INTRODUCTION
In recent years, the nonfarm economy has been developing rapidly; it has made
important contributions to the farmers' income growth and employment. In 2010,
the farmers’ nonfarm income accounted for 62.3% of the rural family income
and the nonfarm income has become main source of farmers’ income. Besides,
the employment in township enterprises reached 158.93 million which accounted
for 38.4% of the total population of rural employment. But nonfarm economy has
caused serious environmental pollution. Now the environment problem in countryside
is becoming more and more serious. So, how to control the pollution in countryside
is very important. In order to solve the environmental problem in some areas,
the government has established industrial park to concentrate the pollution
enterprises and deal with pollution intensively. This study shows that the level
of dealing with the pollution is closely related to the number of manufacturers
in the industrial park. On the basis of the economic model of Reis
(2001), this study takes the proportion of polluting enterprise entering
the park among the whole ones as the concentration of polluting enterprise.
And the concentration is added into the model. This study analyzes its influence
on the optimal growth and environment.
The problem of rural environment pollution has caused much attention from all
sectors of society. The domestic research focuses on testing whether there is
Environmental Kuznets Curve between environmental pollution and economic growth.
Zhao et al. (2011) researched the relationship
using simultaneous equation model. It turned out that there was inverted U shaped
Kuznets Curve. Li et al. (2006) established
a model of per capita GDP and wastewater emission and showed that the economic
growth and environmental pollution complied with environmental Kuznets Curve
which was inverted U type. Xia (2011) showed that:
According to different samples and environmental indicators, the relationship
between the two may not meet environmental Kuznets hypothesis. Han
(2010) and Li et al. (2008) pointed out
that Environmental Kuznets Curve was an objective phenomenon rather than a law.
Foreign literature about the research on this aspect is relatively comprehensive.
A large number of researchers studied the way the environmental externalities
affect the economic optimum growth, environmental pollution and economic growth.
Furtherly, there are lots researches focusing on how to achieve a balance so
as to realize the optimal economic growth. Nielsen et
al. (1995) found a switch from a commandandcontrol regime toward pollution
charges may not only improve the efficiency of environmental regulation but
also raise growth without damaging the environment. Yi
et al. (2012) showed that investment in pollution abatement technology,
the preemptive effect damages option values to a significant degree, causing
investment to take place sooner than in either the singlefirm or the coordinated
case. Wang (2012) showed that the groundwater environment
in karst area may be protected by certain methods, namely developing ecological
agriculture, reducing the contamination, controlling pollution and developing
the monitoring network for groundwater. Withagen (1995)
found that optimal growth was not necessarily balanced and negative environmental
externalities reduced optimal longterm growth rates. Huang
and Cai (1994) showed: If there is a constant rate in consumption and abatement
expenditure, pollution stock will grow slowly. Criado et
al. (2011) showed if the technology progress rate of reducing pollution
was high enough; pollution would converge to a limited stable state. Reis
(2001) showed discovering a technology that eliminates pollution can increase
optimal growth. Masako (2008) showed if agents had
persistent habit stock and cared about their habit, more technological progress
is required for sustained economic growth. Byrne (1997)
showed that growth was dependent on technology improvements. Pollution growth
was higher in a decentralized economy and if environmental issues can be controlled
effectively, the economy would have positive steadystate growth.
In conclusion, foreign researchers mainly have studied the measures to reduce
pollution and improve economic growth. But the current studies do not take the
concentration ratio of polluting enterprise into consideration.
METHODOLOGY
This study added the concentration ratio of polluting enterprises to Optimum
growth model to study how it affects the environment pollution and the optimal
economic growth rate.
RESULTS
This study has concluded that when the growth rate of concentration ratio was
higher, the economic growth rate was higher and at this moment the environment
has less pollution.
THEORETICAL MODEL
Declaration about model and variable: This study built a simple optimum
growth model on the basis of the study of Ana Balcao Reis. Specifically, this
study used an AK technology. Then this study would make a description for all
variables. It takes U, A, C, K, P, D as utility, productivity, consumption,
capital, pollution, the weight of pollution on the utility, respectively. T
means the moment of polluting industries realize fully concentrated, similarly
V(K_{T}) means the value of utility from the moment of polluting industries
realize fully concentrated, ρ means the intertemporal discount rate. z
represents the index of concentration ratio and z∈[0,1]. The parameter
γ, p and λ represent that the concavity of utility function; probability
and shadow price of capital.
Model analysis: This study considers a closed economy. The utility of
the representative agent depends on per capita consumption C and on the flow
of pollution P. This study shows it using the following equation:
This study defines the production function as Y = AK and depreciation of capital
is zero. So:
This study supposes the flow of pollution is proportional to total production
at each moment. That is:
where, z measures the pollution effects of production. An increase in z means
a decrease in pollution. This study can understand z as an index of concentration
ratio of industries; the greater z means the higher concentration of polluting
industries.
If this study ignores pollution externalities, the optimal solution would mean
a constant rate of growth Aρ. This study assumes that Aρ>0, in
this case the economy has positive economic growth.
Now this study determines the optimal solution considering pollution. The solution
depends on the behavior of z. This study assumes increase of concentration allows
production to occur in a less polluting way. So, the production function is
always the same but the pollution implied by a given level of production decreases
with concentration increase. Continuous concentration increase means that the
index z increases at an exogenous constant rate 1/b F:
This study also considers a discontinuity in the process of concentration increase.
To formalize the possibility of polluting industries realize fully concentrated,
this study assumes that there is a constant probability p per unit of time of
realizing fully concentrated that allows producing without polluting.
Let, T be a stochastic variable that denotes the moment of the polluting industries
realize fully concentrated. In all moments after T the level of pollution is
0. This study assumes that the realization happens with probability pdt in the
interval dt. To determine the optimal trajectory for the economy this study
maximizes expected utility:
Let, v(K_{T}) be the value of the second term of (5). After T, for
all t, P = 0 so, the value of z is irrelevant. So:
The optimal solution means that at each moment after the realization C_{t}
= ρK_{t} and K and C grow at a constant rate Aρ So:
By the properties of the Poisson distribution and using condition 6, expected
utility can be expressed as:
Merging this type, the objective function can be rewritten as:
This study maximizes 8 in C subject to Eq. 2, 3
and 4 with given K_{0} and z_{0}. The current
value Hamiltonian is:
The necessary conditions are:
And the transversality condition:
The probability p enters condition 10 in two ways; first it increases the discount
factor; second it decreases the effect of a change in capital on its opportunity
cost. This last effect happens because an increase in capital increases pollution
but it also increases the stock of capital after the realization. So, the utility
increases after that moment, it was shown in condition 6.
These conditions characterize the optimal behavior before the realization of
fully concentrated. It was known that after the realization capital and consumption
grow at a constant rate Aρ. Now this study characterizes the optimal trajectory
and the steady state of the economy before realizing fully concentrated of polluting
industries.
For Aρ>F before the realization K, C and the level of production grow
at the constant rate F and the level of pollution is constant at the steady
state of the optimal trajectory. The shadow price of capital decreases at the
rate F. Taking this into account, conditions 2, 4, 9 and 10 imply that in the
steady state it must have:
From Eq. 2 and 4:
So:
From Eq. 2, 9 and 10:
So:

Fig. 1(ab): 
(a) Optimal trajectory and steady state of economy and their
changes when p increases for Aρ>F and (b) Optimal trajectory and
steady state of economy and their changes when p increases for Aρ<F 
According to Eq. 14 and 15, this study
makes the following phasediagram (Fig. 1). For Aρ>F,
the phasediagram in Fig. 1a shows that the system is saddlepath
stable, converging to the steady state described above, where the rate of growth
is F. Figure 1a shows that along the trajectory of convergence
to the steady state this study always has that C/K>ρ, implying that
the rate of growth of capital is smaller than Aρ.
For Aρ<F, Fig. 1b shows that K/a+bz converges asymptotically
to 0, implying that K is growing slower than z. C/K converges asymptotically
to ρ. The rate of growth of capital and consumption converge to Aρ,
the rate of growth when there is no pollution. Aρ<F means that the
pollution flow is decreasing exogenously at such a high rate that the optimal
solution converges to the solution for the economy with no pollution.
Pollution is proportional to K/a+bz, so, the behavior of K/a+bz shown in the
phasediagram is also the behavior of pollution. For Aρ>F pollution
increases or decreases until reaching the steadystate value, depending on the
initial value of K/a+bz being higher or lower than its steadystate value. For
Aρ<F, pollution decreases along the whole transition path.
An Increase in p: The probability p can be understood as the subjective
probability that polluters into industrial park. The government take appropriate
measures may increase the probability. The Fig. 1a and b
allow the study of what happens in such case. When p increases, the locus (C/K)
rotate to the right and C/K decreases for any positive K/a+bz in the whole optimal
trajectory. At any moment the stock of capital, K and Z are given. Thus, the
adjustment happens through a decrease in consumption at the moment of the increase
in the probability.
CONCLUSION
This study considered the factor of the environmental pollution in an economic
optimum growth model. And this study researched the influence of the concentration
ratio and the possibility on the optimal growth and environment. This study
showed the greater the possibility, economic optimal growth rate would be higher.
Also, this study have concluded that when the growth rate of concentration ratio
was higher, the economic growth rate was higher in the steadystate and at this
moment the environment has less pollution.
According to the analysis of the model, this study put forward the following
advices to improve the concentration ratio. First, government should raise people’s
environmental awareness. Second, build industrial park to improve the concentration
ratio of polluting enterprises. Third, because producers need cost to enter
the industrial park, as well as the various concerns after entering it, many
producers reluctant to enter it. The government should take appropriate measures
to encourage polluters into the industrial park. It is essential to lower the
entering threshold into the industrial park. At the same time, the rational
standard of punishments and subsidies should be established. The reasonable
system of regulations and laws about environmental management also need the
attention.
ACKNOWLEDGMENT
The National Social Science Fund Major Projects (07 and ZD045), the general
project of Ministry of Education of Humanities and Social Science (05jd790133).