【正文】 PK/rK　　which is equivalent to　　MPPN/MPPK=rN/rK　　表1用一個(gè)假想的例子說(shuō)明了這一原則。例如，假定某種作物（如水稻）需要兩種肥料（氮和鉀），而且這兩種肥料相互作用以決定產(chǎn)量，再假定購(gòu)買化肥的資金是有限的，那么，資金該如何在兩種肥料之間進(jìn)行分配呢？　　The notion of opportunity cost can be used to solve other constraint problems. For instance, consider a crop (, rice) that responds to two fertilizers (nitrogen and potash) which interact in determining yield. Suppose also that the amount of yuan available to spend on fertilizers is limited. How should the yuan be spent between the two fertilizers?　　假定使用在N肥上的資金比使用在K肥上的多一元，如果N肥的價(jià)格為rN，有了這額外的一元錢，農(nóng)民可以多買1/rN公斤的N肥，從而使水稻產(chǎn)量增加MPPN/rN公斤，這是多花一元在N肥上所產(chǎn)生的邊際收益。另外，由于鉀肥是在MVP1=MVP2的情況下進(jìn)行分配的，任何肥料的重新分配都將導(dǎo)致利潤(rùn)下降。第三幅圖中的曲線是通過(guò)第一、二圖中曲線的水平相加而得出的。　　It is useful to consider this problem in terms of opportunity cost. Recall that the opportunity cost of fertilizer is the benefit foregone by not using the fertilizer somewhere else. In the above example, the opportunity cost of using fertilizer on crop 1 is the benefit given up from using fertilizer on crop 2, namely MVP2. Using fertilizer on crop 1, however, provides a benefit equal to MVP1. Profits will be maximized when the marginal benefit equals the marginal cost, ., MVP1=MVP2.　　圖3用圖示表示了這個(gè)問(wèn)題。肥料的機(jī)會(huì)成本是由于沒(méi)有機(jī)會(huì)把肥料用于其它作物而損失的經(jīng)濟(jì)效益。如果兩者不相等，利潤(rùn)總能通過(guò)肥料從一種作物移向另一種作物而得到增加。因?yàn)橛糜诘诙N作物肥料的增加使MPP2下降，而第一種作物肥料用量的減少使MPP1上升。從產(chǎn)值上看，作物1的利潤(rùn)降低MVP1=，作物2的利潤(rùn)增加MVP2=?！　he key to this problem is to think about having a fixed amount of fertilizer that is initially allocated between two crops. Figure 2 illustrates this graphically. The rectangle indicates a fixed amount of fertilizer, with the dotted line indicating the allocation of the fertilizer between the two crops. Now consider the impact of shifting one kilogram of fertilizer from one crop to the other.(圖：圖2肥料從一種作物轉(zhuǎn)用到另一種作物的經(jīng)濟(jì)影響)　　假定第一種作物的邊際產(chǎn)量為MPP1，第二種作物的邊際產(chǎn)量為MPP2。圖中的矩形表示固定的肥料量，虛線表示肥料在兩種作物之間的分配?！　ince MVP exceeds r at fertilizer level K constraint, profits would increase if an additional unit of fertilizer could be purchased at price r. This follows because an additional unit of fertilizer increases output by the MPP. The value of this additional output is given by MVP (which equals p MPP). The cost of obtaining this additional revenue is given by r, the price of fertilizer. Since MVP exceeds r, the benefit exceeds the costs and profits rise. The size of this increase in profits is MVP r.　　明確額外肥料的收益有利于理解更復(fù)雜的問(wèn)題。這個(gè)增加產(chǎn)量的價(jià)值為MVP（MVP＝），獲得這個(gè)邊際收益的成本為r，即肥料的價(jià)格。 　　I should point out here that in the remainder of this lecture, p will be used to refer to the price of the output, while r refers to the price of fertilizer. If more than one crop or fertilizer is discussed, the prices shall be denoted by p1, p2, r1, r2, and so on.　　由于在肥料用量為K constraint限制值時(shí)，MVP大于r，所以，如果能以價(jià)格r多購(gòu)買一個(gè)單位的肥料，利潤(rùn)便會(huì)增加。　　As was discussed in Economics of Fertilizer I, the slope of the Profits curve is given by the difference between the slope of the Benefits curve and the slope of the Costs curve ., MVP r. Both MVP and r are graphed in the lower portion of Figure 1.　　這里應(yīng)該說(shuō)明一下，本講座隨后將用P表示產(chǎn)品價(jià)格，r代表肥料價(jià)格?！　igure 1 also indicates the benefit that would be received if the constraint could be removed in some way. If an additional unit of fertilizer were available, for instance, then profits would increase. The amount of this increase in profits is shown by the slope of the Profits curve at K constraint (., the slope of the line AB).　　如第一講中所討論的，利潤(rùn)曲線的斜率為收益曲線和成本曲線的斜率之差，即MVPr。例如，如果可供使用的肥料增加一個(gè)單位，利潤(rùn)便會(huì)增加。當(dāng)然，如果K constraint限制值大于K*，那么只該用K*，余下的部分應(yīng)貯存到明年，或轉(zhuǎn)售他人。　　The 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(rùn)優(yōu)化)　　圖1說(shuō)明了這種情況，達(dá)到最大利潤(rùn)的肥料水平是K*?！　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(jiǎn)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?！　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(jī)會(huì)成本。例如，如果農(nóng)民的貸款量有限，用于購(gòu)買諸如肥料等生產(chǎn)要素的資金就會(huì)短缺。如果氮肥的供應(yīng)沒(méi)有限制，也就沒(méi)有機(jī)會(huì)成本，因?yàn)檫@時(shí)氮肥用于水稻并不涉及到放棄用于小麥的機(jī)會(huì)?！　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(jī)會(huì)成本不過(guò)是資源短缺的另一種說(shuō)法。真正的成本，即機(jī)會(huì)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。　　One 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(jī)會(huì)成本下定義最好從問(wèn)題入手。　　After 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(jī)會(huì)成本 Opportunity Cost　　經(jīng)濟(jì)學(xué)中最重要的概念之一是機(jī)會(huì)成本。首先，我要給機(jī)會(huì)成本下個(gè)定義，然后再用這一概念來(lái)分析怎樣在不同作物之間對(duì)肥料進(jìn)行分配，以及怎樣在不同肥料之間對(duì)資金進(jìn)行分配。　　In 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 ap