Download The Research on Government Financial Input Based on Sustainable Development

The Research on Government Financial Input Based on Sustainable
Development
ZHANG Rugen, XU Zheng
Heilongjiang Institute of Science and Technology, P.R.China, 150027
[email protected]
Abstract: This text studies government's financial input in environmental resources, sets up the
dynamic economic model of environmental resources value to the environmental resources of a country
by which we can get the physical quantity of environmental resources with the change law of time, and
provide its functional relation.. It has important meanings to predict the value trend of the environmental
resources, quantitatively portrays the human living space and development problem.
Keywords: environmental resources, government, model, willingness
1 Introduction
Along with the deteriorated environment, it has resulted a lot of consequences, such as urban air
pollution, the increase in the incidence of various diseases, the reduction of forest resources, the
expansion of desertification, the crisis of water resources and so on. There are many indications that, for
humans, to strengthen environmental protection and achieve sustainable development is imperative.
1.1 The Government's need for environmental input
Because resource objects do not have the market factors, so we can not analyze the value of the
environmental resources from the traditional values of items. While we can use the indirect observation
and indirect methods to value environmental resources. In the West, many scholars adopted the
referendum voting method, monetarizing environmental resources and directly asking questions to the
public , to make a "yes" or "no" answer, such as "Are you willing to pay x yuan to protect certain natural
beauty?"
1.2 The people's idea for environmental protection in China
In China, due to the traditional concept of the common people, "had nothing to do with an armchair" ,
when the environment is not very serious to impact people's livelihood, they will not concern the
environment resource issues let alone to "buy" it. There is a more important reason, our standard of
living is still at the end, the majority of people still at a level of relatively low demand. To enjoy the
environment is generally regarded as a "luxury" and even some people did not think of the enjoyment of
a better living environment. Even if they are aware of environmental degradation, living beyond their
income, they impossibly to pay their low income to protect the environment. Only a handful of top
people who have environmental awareness, such as government officials, intellectuals and scholars etc.
The Government's decision is rational and scientific, therefore, from the perspective of sustainable
development, it is necessary for the government to input on environmental. And we can value
environmental resources from the government point, that is, the government made the payment of action
after the rational decisions which standards for the prices of environmental resources.
2 Government investment model
2.1 The hypothesis of government investment
As environmental resources are different from general commodities, they can not circulate and exchange
in the market. Then we can assume that the market is in the condition of equilibrium at this time. That is,
the price of environmental resources is equal to the marginal implicit price, or equal to the marginal
willingness to pay. The government's investment decision is completely rational and democratic, in other
words, the government’s investment on the environmental resources represents the people's
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environmental preferences or requirements, then the government's annual expenditure in the
environmental field is the citizen’s willingness to pay on the environment.
2.2 To set up government investment model
The government’s input can be divided into two parts according to the input period. First, the input for
the new project, this part represents the people’s demand for new environmental goods. Assume that in
this period the physical quantities of the new environment input is q ti . Must be explained, the so-called
physical quantity refers to the indicators which can be used to measure the number of environmental
goods, such as the water area, the number of scenic attractions, the volume of air pollution, or the
maintenance area of forest and grassland and so on. Only in this way we can link the economics volume
and the environmental quality which two are not related.
Second, the additional investment for the scheme. Suppose the average period for completion is g , then
during the g year the government will have additional input according to the program. We assume
that the amount of annual investment is equal in the construction period. This part of investment has an
indelible contribution to the environment, but it does not belong to the people’s demand for new
environmental goods, so we must take the time value of money into account and record the discount rate
as r .
Let’s suppose in t i i = 1,2, L , n period government’s investment as f ti , the corresponding inputs
）
（
of the two parts as f 1,ti and f 2 ,ti . Additional inputs f 2 ,ti can be divided into phases, denoted as
1
follows: f 2 ,ti
、 f 、……、 f
f 2, t i = f
2
2 ,ti
1
2, t i
+ f
2
2 ,ti
g
2 ,ti
+L+ f
obviously:
g −1
2 ,ti .
But the contribution of their willingness to pay is not the same, the first phase of the willingness to pay
1
should be recorded as f 2 ,ti : the second phase of the amount of input money should be discounted to
its value: t
f 22,ti
1+ r
，……，the
g − 1 year shall be recorded as follows:
f 2g,t−i 1
(1 + r ) g −1
.
By the assumption of the equal investment of each period, we can obtain the following relationship:
 f 21,ti = f 1,ti −1

2
1
 f 2 ,ti = f 2,ti −1 = f 1,ti − 2

M
 M M
 f g −1 = f g −2 = L = f 1
2 ,t i
2 , ti −1
2 , t i − g +1 = f 1,t i − g

As the measurement of willingness to pay is not the same, we assume p (t i ) for t i period of people's
willingness to pay for environmental goods. Moreover, ∆p (t i ) = p(t i ) − p (t i −1 ) , using the theory of
the time value of money, we get the following relationships:
∆p (t i ) = f1,ti +
1
1
f 21,ti + L +
f 2g,t−i 1
1+ r
(1 + r ) g −1
∆p (t i )
= wq (t i ) .
∆t i
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Where, wq (t i ) stands for the price of environmental resources in t i period.
As the environment is not as safe as investment (of course apart from securities investments), so the risk
of environmental inputs is relatively large. This is mainly due to the characteristics of environmental
protection or environmental management, but also due to the current immaturity technological level of
environmental protection or management. So, in general, the chances of success of environmental
resources investment are not particularly large, it is easy to meet with "labor and no gain" situation.
Suppose probability of success as π , then there is a part of each year’s investment to remedy the
failure of previous years investment in environmental protection work. Record in t i year the total
investment on the environmental resources as f ti , the investment in the failure previous years as
f 3,ti .Then there is a relationship f 3,ti = (1 − π ) f ti .This part of the input does not mean people's
demand for environmental goods, obviously can not be measured as a part of the willingness to pay, at
best, only show that people are more interested in the project. Obviously, the there is the following
formula:
f ti = f 1,ti + f 2 ,ti + f 3,ti .
For the new physical quantities of the environment qti should be a marginal decrease, because, as the
work of environmental governance, the new project input is more and more difficult, and the risk
increases. The government may temporarily give up certain input to reduce the new demand of
environment. Of course, it also shows that under the condition of existing income, the people’s marginal
preference for environmental goods decline. Assume that the rate of change is inversely proportional to
with the existing volume of cumulative environmental resources, as follows:
∆q (t i )
λ
=
q (t i )
∆t i
Where, λ is a constant.
Therefore, from the government’s input in environmental resources, we can prospect people's
willingness to pay on the environment. We can create economic models as follows by the willingness to
pay to estimate the value of environmental resources.
Model (1) describes the government's input which can be measured as a differential model of the
variation of currency for the function of willingness to pay, as follows:
 f ti = f 1,ti + f 2,ti + f 3,ti

 f 3,ti = (1 − π ) f ti

 f1,t0 = f 0

 f 2, t 0 = 0
f = 0
 3,t0
(1)
Model (2) describes the changing law of the planned additional investment of money, which is to more
accurately measure the function of willingness to pay. Because the last input and the current input on the
same project are equal, we set up is a recursive differential model:
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 f 2,ti = f 21,ti + f 22,ti + L + f 2g,t−i 1
 1
 f 2,ti = f1,ti −1

2
1
 f 2,ti = f 2,ti −1 = f 1,ti − 2

M
 M M
 f gt−1 = f gt− 2 = L = f 1t
2, i
2 , i −1
2 , i − g +1 = f 1,t i − g

(2 )
Model (3) is based on the theory of time value of money, setting up the time-varying function of the
willingness to pay. Through the mathematical model we can obtain the marginal implicit price of
environmental resources, as follows:
∆p (t i ) = p (t i ) − p (t i −1 )

1
∆p (t i ) = ( f 1,t + 1 f 21,t + L +
f g −1 ) • ∆t i
g −1 2 ,ti
i
i
1
r
+
(1 + r )


 ∆p (t i ) = w (t )
q i
 ∆q

∆t i = t i − t i −1
(3)
Model (4) describes that the new physical environment quantity is inversely proportional to the existing
environment quantity:
λ
 ∆q (t i )
 ∆t = q(t )
i
i


q ( t ) = q
0
 0
λ = cons tan t
(4)
The solution wq (t i ) shall be the price of environmental resources in the t i period.
3 The valuation of environmental resources’ value of use
Now, the four models are solved.
Firstly, in the model (4), supposing ∆t i → 0 , we get a differential equation:
λ
 dq(t )
 dt = q(t )


 q ( 0) = q
0

λ = cons tan t
The solution is q (t ) = 2λ ⋅ t .
When we assume g = a constrain, joining model (1) and model (2), we get a third-order differential
equation:
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f1,ti − f1,ti − g +1 = f i + π ⋅ f i −1 + (1 − π ) f i −2
(5)
To facilitate the presentation, suppose ∆ g f1,ti = f 1,ti − f 1,ti − g + 3 . f 2 ,ti and f 2 ,ti can seek out from
1
2
the recursive relationship of model (2). Then we can conclude the function for the price of
environmental resources step by step
wq (t i ) =
=
( f 1,ti +
w q (t i ) =
∆p (t i )
∆q
∆q (ti )
∆ti
•
∆q (ti )
∆ti
1
1
f 21,ti +
f 22,ti ) ⋅ ∆t i
q (t )
1+ r
(1 + r ) 2
• i
∆t i
λ
Model (5) can be solved, and then substitute the solution into the formula above. But we can also use the
following mathematical process to avoid the g -order differential equations.
wq (t i ) = ( f 1,ti +
= ( f1,ti + f
1
2 ,ti
+f
q (t )
1
1
f 21,ti +
f 22,ti ) ⋅ • i
2
λ
1+ r
(1 + r )
q (t )
r 2 + 2r 2
r
1
f 2 ,ti −
f 2, t i ) ⋅ • i
−
2
1+ r
λ
(1 + r )
2
2 ,ti
n
For writing convenience,
∑∆
i=g
g
f1,ti will be taken out separately and calculated as follows:
n
n
i=g
i=g
∑ ∆ g f1,ti = ∑ ( f i + π ⋅ f i−1 + (1 − π ) f i−2 )
n −2
= 2∑ f i + f n + π ⋅ f n−1 + π ⋅ f 2 + (1 − π ) f1
i= g
n
Substitute
∑∆
i =3
f
3 1,t i
into equation (5) and we will get:
n− 2
wq (t i ) = (2∑ f i + f n + π ⋅ f n −1 + π ⋅ f 2 + (1 − π ) f 1 + f1,t3 + f1,t 2 + f1,t1
i=g
q (t )
r 2 + 2r 2
r
1
−
f 2,ti −
f 2 ,ti ) ⋅ • i
2
λ
1+ r
(1 + r )
Suppose R = π ⋅ f 2 + (1 − π ) f1 + f1,t3 + f1,t2 + f 1,t1 , it is clear that R is a constant.
r 2 + 2r 2
r
f 21,ti +
f 2,ti , so the price of environmental resources is:
1+ r
(1 + r ) 2
n− 2
q (t )
wq (t i ) = (2∑ f i + f n + π ⋅ f n−1 + R − δ ) ⋅ • i
δ =
i= g
λ
When r is smaller, δ will be a very small number, which can be neglected. As a result, we have solved
the function for the price of a country's environmental resources changing with time.
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4 Conclusion
In short, since more and more countries have became aware of the seriousness of ecological problems,
environmental resources will be a major factor in a national sustainable development strategy. And we
are also aware of the responsibility of government in strengthening environmental protection. Therefore,
the function of the relationship between the government environmental inputs and environmental value,
will have an important significance in predicting the value of environmental resources and taking a
timely action in the government's environmental policy.
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