Jinqian DENG，Kangkang SHAN，Yan ZHANG

School of Economics and Management，Southwest University，Chongqing 400715，China

1 Introduction

The rural fundamental and productive fixed-asset investment can improve agricultural comprehensive production capacity，reduce natural risks of agricultural production as well as increase agricultural production and operation efficiency and household business income of rural residents；meanwhile，the increase of agriculture production and operation efficiency yields crowding-out effect on agricultural production labors，expands farmers' career selection channel and increases wages income of rural residents；furthermore，rural fixed-asset investment can improve rural investment environment，especially the improvement of location and reduction of logistics cost，guide non-agricultural production elements flowing into the rural with its economic externality；in the meantime，the increase of new agricultural production and operation entities can activate the capitalization and securitization of rural＂three rights＂elements and benefits the increase of farmers' property income.

It has been proven in theoretical circle that rural fixed-asset investment can make active effect on the increase of farmers' income（De Long.J.B，Summers，1992［1］；Hertz＆Tom，2009［2］；Mo Lianguang，Chen Guangyan，2008［3］；Kong Rong 2009［4］；Wang Yongde，Wen Chunling 2010［5］et al）.Under a certain rural fixed-asset investment scale，to judge the effect degree of rural fixed-asset investment on farmers' income and its optimal efficiency，the practice is to analyze if the gross scale of rural fixed-asset investment complies with its optimal amount boundary set by farmers' income increase based on the gross scale of rural fixed-asset investment.According to classic economic theory，when gross scale of rural fixed-asset investment is closer to objective demand of farmers' income increase，the effect of rural fixed-asset investment on farmers' income increase will be more effective；and vice versa.Therefore，it is unacceptable that rural fixed-asset investment amount is more or less than optimal investment amount required by the realization of farmers' income increase theoretically.Based on this，the article will test and measure the optimal boundary of the effect of rural fixed-asset investment on the changes of farmers' wages，operation and property income，especially the rural fixed-asset investment scale required by the development of rural new production and operation entities and the establishment and improvement of modern agricultural system，and discuss how to realize this optimal investment scale by using econometric model.

2 The evaluation of optimal scale of rural fixed-asset investment from the perspective of farmers' income increase

He Zhenguo has（2006）［6］evaluated the optimal scale of expenditure for supporting agriculture offered by China's finance，and this article will evaluate the optimal scale of rural fixed-asset investment making influence on farmers' income by utilizing its analysis thought.To ensure the accuracy of research，assume that the function expression of farmers' income is as follow

where I refers to rural per capita net income，A means rural fixed asset investment，and X indicates other control variable.The derivation about time t against the functions at the both sides of formula（1）is as follow

For other control variable X in formula（1），we choose rural economic development index（D）and agricultural employment index（N），thus obtaining that the control variable X has the following functional relation：

Meanwhile，the derivation about time t against the functions at the both sides of formula（3）is as follow：

Putting formula（4）into formula（2）will obtain：

To find out income flexibility of all elements obviously，we will continue to transform formula（6）and obtain the following formula

According to classic marginal theory，when MPI＝1，the rural fixed-asset investment scale can achieve the optimum，i.e.marginal cost of rural fixed-asset investment equals to its marginal revenue against farmers' income increase.MPI＞1means the rural fixed-asset investment is insufficient，adding rural fixed-asset investment will be effective on farmers' income increase；and when MPI＜1，rural fixed-asset investment is excessive，so the adjustment of rural fixed-asset investment structure should be strengthened.Only when MPI＝1，the optimal effect of rural fixed-asset investment on farmers' income increase can be achieved，and the efficiency of rural fixed-asset investment can be maximized.Other scales are unacceptable theoretically（Fig.1）.Based on the rules of marginal theory，we can evaluate the optimal scale of rural fixed-asset investment from microcosmic perspective of farmers' income，and add trend term and trend quadratic term（denoted by t and2）into the model considering the effect of other neglected factors on farmers' income（Liu Zhuojun，Yu Changge2006）［7］.The following evaluated basic model can be obtained：

Fig.1 Marginal income and optimal scale of rural fixed-asset investment

Considering the availability of data when selecting evaluation index，and using rural per capita net income index to denote farmers' income level（I）；the raw data of rural fixed-asset investment amount（A）can be found in statistical yearbook，and we will make per capita treatment on rural fixed-asset investment here；use per capita GDP of the first industry to denote rural economic development level（G）；and the number of employed persons of the first industry to denote agricultural employment level（N）.See Table 1 for relevant data.

Table 1 Basic data of relevant indexes such as farmers' income

According to the data required by model evaluation，we process the raw data and remove the effect of price factor，and then recalculate the raw data，and the observation value fitting our specific need is obtained as shown in table 2.

Base on the researched econometric economic model，we conduct OLS evaluation on formula（9）by using eviews6.0 software and data in Table 2 and obtain the following results.

Table 2 Relevant data of rural fixed-asset investment scale and farmers'income

Table 3 OLS evaluation result of farmers' income equation

Inspection results show that the goodness of fit of regression equation is good，the adjusted coefficient of determination stands at 0.6776 and the explanatory variable has stronger explanation ability on explained variable；the regression coefficient of rural fixed-asset investment is significant，and the overall significance level of explanatory variable is also higher.The regression evaluation value of the equation can reflect well the changes of rural per capita net income basically（Fig.1）.The influence coefficient of rural fixed-asset investment on farmers' income is 0.763 5，which indicates that rural fixed-asset investment has significant positive effect on farmers'income，and a 1%increase of rural fixed-asset investment can make farmers' income increase 0.763 5%in average；the elastic coefficient of rural economic development level on farmers' income is 0.542 4，which shows that developing rural economy is an important measure to realize farmers' income increase；and the influence coefficient of the number of agricultural employed persons on farmers' income is0.567 9，meaning that the increase of employment number of the first industry can make the farmers' income increase，which can be explained with the lack of agricultural production labors，the＂hollowing out＂in rural areas and the new generation of farmers'leaving agricultural production，and this also raises the doubts on the view that there are a large amount of surplus labors in rural areas.

Fig.2 Fitting and residual situations of equation regression results

We can obtain

The tendency results of farmers' marginal income brought by rural fixed-asset investment from 1991 to2010measured according to data in formula（11）and Table 1 are shown in Fig.2 below：

The measurement results show that the effects of rural fixed asset investment on farmers' income present a descending trend during the research period，dropping from 2.9 in 1991 to 0.8 in 2010.According to marginal theory and Barro（1990）［8］rule，the optimal income situation of rural fixed-asset investment should be MPI＝1.According to Fig.2，the marginal influence of rural fixed-asset investment on farmers' income has been less than 1 in 2009，which indicates that rural fixed-asset investment has reached optimal scale from the perspective of farmers'income.

If it is assumed that the income flexibility of rural fixed-asset investment remains unchanged in a certain period，i.e.maintaining at the level of0.763 5，when the rural fixed-asset investment reaches the optimal situation（MPI＝1），the ratio of rural fixed asset investment and farmers' income should be 0.763 5 according toα＝MPI·A／I.That is to say，from the perspective of farmers'income，tomake income increase effect of rural fixed-asset investment reach the optimum（MPI＝1），the optimal scale of rural per capita fixed-asset investment should be76.35%of rural per capita net income.

Fig.3 Tendency and variation trend of farmers' marginal income brought by rural fixed-asset investment from 1991 to 2010

3 Conclusion and policy recommendations

The influence of rural fixed-asset investment on farmers' income has boundary in amount and optimal range.According to the results of empirical analysis with model，the optimal scale of rural per capita fixed-asset investment should be 76.35%of rural per capita net income，and under this scale，the marginal influence of rural fixed-asset investment on farmers' income is 1（MPI＝1）.

Meanwhile，the measurement of marginal income of rural fixed-asset investment from 1990 to 2010 shows that its marginal effect on farmers' income presents a diminishing law and has been less than 1 in 2009，therefore，it can be said that the rural fixed asset investment has achieved the optimal scale from the perspective of farmers' income increase，and though continuous addition of rural fixed assets can increase farmers' income，its marginal cost is higher.Asa result，more attention should be paid on structure adjustment while increasing the amount of rural fixed-asset investment now and later，even it can be said that the income increase effect brought by structure adjustment is stronger than that caused by additional investment.Compared with continuous addition of rural fixed-asset investment，the adjustment of fixed-asset investment structure is more important at present：

（i）Increasing rural fixed-asset investment，guiding the investment flowing into economic and social developmental infrastructures such as irrigation and water conservancy，road，education，medical treatment and environment，improving the conditions of rural productive and social infrastructures and enhancing the development vigor of rural economy.

（ii）Strengthening the comprehensive management on the investment of collective fixed assets，integrate space regional planning including basic farmland preservation，development of modern agricultural industry park，new rural construction and development of central towns，guide government investment，social investment and household investment as well as improve investment performance.

（iii）Taking full advantage of non-agricultural employment opportunities and good investment and employment environment generated by rural fixed-asset investment，on the one hand，enhancing non-agricultural employment skill training on migrant workers and making surplus rural labors be employed in non-agricultural positions locally，on the other hand，actively guiding peasant households to participate in some investment projects and expand farmers' income source channel.

（iv）Utilizing the economic externality of rural infrastructure，giving full play to the guiding action of fiscal finance，promoting the securitization and capitalization of rural＂three rights＂and increasing loan amount of rural micro，small and mediumsized enterprises such as family farm and joint stock partnership organization and loan ratio of farmers'household.

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