12肥料经济学--肥料经济学(Ⅰ)--最大利润与最高产量.doc

肥料经济学（）-最大利润与最高产量Murray Fulton教授加拿大萨斯卡彻温大学农经系、合作研究中心引言 Introduction肥料对中国的农业和经济具有极为重要的意义。过去40年来中国农业增长的主要原因之一是肥料使用量的增加。目前中国的化肥年使用量约9千万吨（以产品重量计），成为世界上化肥消费的大国之一。同时，中国也是世界上进口化肥最多的国家，进口量约为1500万吨。Fertilizer is extremely important to Chinese agriculture and to the Chinese economy. One of the major reasons for the increase in agricultural production over the last 40 years is the increase in use of fertilizer. Currently China consumes approximately 90 million metric tons (mmt) of chemical fertilizer (measured in production weight). This makes China one of the largest consumers of fertilizer in the world. China is also the largest importer of fertilizer, importing roughly 15 mmt of chemical fertilizer.除了为作物生产提供养分外，化肥生产和运销在中国经济中也具有重要意义。例如，中国现有近1800个化肥厂，从业人员达220万，政府每年花费数十亿元用于肥料的生产和分销，化肥进口也是中国外汇硬通货支出的重要项目之一。 In addition to providing the nutrients required for crop production, fertilizer production and transportation play an important role in the Chinese economy. The nearly 1,800 fertilizer plants in China, for instance, employ 2.2 million workers. Government investment into fertilizer production and distribution involves expenditures of billions of yuan per year, while the importation of fertilizer is one of the major uses of hard foreign currency.肥料生产经济学 The Economics of Fertilizer Production经济学的主要特性之一是着重研究：为达到某一目标，如何最有效地分配和利用资源，不管是资金、劳动力或肥料。经济学的一个特点是可以用同样的概念和方法针对多种不同的问题或目标进行分析。A key feature of economics is its focus on how best to allocate resources- whether this be money, or labour, or fertilizer - in order to achieve some goal. One of the lessons of economics is that a large number of problems - ie., many different goals - can be analysed with the same set of tools and concepts.具体地说，经济学可对肥料使用中两个完全不同的问题做出解答。其一是应该使用多少肥料以获得最大量的物质指标，如单产量或总产量；其二是应该使用多少肥料以获得最大量的经济指标，如农户的利润，或者一个省或一个国家的纯经济效益。In particular, economics can provide an answer to two very different questions that are often raised with respect to fertilizer. The first concerns how much fertilizer should be used to maximize a physical variable such as yield or total production. The second concerns how much fertilizer should be used to maximize an economic variable such as the profits of the farmer or the economic net benefits of a province or a country.要对这两个问题做出回答，通常的方法是从边际分析入手。就肥料的使用而言，边际分析的重要一步是要了解产量曲线或生产函数。如下面将要显示的，产量曲线的形状与边际收益递减的概念有着密切的关系。The common approach to answering both of these questions involves the application of what is known as marginal analysis. In the case of fertilizer, an important part of marginal analysis involves an understanding of the shape of the yield response curve, or production function. As will be shown, the shape of the yield response curve is closely related to the idea of diminishing marginal returns.鉴于生产函数的重要性，这里首先对它进行分析。在对产量和肥料之间的物质关系了解之后，再对最高产量和最大利润进行阐述。同时，还将对产量优化和利润优化的不同解决方法进行讨论。Because of its importance, the production function is examined first. Once the nature of the physical relationship between fertilizer and yield is understood, the analysis shifts to an examination of the question of maximizing yield, followed by an examination of profit maximization. An explanation of the difference between the solutions to these two problems is also discussed.在展开前面所提及的概念时，会用到中国农业的一些例子，这些资料大部分来源于加拿大钾磷研究所的研究结果，主要涉及钾肥的施用。In developing the concepts outlined above, examples from Chinese agriculture will be used. Many of the examples will be taken from work done by the Potash and Phosphate Institute of Canada (PPIC) and will involve the use of potash.这个讲座所介绍的概念带有理想化的色彩，也就是说，我们假设肥料的使用是没有限制的。下一个讲座，即“肥料经济学（）”，将讨论在存在限制因素的情况下怎样进行分析。The concepts presented in this lecture will consider an ideal world in which there are no constraints to the use of fertilizer. The next lecture, Economics of Fertilizer , will discuss how the analysis needs to be changed in order to examine the presence of constraints.在讨论合理施肥的经济问题时，我要强调这些讲座主要以概念论述为主。也就是说，我们将着重考虑肥料使用中的问题而不涉及细节。因此对于诸如价格或产量的不稳定性、施用时间、施肥位置和深度以及环境因素如有效土壤湿度的影响等等将不予讨论。这些问题都很重要，很多专著已作了研究，在此过多考虑它会分散对本讲座经济学思维框架主题的讨论。In discussing the economics of fertilization, I should stress that the lectures will be largely conceptual in nature. By this I mean they will focus on a way of thinking about problems regarding fertilizer use, rather than providing a great number of specifics. As a result, I will not be discussing factors such as the impact of price or yield uncertainty, the timing, depth and placement of fertilizer application, nor the effect of environmental factors such as moisture availability. While these are important topics about which a great deal has been written, consideration of them would detract from my main purpose of providing a framework for thinking about problems in an economic fashion.生产函数 The Production Function生产函数也称产量反应曲线，在这里表示作物产量与肥料施用量之间的内在关系。它在以下讨论中非常有用，故应以数学形式表示，其表达式如下：y=f（x）The production function is also known as the yield response curve. The production function shows the relationship that exists between the yield of a crop and the amount of fertilizer used. Since it will be useful later to be able to write this relationship in a mathematical form, the production function can be summarized by the expression y = f（x）其中，y表示每亩的产量，x为肥料施用量，f（x）表示y是x的函数。where y is the yield per acre and x is the amount of fertilizer that is applied. The expression f (x) means that y is a function of x.表1表示水稻产量与钾肥施用的关系，资料来源于中加钾肥项目1986年在湖北省的试验结果。图1是根据同样的资料绘制的。Table 1 shows the relationship between rice yield and potash fertilizer usage in Hubei province in 1986. This relationship was established through field research supported by the China/Canada Potash Agronomy Program. Figure 1 graphs this same information.(表：表1 钾肥对水稻的生产函数 （ 1986年 湖北） )Fertilizer Use 施肥 Rice Yields 水稻产量 Yield Change 产量变化量 MPP边际产量 N P2O5 K2O Early早稻 Late晚稻 Early早稻 Late晚稻 Early早稻 Late晚稻 kg/ha 150 60 0 5151 6105 - - 150 60 60 5576 6633 425 528 7.08 8.80 150 60 120 5859 6942 283 309 4.72 5.15 (图：图1 钾肥对水稻的生产函数（1986年，湖北）)表1和图1中的数据所表现的一个重要特性是：随着肥料施用量的增加，追加的肥料所带来的水稻产量的增加量逐渐减小。例如，晚稻每公顷开始施用60公斤氧化钾（K2O）时，产量增加528公斤/公顷。继续增加60公斤/公顷时，产量只增加309公斤/公顷。One of the most important features of the data in Table 1 and Figure 1 is that rice yields become less responsive to the addition of fertilizer as fertilizer use increases. For instance, in late rice, the application of the first 60 kg/ha K2O adds 528 kg/ha to the rice yield. The application of an additional 60 kg/ha, however, adds only 309 kg/ha to the rice yield.产量的增加量随着肥料施用的增加而逐渐减少的趋势称为边际报酬递减。使用边际物质产量（MPP）的定义将使这一概念的表述更加简明: The tendency for the yield response to become less as fertilizer use increases is known as diminishing marginal returns. The concept of diminishing marginal returns can be made more succinct by defining the marginal physical product (MPP)边际物质产量(MPP)=作物产量的变化量 / 肥料用量的变化量Marginal Physical Product (MPP)=Change in Crop Yield / Change in Fertilizer Use表1所示为湖北省早、晚稻钾肥施用的边际产量。计算得到一定肥料用量水平的边际产量。公式中的肥料用量变化量是指一定肥料用量水平与上一用量水平之差。作物产量变化量是指这两个肥料水平对应的两个产量的差值。 Table 1 shows the calculation of the MPP for potash on early and late rice in Hubei. The MPP is calculated for a given level of fertilizer use. The change in fertilizer used in the calculation of MPP is the difference between the given level of fertilizer use and the next smaller level of fertilizer use. The change in yield is calculated as the difference between the yields at these two fertilizer usage levels.例如，用309除以60而得的边际产量为5.15。其中，309是6942与6633之差，它们是钾肥用量分别为120和60公斤/公顷时的相应产量，60是120与60之差。For example, the MPP of 5.15 is calculated by dividing 309 by 60. The value of 309 is the difference between 6942 and 6633, the yields at potash application levels of 120 and 60 kg/ha, respectively. The value of 60 is the difference between 120 and 60.应该强调的是，边际产量的计算并非是用一定的肥料用量水平下的产量与不用肥料的情况下的产量之差除以总的肥料用量。以表1为例来说，用837（即6942-6105）除以120（即120-0）而得出的6.98并不是边际产量。尽管这个数值在计算价值成本比（VCR）时很重要，但在肥料经济学中却并没有实际意义。下面我们会看到，用价值成本比来考察肥料经济会导致极不正确的结论。It should be stressed that the calculation of the MPP does not involve dividing the difference between the yield at a given level of fertilizer and the base yield when no fertilizer is applied by the total amount of fertilizer used. In the example in Table 1, this latter number is obtained by dividing 837 (6942-6105) by 120 (120-0) to give 6.98. While this number plays an important role in the calculation of the Value Cost Ratio (VCR), it plays no useful role in understanding the economics of fertilizer application. As will be shown below, the VCR can produce extremely misleading results when it comes to considering the economics of fertilization.当肥料用量水平差值较大时，通常考虑计算超出两个肥料用量水平范围的边际产量。例如，表1应该解释为，当晚稻的钾肥用量为060公斤/公顷时，边际产量为8.80；当钾肥用量为60120公斤/公顷时，边际产量为5.15。When the difference in the level of fertilizer use is large, it is usually assumed that the MPP that is calculated applies over the range between the two levels of fertilizer use. For example, Table 1 should be interpreted as saying that the MPP of late rice is 8.80 for fertilizer application levels between zero and 60 kg/ha. For fertilizer application levels between 60 and 120kg/ha, the MPP is 5.15.边际产量的重要性在于它表示了肥料的追加用量所带来的产量的增量，如表1中所表现的逐渐下降的边际产量说明，肥料用量的增加所带来的增产幅度越来越小。简言之，边际产量表示，每增加一个单位的肥料用量在产量增加中的作用如何。The importance of the MPP is that it shows what the incremental yield is from an additional application of fertilizer. For instance, the falling MPP presented in Table 1 indicates that the increase in yield that results from an increase in fertilizer usage is becoming smaller and smaller. In short, the MPP provides an indication of how effective additional units of fertilizer are in raising yield.从图形上看，生产函数曲线的斜率即为边际产量。图1中，线段AB的斜率是钾肥用量为060公斤/公顷时的边际产量，线段BC的斜率是钾肥用量范围为60120公斤/公顷时的边际产量。图2绘出早、晚稻的钾肥边际产量与肥料水平的关系，这些曲线斜率的下降表明了边际报酬递减。Graphically, the MPP is given by the slope of the production function. In Figure1, the slope of the line AB gives the MPP of potash over the range of potash use zero to 60kg/ha, while the slope of the line BC gives the MPP of potash over the range of potash use 60 to 120kg/ha. Figure 2 graphs the MPP of potash against the level of fertilizer for both early and late rice. The downward slopes of these curves indicate diminishing marginal returns.(图：图2 钾肥对水稻的边际产量（1986年，湖北）)图3表示的是钾肥的一般生产函数。用数学的术语来表示，边际产量是生产函数的一阶导数，即：Figure 3 presents a more general production function for potash. In mathematical terms, the marginal physical product is given by the first derivative of the production function, ie.,(图：图3 钾肥对水稻的一般生产函数)因此，线段AB的斜率为MPP1，是钾肥用量为K1时的边际产量；线段CD的斜率为MPP2，是钾肥用量为K2时的边际产量。钾肥用量为K3时，边际产量为负值，即MPP30。再说明一下，边际产量与肥料用量水平的关系可以用图表示，边际报酬递减表明边际产量曲线应该向下倾斜。Thus, the slope of the line AB is MPP1, the marginal physical product of fertilizer at a level of fertilizer use K1, while the slope of the line CD is MPP2, the marginal physical product of fertilizer at usage level K2. At fertilizer usage K3, the MPP becomes negative, ie., MPP30. Once again, the MPP can be graphed against the level of fertilizer usage. Diminishing marginal returns indicate that the MPP curve will be downward sloping.图4可用来表示边际产量与用于计算价值成本比（VCR）的主要成份之间的关系。假定肥料的三个用量水平为K1、K2和K3，相应的产量分别为Y1、Y2和Y3。Y0为不施用肥料时的产量水平。计算价值成本比的第一步是计算下列比值： (Y1-Y0) / K1，(Y2-Y0) / K2，(Y3-Y0) / K3。这些比值分别为斜线Y0a、Y0b和Y0C。从图4中可以看到，这些线段的斜率和切线AB、CD及EF的斜率没有任何的关系。例如，肥料用量为K3时，边际产量为负值，而 (Y3-Y0)/K3却是正值。Figure 4 can be used to show the relationship between the MPP and a major component used in the calculation of VCR. Suppose that three levels of fertilizer use have been observed - K1, K2, and K3. Associated with these levels of fertilizer use are yields Y1, Y2, and Y3, respectively. Yield level Y0 is the yield that results when no fertilizer is applied. The first step in calculating the VCR is to calculate the value of the ratios: (Y1-Y0)/K1, (Y2-Y0)/K2, and (Y3-Y0)/K3. The values of these ratios are given by the slopes of the lines Y0a, Y0b, and Y0c. As can be seen from Figure 4, the slope of these lines bears no relation at all to the slope of the tangent lines AB, CD, and EF. For example, at fertilizer usage level K3, the MPP has become negative. However, the ratio (Y3-Y0)/K3 is positive. (图：图4 计算价值成本比所需要的要素)多种肥料的生产函数 Production Function with Multiple Fertilizers在研究肥料用量与作物产量之间的关系时，有必要明确有关的重要变量。例如图1和表1的数据表示两个生产函数，一个是早稻，一个是晚稻。另外，这两个生产函数都是在一定的氮磷肥用量水平下，按照某个特定的省（湖北）在某个特定年份（1986）的实验而得出。When presenting the relationship between fertilizer use and crop yield, it is important that all the variables important in the relationship be understood. For instance, Table 1 and Figure 1 present data for two production functions, one for Early Rice and one for Late Rice. In addition, the production functions shown are based on a given amount of nitrogen and phosphorus fertilizer and are based on trials in a particular province (Hubei) in a particular year (1986).生产函数可以通过显示产量和所研究的各种肥料不同用量水平之间的关系，来说明不同肥料之间的相互作用。例如，表2是施用氮和钾与黄麻产量的关系，资料来源于中加钾肥项目1986年在广东省的大田试验。Production functions can account for the interaction between different types of fertilizer by showing the relationship between yield and the level of usage of all the fertilizers under consideration. As an example, Table 2 shows the relationship between the yield of jute and the amount of nitrogen and potash applied. The data is for Guandong in 1986 and was established through field research supported by the China/Canada Agronomy Program.(表：表2 黄麻产量作为N和K2O用量的函数（1986年，广东） )K2O Level 施钾量 Yield (kg/ha) 产量 MPP of Potash 钾的边际产量 MPP of Nitrogen 氮的边际产量 (kg/ha) N=150 N=225 N=150 N=225 0 3585 3532 -0.7 75 5160 5182 21.0 22.0 0.3 150 6015 6914 11.4 23.1 12.0 225 6135 7107 1.6 2.6 13.0 图5画的是多个生产要素的生产函数关系。为了便于理解，可以把图5看成是6个单生产要素的生产函数：2个为钾在2个不同的氮水平上，4个为氮在4个不同的钾水平上。线段ABCD和ABCD表示钾的两个生产函数，线段AA、BB、CC和DD表示氮的四个生产函数。Figure 5 graphs this relationship in a multiple input production function. It is useful to think of Figure 5 in terms of six single input production functions: two for potash given the two different levels of nitrogen application; and four for nitrogen given the four different levels of potash application. The lines ABCD and ABCD show the two production functions for potash, while the lines AA, BB, CC, and DD show the four production functions for nitrogen.(图：图5 氮肥和钾肥对黄麻的生产函数（1986年，广东）)六个单生产要素的生产函数可计算六组边际产量，例如，在氮用量为150公斤/公顷时，可计算一组钾的边际产量，在氮用量为225公斤/公顷时，可计算另一组边际产量。表2提供了两组边际产量值。The six single input production functions allow for the calculation of six sets of MPPs. For instance, one set of MPPs can be calculated for potash, given that the application of nitrogen is 150kg/ha, while another set of MPPs can be calculated for potash, given that the application of nitrogen is 225kg/ha. Table 2 presents the two sets of MPPs.当氮用量为150公斤/公顷时，黄麻产量对钾的用量在所有的钾用量水平均呈边际报酬递减。而在氮用量为225公斤/公顷时，黄麻产量起初对钾用量出现边际报酬递增。这是因为，边际产量在钾用量为75150公斤/公顷时比钾用量为075公斤/公顷时大。然而，在钾用量为150225公斤/公顷时，又出现边际报酬递减，在此钾肥施用范围，边际产量减至2.6。For a nitrogen application of 150kg/ha, jute yields experience diminishing marginal returns to potash application over all levels of potash application. For a nitrogen application of 225kg/ha, however, jute yields initially experience increasing marginal returns to potash application. This follows because the MPP for potash use between 75 and 150kg/ha is greater than the MPP for potash use between zero and 75kg/ha. For potash applications between 150kg/ha and 225kg/ha, however, there are diminishing marginal returns to potash application. In this range of fertilizer use, the MPP falls to 2.6.图5中，当氮的用量为150公斤/公顷时，钾用量的边际报酬递减反映在生产函数ABCD的斜率随着钾肥用量的增加而逐渐变小。当氮用量为225公斤/公顷时，边际报酬的递增表现为生产函数的斜率从A到B，再到C的逐渐增加，从C到D斜率的下降表明边际报酬开始递减。 In Figure 5, the diminishing marginal returns to potash application when nitrogen application is 150kg/ha are reflected by the slope of the production function ABCD becoming smaller and smaller as the amount of potash applied increases. For a nitrogen application level of 225kg/ha, increasing marginal returns are shown by the increase in the slope of the production function as one moves from A to B to C. The fall in the slope as one moves to D indicates that diminishing marginal returns have set in.表2又表示在钾的各个用量水平，氮肥用量的变化对钾肥边际产量的影响。特别是氮肥用量的增加具有提高钾肥边际产量的作用。例如，当钾肥用量为75150公斤/公顷时，氮肥用量由150公斤/公顷增加到225公斤/公顷使得钾肥的边际产量由11.4增至23.1。Table 2 also shows that a change in the level of nitrogen application affects the MPP of potash use for any given level of potash use. In particular, an increase in the amount of nitrogen applied has the effect of increasing the MPP of potash. As an example, when potash use is between 75kg/ha and 150kg/ha, an increase in nitrogen application from 150 to 225kg/ha increases the MPP of potash from 11.4 to 23.1.没有足够的数据来证明黄麻的产量是否对氮肥施用亦呈边际报酬递减。然而，表2表明，当不施钾时，氮肥的边际产量为负值，也就是说，氮用量由150公斤/公顷增加到225公斤/公顷导致了黄麻产量的降低，而随着钾用量的增加，氮肥的边际产量也增加。 Insufficient data is available to determine whether jute yields are also experiencing diminishing returns to nitrogen application. Table 2 shows, however, that when no potash is applied, the marginal physical product of nitrogen is negative - that is, an increase in nitrogen use from 150kg/ha to 225kg/ha leads to a decrease in jute yields. As the amount of potash applied increases, the MPP of nitrogen increases.氮肥的边际产量随着钾肥用量的增加而增加的现象说明，钾肥对氮肥施用的有效性具有积极的作用。如前所述，氮肥对钾肥的有效性同样具有重要作用。这种内在关系的重要性在于，在决定某种肥料的用量时，必须同时考虑到其它肥料的用量。这种相互依存关系在后面还会作进一步的分析。The increase in the MPP of nitrogen as potash application levels are increased is an indication of the positive impact that potash has on the effectiveness of nitrogen. As was just discussed, nitrogen also has an important effect on the effectiveness of potash. The importance of this interrelatio