【正文】 　　When constraints are present, as is often the case, the proper allocation of fertilizer and fertilizer expendi。　　The point to stress in this lecture is that the data requirements for a proper allocation of fertilizer expenditures whether constraints are present or not ? requires information on the response of yields to different fertilizers, the interaction among different fertilizers in determining yield, and the prices of the outputs produced and the fertilizers used.　　當(dāng)存在限制因素，這是常有的事，肥料種類和購肥資金要在機(jī)會(huì)成本概念的指導(dǎo)下進(jìn)行重新分配?！　n the longer run, it may also make sense to consider the allocation of different fertilizers among different crops when budgets are not constrained。同樣，增施其他肥料如硫肥，有可能會(huì)提高氮、磷和鉀肥的邊際產(chǎn)量，因此需要進(jìn)一步增加這幾種肥料的用量。由于任何一種肥料的用量均會(huì)影響其他肥料的邊際產(chǎn)值，因此，一種肥料的最佳用量不能在不考慮其他肥料的情況下單獨(dú)選定。確定最適肥料分配方案的原則在肥料經(jīng)濟(jì)學(xué)（Ⅰ）中已進(jìn)行了概述。這類問題的解決，涉及到重新分配資金，要使用下面的關(guān)系式：　　P1?MPPN/rN=P2?MPPK/rK　　Of course, the problem is even more plex than simply reallocating fertilizer expenditures among different fertilizers. For instance, early rice is not the only crop that requires fertilizer. When other crops can be grown, the question of the proper allocation of fertilizer among the crops arises. As was pointed out in the theoretical discussion, the answer to this type of question requires reallocating expenditures so that the following relationship holds. 　　p1MPPN/rN=p2MPPK/rK 　　確定肥料該如何分配，需要利用產(chǎn)品和肥料價(jià)格以及肥料在不同作物上的邊際產(chǎn)量等資料。一般來說，解決涉及不同肥料的問題需要了解各種肥料的價(jià)格，需要用前面推導(dǎo)出的關(guān)系，即　　MPPN/MPPK=rN/rK 　　While the solution to the above example is relatively simple to conceptualize because of the overuse of nitrogen and phosphate, in general the solution to problems involving different fertilizers requires knowledge of fertilizer prices. More specifically, it is necessary to use the relationship that was derived earlier, namely 　　MPPN/MPPK=rN/rK　　當(dāng)然，問題也可能比只在不同肥料間重新分配資金復(fù)雜得多。將此購買氮磷肥的錢用于鉀肥還能增加利潤。因?yàn)闇y定出氮肥（至少在高產(chǎn)地區(qū)）和磷肥用量與最高利潤水平相比相對(duì)過高。這在短期內(nèi)是可行的，從長遠(yuǎn)來說，在各種不同的肥料之間對(duì)肥料預(yù)算進(jìn)行重新分配是可能的。相反，高產(chǎn)常與低邊際產(chǎn)量相聯(lián)系，這是大量使用化肥的結(jié)果。有時(shí)，高產(chǎn)伴隨著高邊際產(chǎn)量。但在上例中平均產(chǎn)量不能給出正確的結(jié)論，因高產(chǎn)區(qū)邊際產(chǎn)量較小，把更多的化肥分到這一地區(qū)，實(shí)際上降低了總利潤。遺憾的是，這樣的資料常常得不到，結(jié)果只能用其它的統(tǒng)計(jì)資料。這是因?yàn)榈彤a(chǎn)地區(qū)增加的產(chǎn)量大于高產(chǎn)地區(qū)減少的產(chǎn)量，因此總利潤增加了。應(yīng)當(dāng)注意，由于邊際產(chǎn)量是以農(nóng)民平均用量水平計(jì)算的，這種分析假定，在每個(gè)地區(qū)內(nèi)部，肥料已經(jīng)進(jìn)行了重新分配，以使所有農(nóng)民都得到肥料?！　t is possible, of course, that the constraint is not as severe as outlined above. Suppose, for instance, that there was some flexibility in altering the amounts of potash between regions, but that the total amount of potash available to the province was fixed. In this case, the decision to be made focuses on the allocation of potash between regions. Since the total supply to the province is fixed, allocating more potash to one region results in less potash being allocated to other regions.　　在這種情況下，為了肥料分配最優(yōu)化，需要知道所有地區(qū)鉀肥邊際產(chǎn)量的相對(duì)大小。例如，假定在地區(qū)之間重新分配鉀肥是可能的，但分配給一個(gè)省的總量是固定的，這種情況主要是決定鉀肥在地區(qū)之間的分配。不過要注意，雖然整個(gè)地區(qū)受益了，對(duì)放棄部分鉀肥的農(nóng)民來說，利潤卻下降了。因?yàn)椋瑴p少目前在使用鉀肥的農(nóng)民少量的鉀肥，不會(huì)引起大的減產(chǎn)（邊際產(chǎn)量小），與此同時(shí)，以前沒有鉀肥的農(nóng)民由于用了鉀，會(huì)使產(chǎn)量得到較大幅度的增加（邊際產(chǎn)量大）。像這種情況，某個(gè)地區(qū)不能調(diào)換其所能得到的肥料量，確定最佳肥料分配就只能是如何在本地農(nóng)民中分配每種肥料。在這種分析中，機(jī)會(huì)成本的概念將起到重要的作用。 　　In Eomics of Fertilizer Ⅰ, I presented data that showed farmers in the low yield region of eastcentral Hunan province were limited in the amount of potash they had available. Table 3 presents this data. Of the 44 farmers interviewed in this region, 25 did not use potash. This would indicate that a substantial proportion of all farmers in the region do not have access to potash.　　鉀肥的缺乏可能來自于肥料系統(tǒng)中各種不同的限制因素。如表3所示?！　he third panel of Figure 4 shows the total expenditure on fertilizer required to generate the same level of marginal value product in both crop 1 and crop 2. The curve in the third panel is drawn by horizontally adding together the curves in the first two panels.　　假定可利用的資金總量為Yuanonstraint，其中，YuanNconstraint應(yīng)分配給第一種作物，YuanKconstraint分配給第二種作物，由于YuanNconstraint+YuanKconstraint=Yuanconstraint，所以全部資金都得到了使用。假如產(chǎn)生邊際效益MVPN所需要的N肥量為XN，那么在N肥價(jià)格為rN的情況下。第一幅圖表示使用在第一種作物上的N肥的邊際產(chǎn)值與使用在N肥上資金的關(guān)系；第二幅圖表示使用在第二種作物上的K肥的邊際產(chǎn)值與使用在K肥上資金的關(guān)系。也就是說，當(dāng)利潤達(dá)到最大時(shí)　　P1?MPPN/rN=。　　Suppose an additional yuan is spent on nitrogen on crop 1, rather than on potash on crop 2. With one more yuan, an addition 1/rN kilograms of nitrogen can be purchased. This results in an additional MPP1/rN kilograms of crop 1 output. The value of this additional output is p1MPP1/rN. This is the marginal benefit of spending an additional yuan on nitrogen.　　由于這一元錢用于N肥，就不能再買1/rK公斤的K肥，這意味著相當(dāng)于MPP2/rK公斤的第二種作物就被放棄了，這是機(jī)會(huì)成本。具體地說，第一種作物需要N肥，第二種作物需要K肥。rK= Price Ratio(rN/rK)=　　如果預(yù)算更大些，比如400元/公頃，那么，購買225公斤/公頃的N肥和150公斤/ 公頃的K肥比較合適；如果有資金650元，那么，購買375公斤/公頃的N肥和225公斤/公頃的K肥比較合適?！　able 1 illustrates how this rule can be applied using a hypothetical example. The entries in the top portion of Table 1 indicate the marginal physical products for nitrogen and potash at different levels of nitrogen and potash. Both nitrogen and potash exhibit diminishing marginal returns. The MPPN declines as nitrogen levels increase, while the MPPK declines as potash levels increase. The entries in the bottom portion of Table 1 represent the ratio of MPPN to the MPPK.(表：表 1不同肥料用量水平的邊際產(chǎn)量（假設(shè)的例子） )N (kg/ha) 施氮量 氮的邊際產(chǎn)量 MPPN 鉀的邊際產(chǎn)量 MPPK 氮鉀邊際產(chǎn)量比 MPPN/MPPK K2O (kg/ha) K2O (kg/ha) K2O (kg/ha) 75 150 225 75 150 225 75 150 225 75 150 225 300 375 　　假定如表2所示，再假定只有150元/公頃的有限資金用于肥料，那么，最合適的是購買大至為75公斤/公頃的N肥和75公斤/公頃的K肥，這是這筆有限資金能產(chǎn)生的最大的利潤。N和K肥均表現(xiàn)出邊際報(bào)酬遞減，N肥的邊際產(chǎn)量隨著N肥的增加而下降，K肥的邊際產(chǎn)量也隨著K肥的增加而減少。　　As a result of spending this yuan on nitrogen, 1/rK kilograms of potash can no longer be purchased (rK is the price of potash). The result is that rice output falls by MPPK/rK kilograms. This, of course, is the opportunity cost.　　機(jī)會(huì)成本等于邊際收益便是最大利潤的表達(dá)式，即當(dāng)利潤最大時(shí)　　MPPN/rN=MPPK/rK　　這個(gè)表達(dá)式也可改寫為：　　MPPN/MPPK=rN/rK 　　Equating the opportunity cost to the marginal benefit gives the expression for maximizing profits. That is, profits will be maximized when　　MPPN/rN=MP