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1、肥料经济学（）-存在限制因素情况下的利润优化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在肥料经济学的第一讲中，我阐述了边际报酬递减的概念及其与生产函数形状之间的关系。具体地说，我说明了边际报酬递减就是边际产量随着肥料用量的增加而递减。In my first lecture on the economics of fertilization, I examined the concept of diminishing marginal returns and how this is related to the shape of the
2、production function. More specifically, I showed that diminishing marginal returns is equivalent to a marginal physical product (MPP) that declines with increases in the level of fertilizer that is used.在肥料使用不受限制时，边际产量为零的肥料用量水平可以取得最高产量。然而，最高产量通常不是适宜的目标。从经济学的观点来看，最高产量不能算计使用肥料的成本和收益，权衡成本和收益的常用方法是利润。 I
3、n a situation where no constraints on the use of fertilizer are present, production can be maximized by finding the level of fertilizer use that makes the MPP equal to zero. Maximizing production, however, is usually not the preferred goal. From an economic point of view, maximizing production fails
4、 to account for the costs and benefits of using fertilizer. The usual measure of the trade-off between these costs and benefits is profit.为了使利润值最大，某种特定肥料的边际产量必须等于这种肥料与产品的价格比，当这个比例确定时，肥料的使用量要低于取得最高产量的肥料用量。In order to maximize profit, the MPP of a particular fertilizer should be set equal to the ferti
5、lizer price/output price ratio. When this is done, the amount of fertilizer used is less than that used to maximize production.边际产量应该等于肥料与产品价格比的论点是有假设条件的，即假设农户不受肥料量和资金的限制。正如上讲中讨论的那样，现实情况通常并非如此。世界各地的农民都面临着资金限制或买不到肥料。例如，在加拿大，部分农民受到贷款量的限制而不能随意购买化肥；在中国，由于缺乏信贷，农民同样受到资金不足的限制，此外，还可能受到化肥生产量或进口量不足的限制。The arg
6、ument that the MPP should be set equal to the fertilizer price/output price ratio is based on the assumption that there are no constraints to the amount of fertilizer or the amount of money available to the farmer. As was discussed in the last lecture, this is usually not the case. Farmers all over
7、the world face limits on the amount of money or fertilizer to which they have access. In Canada, for instance, some farmers are restricted in the amount of credit they have available to purchase fertilizer. In China, farmers may also be constrained because of a lack of credit. They may also be const
8、rained because of a lack of fertilizer production or importation.在这一讲，我将分析在存在限制因素的情况下，如何使用肥料以达到最大利润。首先讨论如何将有限的肥料在各种作物之间进行分配，这种分析还将延伸到用于肥料的资金如何在不同肥料之间进行分配，不管肥料是用于一种作物或是用于多种作物。In this lecture I examine the problem of how fertilizer should be used to maximize profits when constraints are in place. Firs
9、t, I examine the problem of how a fixed amount of fertilizer should be allocated among various crops. The analysis is then expanded to consider the allocation of fertilizer expenditures among different fertilizers, whether the fertilizer is applied to a single crop or to a number of crops.我们以介绍基本概念作
10、为讨论这一主题的开始，以使这个问题易于理解。其中最主要的是机会成本概念。首先，我要给机会成本下个定义，然后再用这一概念来分析怎样在不同作物之间对肥料进行分配，以及怎样在不同肥料之间对资金进行分配。I will begin my discussion of this topic by presenting a conceptual framework in which the problem can more easily be understood. The most important element of this framework is the notion of opportunit
11、y cost. After providing a definition of opportunity cost, I use this concept to examine how fertilizer should be allocated among different crops, and how fertilizer expenditures should be allocated among different fertilizers.有了以上概念后，再用湖南省中东部地区的资料来说明这些概念是如何应用的。After I have outlined the conceptual mo
12、del, I will then use data on fertilizer use from a region in east-central Hunan province to illustrate how these concepts can be applied. 机会成本 Opportunity Cost经济学中最重要的概念之一是机会成本。下面会看到，这一概念是回答我所提出的问题的关键。One of the most important concepts in economics is opportunity cost. As I will show, this concept i
13、s key to answering the questions I have just posed.给机会成本下定义最好从问题入手。水稻使用氮肥的成本是什么？答案显然是氮肥的价格，但这并不是真正的成本。真正的成本，即机会成本，是如果把这些氮肥用于另一种作物，如小麦，所能得到的额外产量。换句话说，在水稻上使用氮肥的真正成本是丧失了氮肥用于其它作物的机会。Opportunity cost is best defined with the help of a question. What is the cost of using nitrogen fertilizer on a rice crop
14、? While the obvious answer is the price of nitrogen, this in fact is not the real cost. The true cost - or the opportunity cost - is the value of the extra output that could be produced if the nitrogen were used on another crop such as wheat. In other words, the real cost of using nitrogen on rice i
15、s the loss of the opportunity of using it on a different crop.机会成本不过是资源短缺的另一种说法。在上述例子中，只有在氮肥量有限时，把氮肥用于水稻才存在着机会成本。如果氮肥的供应没有限制，也就没有机会成本，因为这时氮肥用于水稻并不涉及到放弃用于小麦的机会。Opportunity cost is simply another way of saying that resources are scarce. In the example above, using nitrogen on rice will only have an op
16、portunity cost if the amount of nitrogen is limited. If there was an unlimited supply of nitrogen, then there would be no opportunity cost, since using nitrogen on rice would not involve giving up the opportunity to use it on wheat.限制因素的存在说明了资源的短缺。例如，如果农民的贷款量有限，用于购买诸如肥料等生产要素的资金就会短缺。如果政府能买回来分配的肥料量有限，肥料就会不足。The presence of constraints means resou
