【正文】 plied 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(gè)問題易于理解。　　The 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(dá)到最大利潤(rùn)。世界各地的農(nóng)民都面臨著資金限制或買不到肥料。　　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(jià)格比的論點(diǎn)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。從經(jīng)濟(jì)學(xué)的觀點(diǎn)來看，最高產(chǎn)量不能算計(jì)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(rùn)?！　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(shí)，邊際產(chǎn)量為零的肥料用量水平可以取得最高產(chǎn)量。肥料經(jīng)濟(jì)學(xué)（Ⅱ）存在限制因素情況下的利潤(rùn)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(jì)學(xué)的第一講中，我闡述了邊際報(bào)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(bào)酬遞減就是邊際產(chǎn)量隨著肥料用量的增加而遞減。然而，最高產(chǎn)量通常不是適宜的目標(biāo)。 　　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(rùn)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(jià)格比，當(dāng)這個(gè)比例確定時(shí)，肥料的使用量要低于取得最高產(chǎn)量的肥料用量。正如上講中討論的那樣，現(xiàn)實(shí)情況通常并非如此。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(gòu)買化肥；在中國(guó)，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(jìn)口量不足的限制。首先討論如何將有限的肥料在各種作物之間進(jìn)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(jìn)行分配，不管肥料是用于一種作物或是用于多種作物。其中最主要的是機(jī)會(huì)成本概念?！　 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。下面會(huì)看到，這一概念是回答我所提出的問題的關(guān)鍵。水稻使用氮肥的成本是什么？答案顯然是氮肥的價(jià)格，但這并不是真正的成本。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(jī)會(huì)。在上述例子中，只有在氮肥量有限時(shí)，把氮肥用于水稻才存在著機(jī)會(huì)成本?！　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。如果政府能買回來分配的肥料量有限，肥料就會(huì)不足。確定這個(gè)機(jī)會(huì)成本是確定如何分配有限資源以達(dá)到最大利潤(rùn)的第一步。在這種情況下，決策標(biāo)準(zhǔn)很簡(jiǎn)單：如果可供利用的肥料量小于使利潤(rùn)達(dá)到最大值所需要的肥料量，則使用全部肥料。如果可供使用的肥料量K constraint限制值小于K*，那么農(nóng)民應(yīng)該用K constraint?！　igure 1 illustrates this case. The level of fertilizer that maximizes profits is K*. If the amount of fertilizer available, K constraint, is less than K*, then the farmer should use the amount K constraint. Of course, if K constraint is greater than K*, then only K* should be used. Any remainder should be stored for another year, or sold to someone else.　　圖1還表明，如果能以某種方式消除限制因素，就會(huì)增加收益。利潤(rùn)的增加量為利潤(rùn)曲線在K constraint限制值這一點(diǎn)的斜率（即直線AB的斜率）。MVP和r都表示在圖1的下圖中。如果作物和肥料不只一種，則相應(yīng)用PP2和rr2來表示，以此類推。這是因?yàn)?，肥料單位用量的增加使產(chǎn)量增加了MPP。由于MVP大于r，因而收益大于成本，利潤(rùn)增加，利潤(rùn)的增加量為MVPr。例如，假定現(xiàn)在有兩種作物，兩種作物都對(duì)同一種肥料有反應(yīng)，如果肥料量有限，應(yīng)該如何在這兩種作物之間分配這種肥料呢？　　Identifying the benefits of additional fertilizer is useful in understanding more plex problems. For instance, suppose now that two crops are produced and that both crops respond to the same fertilizer. If there is a limited amount of fertilizer available, how should this fertilizer be allocated between the two crops?　　這個(gè)問題的關(guān)鍵是想想有限的肥料量最初在兩種作物之間的分配，這表示在圖2中?，F(xiàn)在考慮把一公斤肥料從一種作物轉(zhuǎn)移到另一種作物的結(jié)果。把一公斤肥料從作物1轉(zhuǎn)到作物2，使作物1的產(chǎn)量下降MPP1，而作物2的產(chǎn)量增加MPP2?！　uppose that the marginal physical product of the first crop is identified as MPP1, while the marginal physical product of the second crop is MPP2. Shifting one kilogram of fertilizer from crop 1 to crop 2 reduces the yield of crop 1 by MPP1 and increases the yield of crop 2 by MPP2. In value terms, the shift of fertilizer from crop 1 reduces profits by MVP1 (equals p1MPP1), while the shift of fertilizer to crop 2 increases profits by MVP2 (equals p2MPP2).　　只要MVP2大于MVP1，就該繼續(xù)把肥料從第一種作物移向第二種作物，但由于邊際報(bào)酬遞減，隨著肥料轉(zhuǎn)移的增加，MVP2和MVP1之間的差異將變小?！　s long as MVP2 is greater than MVP1, it will make sense to continue to shift fertilizer from crop 1 to crop 2. Because of diminishing marginal returns, however, the difference between MVP2 and MVP1 bees smaller as more and more fertilizer is shifted. This occurs because the addition of fertilizer to crop 2 causes MPP2 to fall, while the removal of fertilizer from crop 1 causes MPP1 to rise. 　　為了使利潤(rùn)值最大，肥料應(yīng)在兩種作物間進(jìn)行調(diào)節(jié)，直到MVP1=MVP2?！　o maximize profits, fertilizer should be shifted between the two crops until MVP1=MVP2. If these two expressions are not equal, profits can always be increased by moving fertilizer from one crop to the other.　　用機(jī)會(huì)成本的概念來考慮這個(gè)問題也很有用。在上例中，把肥料用于第一種作物的機(jī)會(huì)成本是放棄用于第二種作物應(yīng)產(chǎn)生的收益MVP2，但把肥料用于第一種作物所提供的收益等于MVP1，當(dāng)邊際收益等于邊際成本，即MVP1=MVP2時(shí)，利潤(rùn)達(dá)到最大。第一幅圖表示第一種作物各個(gè)邊際產(chǎn)值水平所需要