【正文】 肥料經(jīng)濟學(xué)（Ⅱ）存在限制因素情況下的利潤優(yōu)化Murray Fulton教授加拿大薩斯卡徹溫大學(xué)農(nóng)經(jīng)系、合作研究中心　　引言 Introduction　　在肥料經(jīng)濟學(xué)的第一講中，我闡述了邊際報酬遞減的概念及其與生產(chǎn)函數(shù)形狀之間的關(guān)系。具體地說，我說明了邊際報酬遞減就是邊際產(chǎn)量隨著肥料用量的增加而遞減?！　n 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 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時，邊際產(chǎn)量為零的肥料用量水平可以取得最高產(chǎn)量。然而，最高產(chǎn)量通常不是適宜的目標。從經(jīng)濟學(xué)的觀點來看，最高產(chǎn)量不能算計使用肥料的成本和收益，權(quán)衡成本和收益的常用方法是利潤。 　　In 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 to account for the costs and benefits of using fertilizer. The usual measure of the tradeoff between these costs and benefits is profit.　　為了使利潤值最大，某種特定肥料的邊際產(chǎn)量必須等于這種肥料與產(chǎn)品的價格比，當這個比例確定時，肥料的使用量要低于取得最高產(chǎn)量的肥料用量。　　In order to maximize profit, the MPP of a particular fertilizer should be set equal to the fertilizer price/output price ratio. When this is done, the amount of fertilizer used is less than that used to maximize production.　　邊際產(chǎn)量應(yīng)該等于肥料與產(chǎn)品價格比的論點是有假設(shè)條件的，即假設(shè)農(nóng)戶不受肥料量和資金的限制。正如上講中討論的那樣，現(xiàn)實情況通常并非如此。世界各地的農(nóng)民都面臨著資金限制或買不到肥料。例如，在加拿大，部分農(nóng)民受到貸款量的限制而不能隨意購買化肥；在中國，由于缺乏信貸，農(nóng)民同樣受到資金不足的限制，此外，還可能受到化肥生產(chǎn)量或進口量不足的限制?！　he argument 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 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 constrained because of a lack of fertilizer production or importation.　　在這一講，我將分析在存在限制因素的情況下，如何使用肥料以達到最大利潤。首先討論如何將有限的肥料在各種作物之間進行分配，這種分析還將延伸到用于肥料的資金如何在不同肥料之間進行分配，不管肥料是用于一種作物或是用于多種作物?！　n this lecture I examine the problem of how fertilizer should be used to maximize profits when constraints are in place. First, 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.　　我們以介紹基本概念作為討論這一主題的開始，以使這個問題易于理解。其中最主要的是機會成本概念。首先，我要給機會成本下個定義，然后再用這一概念來分析怎樣在不同作物之間對肥料進行分配，以及怎樣在不同肥料之間對資金進行分配?！　 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 opportunity 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，再用湖南省中東部地區(qū)的資料來說明這些概念是如何應(yīng)用的?！　fter I have outlined the conceptual model, I will then use data on fertilizer use from a region in eastcentral Hunan province to illustrate how these concepts can be applied. 　　機會成本 Opportunity Cost　　經(jīng)濟學(xué)中最重要的概念之一是機會成本。下面會看到，這一概念是回答我所提出的問題的關(guān)鍵?！　ne of the most important concepts in economics is opportunity cost. As I will show, this concept is key to answering the questions I have just posed.　　給機會成本下定義最好從問題入手。水稻使用氮肥的成本是什么？答案顯然是氮肥的價格，但這并不是真正的成本。真正的成本，即機會成本，是如果把這些氮肥用于另一種作物，如小麥，所能得到的額外產(chǎn)量。換句話說，在水稻上使用氮肥的真正成本是喪失了氮肥用于其它作物的機會?！　pportunity cost is best defined with the help of a question. What is the cost of using nitrogen fertilizer on a rice crop? 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 is the loss of the opportunity of using it on a different crop.　　機會成本不過是資源短缺的另一種說法。在上述例子中，只有在氮肥量有限時，把氮肥用于水稻才存在著機會成本。如果氮肥的供應(yīng)沒有限制，也就沒有機會成本，因為這時氮肥用于水稻并不涉及到放棄用于小麥的機會?！　pportunity cost is simply another way of saying that resources are scarce. In the example above, using nitrogen on rice will only have an opportunity 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.　　限制因素的存在說明了資源的短缺。例如，如果農(nóng)民的貸款量有限，用于購買諸如肥料等生產(chǎn)要素的資金就會短缺。如果政府能買回來分配的肥料量有限，肥料就會不足?！　he presence of constraints means resources are scarce. For instance, if farmers have limited credit, then money is scarce for the purchase of inputs such as fertilizer. If a government is constrained in the amount of fertilizer it is allocated or can purchase, then fertilizer is scarce.　　因此，限制因素涉及到機會成本。確定這個機會成本是確定如何分配有限資源以達到最大利潤的第一步?！　onstraints, therefore, involve opportunity costs. Identifying this opportunity cost is the first step in deciding how limited resources should be allocated in order to maximize profits.　　可利用肥料的限制因素－理論分析 Constraints in the Availability of Fertilizer Theory　　肥料限制最簡單的一種情形是生產(chǎn)一種作物，而且這種作物只需要一種肥料。在這種情況下，決策標準很簡單：如果可供利用的肥料量小于使利潤達到最大值所需要的肥料量，則使用全部肥料?！　he simplest case of a fertilizer constraint is where one crop is produced and where this crop responds to only one kind of fertilizer. In this case the decision rule is straightforward: If the amount of fertilizer available is less than the amount that would maximize profits, then use all the fertilizer.(圖：圖1 肥料量有限情況下的利潤優(yōu)化)