 Scrap and waste
24 Electricity, steam, and hot-water production and supply (excluding hydroelectric power)
25 Gas production and supply
26 Construction (excluding water conservancy construction)
27 Freight transport and warehousing (excluding river freight transport)
28 Post and telecommunications
29 Wholesale and retail trade
Calculate and Forecast Shadow Price of Water Resources in China 14
30 Dining and drinking places
31 Passenger transport (excluding river passenger transport)
32 Finance and insurance
33 Real estate
34 Social services (excluding wastewater treatment)
35 Health services, sports, and social welfare
36 Education, culture and arts, radio, film, and television
37 Scientific research
38 General technical services (excluding management on water conservancy and water
ecological environment protection [non-construction])
39 Public administration and other sectors
There are 12 water conservancy sectors:
40 Construction of flood and drought control
41 Management of flood and drought control
42 Construction of ecological water environment protection
43 Ecological water environment protection (non-construction)
44 Wastewater treatment
45 Construction of water supply and comprehensive use projects
46 Management of water supply and comprehensive use projects
47 Agriculture and rural household water supply
48 Urban and industrial water supply
Calculate and Forecast Shadow Price of Water Resources in China 15
49 Hydroelectric power
50 River transport
51 Freshwater fish farming
Table 1. PP , IP , RW and actual industrial water price
for Chinese nine river basins in 1999
1999 industrial water price
IP
PP
River basin
(RMB/ton) (RMB/ton)
( RMB/ton)
RW
Southeast Rivers Basin (SE)
0.14
0.18
0.02
0.14
Zhujiang River Basin (ZH)
0.19
0.24
0.03
0.22
Yangtze River Basin (YT)
0.15
0.25
0.03
0.22
Southwest Rivers Basin (SW)
0.02
0.18
0.04
0.15
Huaihe River Basin (HA)
0.43
0.77
0.33
0.44
Songhuajiang and Liaohe Rivers Basin (SL)
0.45
1.60
0.57
-
Inland Rivers Basin (IL)
0.37
2.10
1.12
0.83
The Yellow River Basin (YE)
0.64
3.55
2.15
1.03
Haihe and Luanhe Rivers Basin (HL)
1.57
5.13
2.34
1.50
The data comes from: National Economy and Trade Commission: The statistics for some kinds of water price
of 378 cities in China in 1999, http://www.cnwaternews.com/news/sjxx/, China Daily of Water Supply and
Water Saving, http://news.xinhuanet.com/zhengfu/2004-08/05/content_1716520.htm, etc.
Table 2.Yearly Data of RW for the Whole Nation and its nine River Basins from 1998 to
2004
District
1998
1999
2000
2001
2002
2003
2004
The Whole Nation
0.16
0.20
0.20
0.21
0.19
0.19
0.23
Southeast Rivers Basin (SE)
0.12
0.14
0.15
0.15
0.14
0.20
0.25
Zhujiang River Basin (ZH)
0.16
0.19
0.19
0.14
0.16
0.24
0.24
Yangtze River Basin (YT)
0.13
0.15
0.17
0.20
0.15
0.17
0.21
Southwest Rivers Basin (SW)
0.01
0.02
0.02
0.02
0.02
0.02
0.02
Huaihe River Basin (HA)
0.40
1.02
0.45
1.03
0.87
0.26
0.74
Songhuajiang and Liaohe Rivers Basin (SL)
0.22
0.45
0.44
0.42
0.41
0.31
0.35
Calculate and Forecast Shadow Price of Water Resources in China 16
Inland Rivers Basin (IL)
0.35
0.37
0.38
0.36
0.39
0.44
0.46
The Yellow River Basin (YE)
0.58
0.64
0.69
0.77
0.82
0.43
0.59
Haihe and Luanhe Rivers Basin (HL)
1.20
2.22
1.48
1.96
2.51
1.17
1.23
Data Source: 1998-2004 China Water Resources Bulletin, Beijing: the ministry of water resources of the
People’s Republic of China press
Table 3. Forecasted Results of RW , IP and PP in 2000 year price for the Whole China
and its nine Major River Basins in Year 2020 and 2030
2020
RW
District
IP
(RMB/ton)
2030
PP
RW
(RMB/ton)
IP
(RMB/ton)
PP
(RMB/ton)
The Whole Country
0.23
4.26
2.08
0.24
5.61
2.67
Southeast Rivers Basin (SE)
0.25
2.26
1.14
0.26
3.25
1.61
Zhujiang River Basin (ZH)
0.24
2.21
1.11
0.26
3.18
1.58
Yangtze River Basin (YT)
0.21
1.91
0.96
0.23
2.80
1.40
Southwest Rivers Basin (SW)
0.02
0.98
0.51
0.02
1.32
0.78
Huaihe River Basin (HA)
0.75
5.72
2.72
0.78
7.42
3.43
0.35
3.13
1.56
0.38
4.34
2.12
Inland Rivers Basin (IL)
0.46
3.99
1.96
0.46
5.39
2.58
The Yellow River Basin (YE)
0.60
4.86
2.34
0.63
6.42
3.02
Haihe and Luanhe Rivers Basin (HL)
1.32
8.01
3.67
1.39
9.99
4.45
Songhuajiang
and
Liaohe
Rivers
Basin(SL)
Calculate and Forecast Shadow Price of Water Resources in China 17
6
5
4
RW
IP( RMB/ton)
PP( RMB/ton)
3
2
1
0
SE
ZH
YT
SW
HA
SL
IL
YE
HL
Figure 1. PP , IP and RW for Chinese nine major river basins in 1999