The Production Function · 生产函数
| English | 中文 | Pinyin · 拼音 |
|---|---|---|
| output/ˈaʊtpʊt/ | 产出 | chǎn chū |
| production function/prəˈdʌkʃn ˈfʌŋkʃn/ | 生产函数 | shēng chǎn hán shù |
| short run/ʃɔːt rʌn/ | 短期 | duǎn qī |
| long run/lɒŋ rʌn/ | 长期 | cháng qī |
| inputs/ˈɪnpʊts/ | 投入 | tóu rù |
| fixed/fɪkst/ | 固定 | gù dìng |
| variable/ˈveərɪəbl/ | 可变 | kě biàn |
| average product/ˈævrɪdʒ ˈprɒdʌkt/ | 平均产量 | píng jūn chǎn liàng |
| total product/ˈtəʊtl ˈprɒdʌkt/ | 总产量 | zǒng chǎn liàng |
| marginal product/ˈmɑːdʒɪnl ˈprɒdʌkt/ | 边际产量 | biān jì chǎn liàng |
| law of diminishing marginal returns/lɔː ɒv dɪˈmɪnɪʃɪŋ ˈmɑːdʒɪnl rɪˈtɜːnz/ | 边际收益递减规律 | biān jì shōu yì dì jiǎn guī lǜ |
One oven, more and more bakers
- Put one baker in a kitchen with a single oven — plenty of output.
- Add a second, a third, a fourth... the kitchen gets crowded.
- Each new baker still helps, but adds less than the one before.
- This simple story is the heart of the production function 生产函数.
一个烤箱,越来越多的面包师
- 让一个面包师在只有一个烤箱的厨房里干活——产量不错。
- 加第二个、第三个、第四个……厨房挤起来了。
- 每个新来的仍有帮助,但增加的比前一个更少。
- 这个简单的故事,正是生产函数(production function)的核心。
Short run vs long run
- The production function links inputs 投入 to output 产出 — the most a firm can make.
- In the short run 短期, at least one input is fixed 固定 (usually the factory); only variable 可变 inputs like workers can change.
- In the long run 长期, every input is variable — the firm can resize completely.
短期与长期
- 生产函数把投入(inputs)和产出(output)联系起来——企业最多能生产多少。
- 在短期(short run),至少有一个投入是固定(fixed)的(通常是工厂);只有像工人这样的可变(variable)投入能改变。
- 在长期(long run),每一个投入都是可变的——企业能彻底改变规模。
Short run or long run? · 短期还是长期?
In the short run at least one input is fixed; only variable inputs can change. In the long run every input is variable. · 短期至少有一个投入固定,只有可变投入能改变;长期每个投入都可变。
In the short run, a firm has: · 在短期,企业:
The short run has at least one fixed input; the long run has none. · 短期至少有一个固定投入;长期一个都没有。
Select all · 所有 that are usually variable inputs in the short run. · 选出所有在短期通常属于可变投入的项目。
Labour, materials and utilities flex in the short run; the factory is the fixed input. · 劳动、材料和公用事业在短期可变;工厂是固定投入。
Total, marginal, average product
- Total product 总产量 (TP) is all the output from all the workers together.
- Marginal product 边际产量 (MP) is the extra output from one more worker: $MP = \dfrac{\Delta TP}{\Delta L}$.
- Average product 平均产量 (AP) is output per worker: $AP = \dfrac{TP}{L}$.
总产量、边际产量、平均产量
- 总产量(total product,TP)是所有工人一起生产的全部产出。
- 边际产量(marginal product,MP)是多一个工人带来的额外产出:$MP = \dfrac{\Delta TP}{\Delta L}$。
- 平均产量(average product,AP)是每个工人的产出:$AP = \dfrac{TP}{L}$。
Marginal product is: · 边际产量是:
MP = ΔTP/ΔL — the change in total product from adding a worker. (Output per worker is average product.) · MP = ΔTP/ΔL——增加一个工人引起的总产量变化。(每个工人的产出是平均产量。)
A bakery makes 24 loaves with 2 workers and 33 loaves with 3 workers. What is the marginal product of the 3rd worker? · 一家面包店 2 个工人做 24 个面包,3 个工人做 33 个。第 3 个工人的边际产量是多少?
MP of the 3rd worker = 33 − 24 = 9 loaves. · 第 3 个工人的边际产量 = 33 − 24 = 9 个面包。
The law of diminishing marginal returns
- Keep adding workers to a fixed factory and, past some point, each adds less than the last.
- This is the law of diminishing marginal returns 边际收益递减规律.
- Workers crowd the same machines, so marginal product falls.
- When MP is still positive, TP keeps rising — just more slowly. When MP hits zero, TP is at its peak.
边际收益递减规律
- 不断往一个固定的工厂里加工人,过了某一点,每个人增加的都比上一个更少。
- 这就是边际收益递减规律(law of diminishing marginal returns)。
- 工人们挤在同样的机器旁,所以边际产量下降。
- 当 MP 仍为正时,TP 继续上升——只是更慢。当 MP 降到零,TP 达到最高。
Diminishing marginal returns means each extra worker (added to a fixed factory) eventually adds less output than the one before. · 边际收益递减是指(加到固定工厂上的)每个额外工人,最终增加的产出都比上一个少。
Past some point, crowding the fixed input makes marginal product fall. · 过了某一点,固定投入被挤占,边际产量下降。
Total product is at its maximum when marginal product equals ______. · 当边际产量等于______时,总产量达到最大。
While MP is positive TP rises; at MP = 0 it peaks; when MP is negative TP falls. · MP 为正时 TP 上升;MP = 0 时达到峰值;MP 为负时 TP 下降。
The production function turns inputs into output. In the short run some input is fixed; in the long run all are variable. As you add a variable input to a fixed one, marginal product eventually falls — the law of diminishing marginal returns.
生产函数把投入变成产出。在短期某个投入是固定的;在长期全部可变。当你把一个可变投入不断加到固定投入上,边际产量终会下降——这就是边际收益递减规律。