关于需求函数图象的问题。。请高手解答

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数学上定义一个函数f=f(x),x是自变量，画成数轴的话，x就是横轴，也就是说自变量是横轴
可是为什么需求函数Q=f(P)中，P是自变量，确画成了纵轴？
百思不得其解。。
这是为啥呀？

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关键词：函数图象 需求函数 百思不得其解 自变量 数学 函数图象 自变量

说法不一。我的个人理解：后面的很多图像都是Q做自变量，多个货币衡量的变量做因变量进行比照。这么做便于图解分析吧。

WangLuoxuan 发表于 2011-8-19 13:00
说法不一。我的个人理解：后面的很多图像都是Q做自变量，多个货币衡量的变量做因变量进行比照。这么做便于图 ...

Q做自变量，那不就变成了需求函数的反函数了？

codyz 发表于 2011-8-19 13:02
Q做自变量，那不就变成了需求函数的反函数了？

Q-P 数学记号不变，反函数、原函数图像没区别啊。

在需求函数里面P是自变量，没错。但是后面生产论还有很多Q是自变量，并且用到P来比照的图像。把Q放在横轴很方便啊。

WangLuoxuan 发表于 2011-8-19 13:05
Q-P 数学记号不变，反函数、原函数图像没区别啊。

在需求函数里面P是自变量，没错。但是后面生产论还有 ...

哦哦，这样啊。。。
我记得以前上课的时候问老师，老师说这样比较直观，当时一直不理解什么叫做直观。。。

谢了呀。。

补充个小历史：这都是马歇尔的错误沿用至今变成了教科书的主流。

楼上说得对，马歇尔在书中就是这么用的，所以沿用至今。。

沿用，是确定的。但是否错误决定于马歇尔时代对Q-P相互决定关系的考量。至少不是将自变量误用在纵轴。下面是曼昆的一点说法，当然他自己也说“我不是搞历史的”。

http://gregmankiw.blogspot.com/2 ... ply-and-demand.html

ednesday, September 27, 2006
Who invented supply and demand?
A blog reader emails me:

    Hi-

    I'm a devoted reader of your blog, and I use your textbook with the Boston Public School seniors whom I teach in Brighton. They love your book. Thanks for doing it!

    Today in class, they asked two great questions that I couldn't answer, so I turn to...

    Question 1. Who invented the supply and demand graph? (I said Heilbroner. Is that right?) 1B. What is there to read about the history of the graph itself? That is, when was it created? By whom? Was it adopted immediately? etc.

    Question 2. Why is quantity on the X axis? Shouldn't it be on the Y axis?

    Thanks again for all you do,

    [name withheld]
    Public School Econ teacher

The model dates long before Heilbroner. Here is the answer according to Wikipedia:

    the partial equilibrium supply and demand economic model [was] originally developed by Antoine Augustin Cournot (published in a book in 1838) and thirty years later broadly publicized by Alfred Marshall.

That sounds right to me. I should note that Marshall's 1890 text was the standard for its day. You can find Marshall online, but unfortunately the online version omits the footnotes. In quickly looking through the copy I have on my shelf, I found supply-and-demand graphs in footnotes, but none in the main text. You can, however, read the discussion of supply and demand in Book V.

On the axis question: The instructor is right that, given the way we now teach supply and demand, it makes more sense to have price on the horizontal axis. The price is viewed as the variable that determines quantity supplied and quantity demanded, and we usually put the dependent variable (which here is quantity) on the vertical axis.

So why is it switched? Here is a guess. The early economists may have been imagining that, in the very short run, a given quantity of goods was supplied to the market (an agricultural harvest, for example). The supply curve is then vertical, and the price adjusts to ensure that quantity demanded equals this exogenous quantity supplied. So, in this very short run, the price seems more like the dependent variable. Now, however, the choice of axes is based more on historical convention than logic.

I am not an historian of economic thought, so these answers may be off base. But I am sure the commenters will correct me if I am mistaken.

Update: A comment directs us to a good article on the topic from the Richmond Fed.

Update 2: My Harvard colleague Robert Barro emails me his insights on the matter:

    As I recall, Hicks in Value and Capital thought in terms of demand price and supply price. The demand price is how much a person was willing to pay for an additional unit of goods (starting from some initial quantity, Q). The supply price is how much a producer would have to be paid to provide an additional unit of goods. This construction--which I think comes from Marshall--makes it natural to have P on the vertical axis and Q on the horizontal.