生产可能性曲线

Constructing a Production Possibilities Curve

To construct a production possibilities curve, we will begin with the case of a hypothetical firm, Alpine Sports, Inc., a specialized sports equipment manufacturer. Christie Ryder began the business with a single ski production facility near Killington ski resort in central Vermont. Ski sales grew, and she also saw demand for snowboards rising—particularly after snowboard competition events were included in the 2002 Winter Olympics in Salt Lake City. She added a second plant in a nearby town. The second plant, while smaller than the first, was designed to produce snowboards as well as skis. She also modified the first plant so that it could produce both snowboards and skis. Two years later she added a third plant in another town. While even smaller than the second plant, the third was primarily designed for snowboard production but could also produce skis.
::为了建立生产可能性曲线,我们将首先考虑一个假设公司,Alpine体育有限公司,一家专门的体育设备制造商。Christie Ryder在佛蒙特州中部的Killington滑雪胜地附近,从一家滑雪生产设施开始经营。滑雪销售增加,她也看到对雪板的需求上升,特别是在盐湖市2002年冬季奥林匹克运动会中包括了雪板竞争事件之后。她在附近的一个城镇增加了第二个工厂。第二个工厂虽然小于第一个工厂,但设计用来生产雪板和滑雪板。她还改造了第一个工厂,以便生产雪板和滑雪板。两年后,她又在另一个城镇增加了第三个工厂。第三个工厂比第二个工厂还要小,但比第二个工厂还小,主要设计用于雪板生产,但也可以生产滑雪。

We can think of each of Ms. Ryder’s three plants as a miniature economy and analyze them using the production possibilities model. We assume that the factors of production and technology available to each of the plants operated by Alpine Sports are unchanged.
::我们可以将赖德女士的三个工厂中的每一个都视为一个微型经济,并且用生产可能性模型来分析它们。 我们假设阿尔卑斯山体育公司经营的每个工厂的生产和技术因素没有变化。

Suppose the first plant, Plant 1, can produce 200 pairs of skis per month when it produces only skis. When devoted solely to snowboards, it produces 100 snowboards per month. It can produce skis and snowboards simultaneously as well.
::假设第一座工厂,Plant 1 每月只生产滑雪板,可以生产200双滑雪板。它只生产滑雪板,每月生产100个滑雪板。它也可以同时生产滑雪板和滑雪板。

The table in  [Figure 1 - A Production Possibilities Curve]  gives three combinations of skis and snowboards that Plant 1 can produce each month. Combination A involves devoting the plant entirely to ski production; combination C means shifting all of the plant’s resources to snowboard production; combination B involves the production of both goods. These values are plotted in a production possibilities curve for Plant 1. The curve is a downward-sloping straight line, indicating that there is a linear, negative relationship between the production of the two goods.
::[图1 - 生产可能性曲线]中的表格给出了第1工厂每月可以生产的滑雪板和雪板的三种组合。 组合A涉及将工厂全部用于滑雪生产;组合C意味着将工厂的所有资源都转移到滑雪板生产;组合B涉及这两种货物的生产。这些价值在工厂1的生产可能性曲线中绘制。 曲线是一个向下倾斜的直线,表明两种货物的生产之间存在线性负关系。

Neither skis nor snowboards is an independent or a dependent variable in the production possibilities model; we can assign either one to the vertical or to the horizontal axis. Here, we have placed the number of pairs of skis produced per month on the vertical axis and the number of snowboards produced per month on the horizontal axis.
::滑雪或滑雪板在生产可能性模型中都不是独立或依附的变量;我们可以将一只划入垂直轴或水平轴。在这里,我们已经将每月生产的双滑雪车数放在垂直轴上,并将每月生产的雪车数放在水平轴上。

The negative slope of the production possibilities curve reflects the scarcity of the plant’s capital and labor. Producing more snowboards requires shifting resources out of ski production and thus producing fewer skis. Producing more skis requires shifting resources out of snowboard production and thus producing fewer snowboards.
::生产可能性曲线的负斜坡反映了工厂资本和劳动力的稀缺性。 生产更多的雪板需要从滑雪板生产中转移资源,从而减少滑雪板生产。 生产更多的滑雪板需要从滑雪板生产中转移资源,从而减少雪板生产。

The slope of Plant 1’s production possibilities curve measures the rate at which Alpine Sports must give up ski production to produce additional snowboards. Because the production possibilities curve for Plant 1 is linear, we can compute the slope between any two points on the curve and get the same result. Between points A and B, for example, the slope equals −2 pairs of skis/snowboard (equals −100 pairs of skis/50 snowboards). (Many students are helped when told to read this result as “−2 pairs of skis   per   snowboard.”) We get the same value between points B and C, and between points A and C.
::植物1的生产可能性斜坡曲线测量阿尔卑斯山体育必须放弃滑雪生产以生产更多雪板的速度。 由于工厂1的生产可能性曲线是线性的,我们可以计算曲线上任何两个点之间的斜坡,并得出相同的结果。 例如,在A点和B点之间,斜坡等于2对滑雪板/雪板(等于-100对滑雪鞋/50雪板)。 (当人们告诉许多学生阅读这一结果为“每雪板2对滑雪板”时,我们得到B点和C点之间以及A点和C点之间的相同价值。 )

To see this relationship more clearly, examine [Figure 2 - The Slope of a Production Possibilities Curve] . Suppose Plant 1 is producing 100 pairs of skis and 50 snowboards per month at point B. Now consider what would happen if Ms. Ryder decided to produce 1 more snowboard per month. The segment of the curve around point B is magnified in  [Figure 2 - The Slope of a Production Possibilities Curve] .  The slope between points B and B′ is −2 pairs of skis/snowboard. Producing 1 additional snowboard at point B′ requires giving up 2 pairs of skis. We can think of this as the opportunity cost of producing an additional snowboard at Plant 1. This opportunity cost equals the absolute value of the slope of the production possibilities curve.
::为了更清楚地看到这种关系,请审查[图2——生产可能性曲线的曲线]。假设工厂1在B点每月生产100双滑雪板和50个雪板。现在考虑如果Ryder女士决定每月再生产1个雪板,会发生什么情况。B点周围的曲线部分在[图2——生产可能性曲线的曲线]中放大。B点和B点之间的斜坡是2对滑雪板/雪板。在B点再生产1个雪板需要放弃2双滑雪板。我们可以认为这是在工厂1再生产一个雪板的机会成本。这个机会的成本等于生产可能性曲线的绝对价值。

The slopes of the production possibilities curves for each plant differ. The steeper the curve, the greater the opportunity cost of an additional snowboard. Here, the opportunity cost is lowest at Plant 3 and greatest at Plant 1.
::每个工厂的生产可能性曲线的坡度不同,曲线越陡,增加雪板的机会成本就越高,这里,第3工厂的机会成本最低,第1工厂的机会成本最高。

Comparative Advantage and the Production Possibilities Curve

To construct a combined production possibilities curve for all three plants, we can begin by asking how many pairs of skis Alpine Sports could produce if it were producing only skis. To find this quantity, we add up the values at the vertical intercepts of each of the production possibilities curves in   [Figure 3 - Production Possibilities at Three Plants] . These intercepts tell us the maximum number of pairs of skis each plant can produce. Plant 1 can produce 200 pairs of skis per month, Plant 2 can produce 100 pairs of skis at per month, and Plant 3 can produce 50 pairs. Alpine Sports can thus produce 350 pairs of skis per month if it devotes its resources exclusively to ski production. In that case, it produces no snowboards.
::为了为所有三个工厂构建一个综合生产可能性曲线,我们可以首先询问,如果阿尔卑斯山体育公司只生产滑雪板,它可以生产多少双滑雪板。为了找到这一数量,我们将在[图3 -- -- 三个工厂的生产可能性]中每个生产可能性曲线的垂直拦截中加起来。这些拦截告诉我们每个工厂能够生产的滑雪机的最大数量。 第1工厂每月可以生产200双滑雪机,第2工厂每月可以生产100双滑雪机,第3工厂可以生产50双。 因此,如果Alpine体育公司将资源全部用于滑雪生产,它可以每月生产350双滑雪机。 也就是说,它不会生产雪板。

Now suppose the firm decides to produce 100 snowboards. That will require shifting one of its plants out of ski production. Which one will it choose to shift? The sensible thing for it to do is to choose the plant in which snowboards have the lowest opportunity cost—Plant 3. It has an advantage not because it can produce more snowboards than the other plants (all the plants in this example are capable of producing up to 100 snowboards per month) but because it is the least productive plant for making skis. Producing a snowboard in Plant 3 requires giving up just half a pair of skis.
::假设公司决定生产100个雪板。 这就需要将其中1个工厂从滑雪生产中移出。它选择哪个工厂来换?它明智的做法是选择雪板拥有最低机会成本的工厂 — — Plant 3。 它有一个优势,不是因为它可以比其他工厂生产更多的雪板(这个例子中的所有工厂都能够每月生产多达100个雪板),而是因为它是造滑雪生产效率最低的工厂。 在3号工厂生产雪板需要放弃一半的滑雪板。

Economists say that an economy has a     in producing a good or service if the opportunity cost of producing that good or service is lower for that economy than for any other. Plant 3 has a comparative advantage in snowboard production because it is the plant for which the opportunity cost of additional snowboards is lowest. To put this in terms of the production possibilities curve, Plant 3 has a comparative advantage in snowboard production (the good on the horizontal axis) because its production possibilities curve is the flattest of the three curves.
::经济学家说,如果生产这种商品或服务的机会成本比其他任何经济体低,那么经济在生产这种商品或服务方面就有生产商品或服务的优势。 工厂3在雪板生产方面具有比较优势,因为增加雪板的机会成本最低的是工厂。 换句话说,从生产可能性曲线来看,工厂3在雪板生产(横向轴线上的商品)方面具有比较优势,因为其生产可能性曲线是三个曲线的峰值。

The combined production possibilities curve for the firm’s three plants is shown in  [Figure 4 - The Combined Production Possibilities Curve for Alpine Sports] . We begin at point A, with all three plants producing only skis. Production totals 350 pairs of skis per month and zero snowboards. If the firm were to produce 100 snowboards at Plant 3, ski production would fall by 50 pairs per month (recall that the opportunity cost per snowboard at Plant 3 is half a pair of skis). That would bring ski production to 300 pairs, at point B. If Alpine Sports were to produce still more snowboards in a single month, it would shift production to Plant 2, the facility with the next-lowest opportunity cost. Producing 100 snowboards at Plant 2 would leave Alpine Sports producing 200 snowboards and 200 pairs of skis per month, at point C. If the firm were to switch entirely to snowboard production, Plant 1 would be the last to switch because the cost of each snowboard there is 2 pairs of skis. With all three plants producing only snowboards, the firm is at point D on the combined production possibilities curve, producing 300 snowboards per month and no skis.
::该公司三家工厂的综合生产可能性曲线见[图4 -- -- 阿尔卑斯体育综合生产可能性曲线]。我们从A点开始,所有三家工厂只生产滑雪板。每月生产350对滑雪机,零雪板。如果该公司在3号工厂生产100个雪板,滑雪机的产量每月将下降50对(回顾3号工厂每雪板的机会成本是半对滑雪机)。这将使滑雪机生产达到300对,在B点。如果Alpine体育公司在一个月内生产更多的雪板,那么它将把生产转移到工厂2,该厂的产量将达到次低的机会成本。在2号工厂生产100对滑雪机,这将使Alpine体育公司每月生产200个雪板和200对滑雪机,在C点。如果该公司完全切换雪机生产,那么1号工厂将是最后的切换,因为每家雪板机的成本是2对雪板。所有3个工厂都无法生产雪板,每家在D号厂生产,每个雪板厂都不可能生产。

Notice that this production possibilities curve, which is made up of linear segments from each assembly plant, has a bowed-out shape; the absolute value of its slope increases as Alpine Sports produces more and more snowboards. This is a result of transferring resources from the production of one good to another according to comparative advantage. We shall examine the significance of the bowed-out shape of the curve in the next section.
::请注意,由每个装配厂线形部分组成的这一生产可能性曲线具有弯曲形状;随着阿尔卑斯山体育生产越来越多的雪板,其斜坡的绝对值会增加,这是根据相对优势将资源从一种商品的生产转移到另一种商品生产的结果。我们将在下一节中研究曲线弯曲的弯曲形状的意义。

The Law of Increasing Opportunity Cost

We see in  [ Figure 4 - The Combined Production Possibilities Curve for Alpine Sports]  that, beginning at point A and producing only skis, Alpine Sports experiences higher and higher opportunity costs as it produces more snowboards. The fact that the opportunity cost of additional snowboards increases as the firm produces more of them is a reflection of an important economic law. The     holds that as an economy moves along its production possibilities curve in the direction of producing more of a particular good, the opportunity cost of additional units of that good will increase.
::我们从[图4 -- -- 阿尔卑斯山体育联合生产机会曲线]中看到,阿尔卑斯山体育从A点开始,只生产滑雪鞋,随着更多雪板的产生,其机会成本会更高、更高。 随着公司生产更多雪板,增加雪板的机会成本会增加,这一事实反映了一个重要的经济法律。 认为随着经济沿着生产可能性曲线向生产更多特定产品的方向发展,增加该产品单位的机会成本将会增加。

We have seen the law of increasing opportunity cost at work traveling from point A toward point D on the production possibilities curve in  [Figure 4 - The Combined Production Possibilities Curve for Alpine Sports] . The opportunity cost of each of the first 100 snowboards equals half a pair of skis; each of the next 100 snowboards has an opportunity cost of 1 pair of skis, and each of the last 100 snowboards has an opportunity cost of 2 pairs of skis. The law also applies as the firm shifts from snowboards to skis. Suppose it begins at point D, producing 300 snowboards per month and no skis. It can shift to ski production at a relatively low cost at first. The opportunity cost of the first 200 pairs of skis is just 100 snowboards at Plant 1, a movement from point D to point C, or 0.5 snowboards per pair of skis. We would say that Plant 1 has a comparative advantage in ski production. The next 100 pairs of skis would be produced at Plant 2, where snowboard production would fall by 100 snowboards per month. The opportunity cost of skis at Plant 2 is 1 snowboard per pair of skis. Plant 3 would be the last plant converted to ski production. There, 50 pairs of skis could be produced per month at a cost of 100 snowboards, or an opportunity cost of 2 snowboards per pair of skis.
::从A点到D点,在[图4 -- -- 阿尔卑斯体育综合生产机会曲线]的生产可能性曲线上,我们已看到增加工作机会成本的法律。头100个雪橇的每个机会成本等于半双滑雪板;下100个雪板的每个机会成本为1双滑雪板,每个机会成本为1双滑雪板,最后100个雪板中的每个都有2对滑雪板的机会成本。法律还适用于公司从雪板到滑雪板的转变。假设它从D点开始,每月生产300个雪板,没有滑雪板。它首先可以以相对较低的成本转向滑雪生产。头200对滑雪板的机会成本只有1号厂的100个雪板;从D点到C点的移动,或每双滑雪板的移动为0.5个雪板。我们可以说,1号工厂的相对优势在滑雪板生产上。下100对雪板的生产将从每月生产100个雪板,每月生产100个雪板。在2号雪板厂生产的一个机会是1个雪板,最后1号雪板生产成本为2号雪板。

The bowed-out production possibilities curve for Alpine Sports illustrates the law of increasing opportunity cost. Scarcity implies that a production possibilities curve is downward sloping; the law of increasing opportunity cost implies that it will be bowed out, or concave, in shape.
::阿尔卑斯山体育组织(Alpine Sports)的低调生产可能性曲线显示了增加机会成本的规律。 稀缺意味着生产可能性曲线正在向下倾斜;增加机会成本的规律意味着它将会被降级或组合成形。

The bowed-out curve of   [Figure 4 - The Combined Production Possibilities Curve for Alpine Sports]  becomes smoother as we include more production facilities. Suppose Alpine Sports expands to 10 plants, each with a linear production possibilities curve. Panel (a) of  [Figure 5 - Production Possibilities for the Economy]  shows the combined curve for the expanded firm, constructed as we did in   [Figure 4 - The Combined Production Possibilities Curve for Alpine Sports] . This production possibilities curve includes 10 linear segments and is almost a smooth curve. As we include more and more production units, the curve will become smoother and smoother. In an actual economy, with a tremendous number of firms and workers, it is easy to see that the production possibilities curve will be smooth. We will generally draw production possibilities curves for the economy as smooth, bowed-out curves, like the one in Panel (b). This production possibilities curve shows an economy that produces only skis and snowboards. Notice the curve still has a bowed-out shape; it still has a negative slope. Notice also that this curve has no numbers. Economists often use models such as the production possibilities model with graphs that show the general shapes of curves but that do not include specific numbers.
::[图4 -- -- 阿尔卑斯山体育联合生产可能性曲线]的下游曲线随着我们加入更多的生产设施而变得更加平滑。如果阿尔卑斯山体育会扩展到10个工厂,每个工厂都有线性生产可能性曲线。[图5 -- -- 经济生产可能性]的小组(a)显示了扩大公司的综合曲线,正如我们在[图4 -- -- 阿尔卑斯山体育联合生产可能性曲线]中所做的那样,这个生产可能性曲线包括10个线性部分,几乎是一个平滑的曲线。随着我们包括越来越多的生产单位,曲线将变得更加平滑和顺畅。在实际经济中,每个工厂都有一条线性生产可能性曲线。在有大量的公司和工人的情况下,很容易看到生产可能性曲线将是平滑的。我们通常会像在[图4 -- -- 阿尔卑斯山体育联合生产可能性曲线]中所做的那样为经济绘制生产可能性曲线。这种生产可能性曲线显示的经济只产生滑雪和滑雪板。注意到曲线的形状仍然是下向的,但没有下向式的形状;曲线将更加平滑滑滑和滑,在实际经济中,它也经常使用这种曲线的曲线显示这种曲线的曲线的曲线。这个曲线上显示这种曲线。