下一美元該怎么花?

From an e conomist's perspective, making choices involves making decisions 'at the margin' -- that is, making decisions based on small changes in resources:

從經(jīng)濟(jì)學(xué)家的角度來看，做出選擇包括“在邊際”做出決定——也就是說，根據(jù)資源的微小變化做出決定：

How should I spend the next hour?

我該如何度過接下來的一個(gè)小時(shí)?

How should I spend the next dollar?

下一美元該怎么花?

In fact, e conomist Greg Mankiw lists under the "10 principles of economics" in his popular economics textbook the notion that "rational people think at the margin." On the surface, this seems like a strange way of considering the choices made by people and firms.

事實(shí)上，經(jīng)濟(jì)學(xué)家格雷格·曼昆在他廣受歡迎的經(jīng)濟(jì)學(xué)教科書中的“經(jīng)濟(jì)學(xué)的十大原則”下列出了“理性的人在邊緣思考”。從表面上看，這似乎是一種奇怪的方式來考慮人們和公司做出的選擇。

It is rare that someone would consciously ask themselves -- "How will I spend dollar number 24,387?" or "How will I spend dollar number 24,388?" The idea of marginal analysis doesn't require that people explicitly think in this way, just that their actions are consistent with what they would do if they did think in this way.

很少有人會(huì)有意識(shí)地問自己——“我將如何花24,387美元?”或者“我將如何花24,388美元?”邊際分析的思想并不要求人們明確地以這種方式思考，只要求他們的行為與他們以這種方式思考會(huì)做的事情是一致的。

Marginal analysis can be applied to both individual and firm decision making.

邊際分析既適用于個(gè)人決策，也適用于企業(yè)決策。

For firms, profit maximization is achieved by weighing marginal revenue versus marginal cost.

對(duì)于企業(yè)來說，利潤(rùn)最大化是通過權(quán)衡邊際收益與邊際成本來實(shí)現(xiàn)的。

For individuals, utility maximization is achieved by weighing the marginal benefit versus marginal cost. Note, however, that in both contexts the decision maker is performing an incremental form of cost-benefit analysis.

對(duì)個(gè)人來說，效用最大化是通過權(quán)衡邊際效益和邊際成本來實(shí)現(xiàn)的。但請(qǐng)注意，在這兩種情況下，決策者都在執(zhí)行一種增量形式的成本效益分析。

Let’s see an example:

讓我們來看一個(gè)例子：

To gain some more insight, consider the decision regarding how many hours to work, where the benefits and costs of working are designated by the following chart:

為了更深入的了解，我們來權(quán)衡一下關(guān)于工作時(shí)間的決定，工作的收益和成本是由下面的圖表指定的:

Hour - Hourly Wage - Value of Time

工作時(shí)間 - 每小時(shí)的工資 - 時(shí)間的價(jià)值

Hour 1: $10 - $2

Hour 2: $10 - $2

Hour 3: $10 - $3

Hour 4: $10 - $3

Hour 5: $10 - $4

Hour 6: $10 - $5

Hour 7: $10 - $6

Hour 8: $10 - $8

Hour 9: $15 - $9

Hour 10: $15 - $12

Hour 11: $15 - $18

Hour 12: $15 - $20

The hourly wage represents what one earns for working an extra hour - it is the marginal gain or the marginal benefit.

每小時(shí)的工資代表了一個(gè)人額外工作一小時(shí)的收入——這是邊際收益或邊際效益。

The value of time is essentially an opportunity cost -- it is how much one values having that hour off. In this example, it represents a marginal cost -- what it costs an individual to work an additional hour. The increase in marginal costs is a common phenomenon; one usually doesn't mind working a few hours since there are 24 hours in a day. She still has plenty of time to do other things. However, as an individual starts to work more hours, it reduces the number of hours she has for other activities. She has to start giving up more and more valuable opportunities to work those extra hours.

時(shí)間的價(jià)值本質(zhì)上是一個(gè)機(jī)會(huì)成本——它是一個(gè)人休息一個(gè)小時(shí)的價(jià)值。在這個(gè)例子中，它代表了邊際成本——一個(gè)人額外工作一小時(shí)的成本。邊際成本的增加是一個(gè)普遍現(xiàn)象;人們通常不介意工作幾個(gè)小時(shí)，因?yàn)橐惶煊?4小時(shí)，她還有足夠的時(shí)間做其他事情。然而，當(dāng)一個(gè)人開始工作更長(zhǎng)時(shí)間時(shí)，這就減少了她從事其他活動(dòng)的時(shí)間。她不得不開始放棄越來越多的寶貴機(jī)會(huì)來加班。

It is clear that she should work the first hour, as she gains $10 in marginal benefits and loses only $2 in marginal costs, for a net gain of $8.

顯然，她應(yīng)該在第一個(gè)小時(shí)工作，因?yàn)樗倪呺H收益是10美元，而邊際成本只有2美元，凈收益是8美元。

By the same logic, she should work the second and third hours as well. She will want to work until the time at which the marginal cost exceeds the marginal benefit. She will also want to work the 10th hour as she receives a net benefit of $3 (marginal benefit of $15, marginal cost of $12). However, she will not want to work the 11th hour, as the marginal cost ($18) exceeds the marginal benefit ($15) by three dollars.

按照同樣的邏輯，她也應(yīng)該在第2和第3個(gè)小時(shí)工作。她會(huì)一直工作到邊際成本超過邊際效益的時(shí)候。到第10個(gè)小時(shí)的時(shí)候她還是愿意工作，因?yàn)樗膬羰找鏋?美元(邊際收益為15美元，邊際成本為12美元)。然而，第11個(gè)小時(shí)的工作她就不會(huì)愿意做了，因?yàn)檫呺H成本(18美元)比邊際效益(15美元)還要高出3美元。

Thus marginal analysis suggests that rational maximizing behavior is to work for 10 hours. More generally, optimal outcomes are achieved by examining marginal benefit and marginal cost for each incremental action and performing all of the actions where marginal benefit exceeds the marginal cost and none of the actions where marginal cost exceeds the marginal benefit. Because marginal benefits tend to decrease as one does more of an activity but marginal costs tend to increase, the marginal analysis will usually define a unique optimal level of activity.

因此，邊際分析表明，合理的最大化行為是工作10小時(shí)。更籠統(tǒng)的說，通過檢查每個(gè)增量行動(dòng)的邊際效益和邊際成本，并執(zhí)行邊際效益超過邊際成本的所有行動(dòng)，以及邊際成本沒有超過邊際效益的任何行動(dòng)，均可獲得最佳結(jié)果。因?yàn)檫呺H收益會(huì)隨著一項(xiàng)活動(dòng)的增加而減少，而邊際成本卻增加，因此邊際分析通常會(huì)定義一個(gè)唯一的最佳活動(dòng)水平。