期望利润微观经济学计算公式（Alevel经济学习A笔记成本和收入之）

a-level economics revision guides and question banks covering labour markets, supply and demand, market structure and all core economics a-level topics.

以下内容我们会持续更新：

今天带给大家Alevel经济笔记是：

成本和收入-“边际收益递减规律”The Law of Diminishing Marginal Returns

Although this topic is called 'Costs and revenues', it is important that we look at the law of diminishing marginal returns first because it is from this law that the cost curves are derived. To start with, we need to define a few terms.

尽管这个话题被称为“成本和收入”，但重要的是我们首先要研究边际收益递减规律，因为正是从这个规律得出了成本曲线。首先，我们需要定义一些术语。

Total, average and Marginal product

总产品、平均产品和边际产品

Before commencing the bulk of the topic, it is important to make a few assumptions. The following analysis applies to the short run only.

The short run is defined as the period of time where at least one factor of production is fixed.

Only in the long run can we assume that the amount of capital (e.g. machines) can vary.

在开始本主题的大部分内容之前，重要的是要做出一些假设。以下分析仅适用于短期。短期定义为至少一个生产要素固定的时期。只有从长远来看，我们才能假设资本（例如机器）的数量会发生变化。

For simplicity, we will only be dealing with capital and labour, and ignoring the other two factors of production; land and the entrepreneur.

So, in the short run, we will assume that capital is fixed, but the firm can vary the amount of labour used.

为简单起见，我们将只处理资本和劳动力，而忽略其他两种生产要素；土地和企业家。因此，在短期内，我们将假设资本是固定的，但公司可以改变使用的劳动力数量。

Now we need to define the terms that we will be using.

• Total product This is the quantity of output produced by a given number of workers over a given period of time. Remember the amount of capital (or machines) is fixed.总产品这是给定数量的工人在给定时间段内生产的产出量。请记住，资本（或机器）的数量是固定的。
• Average productThis is the quantity of output per unit of input. In this model, the input is labour. In other words, we are dealing with the output per worker, on average.平均产品这是每单位投入的产出量。在这个模型中，输入是劳动力。换句话说，我们正在处理平均每个工人的产出。
• Marginal productThe addition to total output produced by one extra unit of input (again, labour). It is the extra output produced at the margin (i.e. by adding a marginal unit of labour).边际产品增加一单位额外投入（同样是劳动力）所产生的总产出。它是边际生产的额外产出（即通过增加一个边际劳动单位）。

At this point it is worth looking at the relationship between the total, average and the marginal in more detail.

It will come up again when we look at costs and then revenues, so it is important that you understand it fully.

在这一点上，值得更详细地研究总、平均和边际之间的关系。当我们查看成本和收入时，它会再次出现，因此您必须充分理解它。

Look at the table below. Let us assume that the firm in question is making computer laser printers and they have four machines in the factory (capital = 4).

请看下表。让我们假设有问题的公司正在制造计算机激光打印机，并且他们在工厂中有四台机器（资本 = 4）。

Capital	Labour (L)	Marginal product (MP)	Total product (TP)	Average product (AP)
4	0	-	0	-
4	1	5	5	5.0
4	2	8	13	6.5
4	3	10	23	7.7
4	4	11	34	8.5
4	5	10	44	8.8
4	6	7	51	8.5
4	7	4	55	7.9
4	8	1	56	7.0
4	9	-2	54	6.0

Remember that capital is fixed in the short run. I have assumed that capital is fixed at 4 units (or machines, in this case).

请记住，资本在短期内是固定的。我假设资本固定为 4 个单位（或机器，在这种情况下）。

The second column shows the progressive addition of units of labour.

第二列显示了劳动单位的逐步增加。

The third column shows marginal product (MP).

Each figure represents the output produced as a result of adding an extra worker.

So, for instance, the addition of the seventh worker results in an increase in output of 4 units.

Once the fourth worker is added, another 11 units are produced, etc.

Notice that marginal product rises quite quickly, peaks at 11, and then begins to fall, reaching a negative figure for the ninth worker.

Diminishing Marginal Returns (DMR) set in after the fourth worker. Go to the last section in this Learn It for the full explanation of DMR.

第三列显示边际产品(MP)。每个数字代表添加一个额外工人所产生的产出。因此，例如，增加第七个工人会导致产量增加 4 个单位。一旦增加了第四个工人，就会再生产 11 个单位，依此类推。请注意，边际产品上升很快，在 11 处达到峰值，然后开始下降，第九个工人达到负数。在第四个工人之后出现边际收益递减（DMR）。有关 DMR 的完整说明，请转到本 Learn It 的最后一部分。

The fourth column gives total product (TP). This is calculated quite easily by adding, cumulatively, the marginal products. The first worker makes 5 units, so the total is 5.

The second worker adds a further 8 units, so the total is now 13 (5 8), and so on. In fact, you can work out the marginals from the totals. Take the sixth worker, for example.

His marginal product is 7. This can be calculated by taking the TP from six workers and subtracting the TP from five workers (51 - 44). Algebraically:

第四列给出总产品（TP）。这很容易通过累加边际产品来计算。第一个工人生产 5 个单位，所以总数为 5。第二个工人又增加了 8 个单位，所以现在总数为 13 (5 8)，依此类推。事实上，您可以从总数中计算出边际。以第六名工人为例。他的边际产量是 7。这可以通过从 6 名工人中获取 TP 并从 5 名工人（51 - 44）中减去TP来计算。代数：

The fifth column gives average product (AP). The figures in this column represent output (or product) per worker.

The average product once the eighth worker has been added is 7.

This was calculated by taking the TP with eight workers and dividing by the number of workers (also eight). Algebraically:

第五列给出平均产品（AP）。此列中的数字代表每个工人的产出（或产品）。添加第八名工人后的平均产品为 7。这是通过将TP与八名工人相除并除以工人人数（也是八名）来计算的。代数：

Now try and work out the table below to see if you understand what is going on. Click the relevant area in the table to display the answer.

现在试着计算下表，看看你是否明白发生了什么。单击表中的相关区域以显示答案。

Here are the relevant curves. They have been plotted using the figures from the first table; not the one you have just filled in.

以下是相关曲线。它们是使用第一个表中的数字绘制的；不是你刚刚填写的那个。

Notice that the point at which diminishing marginal returns sets in is to the left of the point where diminishing average returns begins.

Also, the total product keeps rising even though the marginal, and the average, product is falling.

This is not hard to understand. Just because the marginal product is falling, it is still positive.

Hence, these extra workers may well be adding less than previous workers, but they are still contributing to the grand total. Total product keeps rising, albeit at a diminishing rate.

It is only when the marginal product is negative, with the addition of the ninth worker that total product starts to fall.

请注意，边际收益递减开始的点位于平均收益递减开始点的左侧。此外，尽管边际产品和平均产品在下降，但总产品仍在上升。这不难理解。只是因为边际产量在下降，它仍然是正的。因此，这些额外的工人可能比以前的工人增加的少，但他们仍然对总数做出了贡献。总产品不断上升，尽管速度呈递减趋势。只有当边际产量为负时，随着第九个工人的加入，总产量开始下降。

Finally, notice that the marginal product curve cuts the average product curve at its highest point, where it is momentarily flat.

It is important that you understand why this happens because this concept is applied to the cost and revenue curves.

I think it deserves its own little section:

最后，请注意边际产品曲线在最高点切割平均产品曲线，在该点它暂时平坦。了解为什么会发生这种情况很重要，因为这个概念适用于成本和收入曲线。我认为它值得拥有自己的小部分：

Why the marginal curve cuts the average curve where it is momentarily flat

为什么边际曲线会在暂时平坦的地方切割平均曲线

Imagine you are with a group of friends, waiting at the bus stop in anticipation of a great Friday night out.

You all decide to check that you have enough money for the frivolities that lie ahead.

想象一下，你和一群朋友在公共汽车站等车，期待周五晚上的美好时光。你们都决定检查自己是否有足够的钱来应付眼前的琐事。

There are nine of you and, coincidentally, you all have exactly £20 each.

This means that the average amount of money that each of you holds is also £20.

你们有九个人，巧合的是，你们每个人正好有 20 英镑。这意味着你们每个人持有的平均金额也是 20 英镑。

Your tenth friend is late, but finally arrives. He only has £10 on him.

This means that between you the total amount of money is £190, and the new average is £190 divided by 10, which is £19.

The arrival of your tenth friend has reduced the average because the amount he added to the total, the marginal, was less than the prevailing average.

你的第十个朋友迟到了，但终于到了。他身上只有10英镑。这意味着你们之间的总金额为 190 英镑，新的平均金额为 190 英镑除以 10，即 19 英镑。你的第十个朋友的到来降低了平均值，因为他添加到总数中的边际量低于当前的平均值。

If your tenth friend had had £30 on him, the new total would have been £210, and the new average would have been £210 divided by 10, which is £21.

The arrival of your tenth friend would have increased the average because the amount he added to the total, the marginal, was more than the prevailing average.

如果你的第十个朋友身上有 30 英镑，那么新的总数将是 210 英镑，新的平均数将是 210 英镑除以 10，即 21 英镑。你的第十个朋友的到来会增加平均值，因为他添加到总数中的金额，即边际，超过了普遍的平均值。

If your tenth friend had also exactly £20 on him, then the average would have remained unchanged; £200 divided by 10 is still £20.

如果你的第十个朋友也正好有 20 英镑，那么平均值将保持不变；200 英镑除以 10 仍然是 20 英镑。

This is exactly what is going on with the average and marginal product curves.

When the marginal curve is above the average curve, then the average is rising.

When the marginal curve is below the average curve, then the average is falling.

When the marginal is the same as the average (which is where they cross) then the average remains the same.

这正是平均和边际产品曲线的情况。当边际曲线高于平均曲线时，平均线在上升。当边际曲线低于平均曲线时，则平均值正在下降。当边际与平均值相同（它们交叉的地方）时，平均值保持不变。

The issue is not whether the marginal is rising or falling, but whether it is above or below the average curve.

In the diagram, you can see that the marginal product curve rises to start with and then begins to fall, but the average product curve only starts to fall when the marginal product curve drops below the average product curve.

问题不在于边际是上升还是下降，而是高于或低于平均曲线。在图中，您可以看到边际产量曲线开始上升然后开始下降，但平均产量曲线只有在边际产量曲线下降到平均产量曲线下方时才开始下降。

The law of diminishing marginal returns

边际收益递减规律

Note: the textbook definition: If a firm increases output by adding variable labour to fixed capital then eventually diminishing marginal returns (physical product of labour) will set in.

In other words, at some point an extra worker will add less output to the grand total than the previous worker.

注意：教科书的定义：如果一家公司通过在固定资本中增加可变劳动来增加产量，那么最终边际收益递减（劳动的实物产品）将会出现。换句话说，在某个时候，一个额外的工人会给总产量增加更少的产量总比以前的工人。

In our initial example, the factory has four machines. As the first, second, third and fourth workers are added; they each have at least one machine each to work on.

In fact the marginal product continually increases because each worker can do a different job and so get the products finished quicker.

在我们最初的示例中，工厂有四台机器。随着第一、二、三、四名工人的加入；他们每个人至少有一台机器可以工作。事实上，边际产品不断增加，因为每个工人可以做不同的工作，从而更快地完成产品。

But when you add the fifth, sixth, seventh, etc. workers, somebody will be standing around doing nothing and adding little to total output.

The marginal product is still positive, perhaps they can take over when one of the initial workers gets tired, but the total product rises at a slower rate.

The ninth worker has a negative marginal product. His addition has resulted in a fall in total output.

We have now reached the point where 'too many cooks spoil the broth', as the saying goes.

但是当你加上第五个、第六个、第七个等工人时，就会有人站在一旁无所事事，对总产量的贡献微乎其微。边际产品仍然是正的，也许当最初的工人之一累了时他们可以接手，但总产品的增长速度较慢。第 9 个工人的边际产品为负。他的加入导致总产量下降。俗话说，我们现在已经到了“厨师太多会破坏肉汤”的地步。

It is for these reasons that the marginal product curve looks as it does (rises, peaks and then falls).

Also, the shape of the average product curve is directly dependent on the marginal product curve for the reasons explained in the section called 'Why the marginal curve cuts the average curve where it is momentarily flat'.

So we have explained where these product curves come from. At the end of the next Learn-It (called 'Costs and their curves') you will see that the cost curves are derived from these product curves.

In other words, the cost curves are derived from the law of diminishing marginal returns.

正是由于这些原因，边际产品曲线看起来就是这样（上升、达到峰值然后下降）。此外，平均产品曲线的形状直接取决于边际产品曲线，原因在“为什么边际曲线会在平均曲线暂时平坦的地方切割平均曲线”一节中进行了解释。所以我们已经解释了这些产品曲线的来源。在下一个 Learn-It（称为“成本及其曲线”）结束时，您将看到成本曲线源自这些产品曲线。换句话说，成本曲线是从边际收益递减规律推导出来的。

The title of this Learn-It is 'the law of diminishing marginal returns'.

Why is it a law?

It is something that is accepted by just about all economists as being true in all situations, just like nearly everybody accepts the laws of the land.

这个Learn-It的标题是“边际收益递减规律”。为什么是法律？这是几乎所有经济学家都接受的东西，在所有情况下都是正确的，就像几乎每个人都接受这片土地的法律一样。

今天的Alevel经济笔记就更新到这里，如果大家对Alevel经济学感兴趣可以关注我们，

之前更新：

1、Alevel经济学习笔记：总需求和总供给篇-The Circular Flow of Income

2、Alevel经济学习笔记：总需求和总供给篇-The '45 Degree' Diagram

3、Alevel经济学习笔记：总需求和总供给篇-Aggregate Demand

后续我们还会更新我以下版块的内容~

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