# Marshall’s maths

Posted on: March 4, 2008

Bluematter quotes Alfred Marshall:

(1) Use mathematics as shorthand language, rather than as an engine of inquiry. (2) Keep to them till you have done. (3) Translate into English. (4) Then illustrate by examples that are important in real life (5) Burn the mathematics. (6) If you can’t succeed in 4, burn 3. This I do often.

It seems to me to be fairly good advice, but Bluematter’s not convinced that either the maths or the real world examples are useful! Let’s examine a real world example to illustrate the issue.

Suppose that we were interested in tax policy (stranger things have happened). It is quite conceivable that we might want to know the impact on peoples’ labour decisions from our tax. So how would one go about analysing it? Well, one would need to consider the impact of our tax via both income and substitution effects, and then sum those effects to see what effect it had on labour supply. If you are one who shuns maths, pause here to consider how you would describe the decomposition of the movement in labour supply. Ask yourself if you could do it more concisely and more precisely than this.

$displaystyle{frac{partial x(p, w)}{partial p} = frac{partial h(p, u)}{partial p} - frac{partial x(p, w)}{partial w } x(p, w)}$

Slutsky’s equation sums up in one line what would take paragraphs of English to describe. Even in those many paragraphs it would be difficult to be as precise as Slutsky is with his single line. Maths simply gives us a language to accurately discuss complex systems. Natural languages, such as English, aren’t designed to concisely do this and provide inadequate tools for talking about such systems.

The most common criticism I hear of economics is that it would be impossible to describe human behaviour because it is too complex. I don’t want to dive into that, but if we are to attempt to describe complex things then we need a language capable of talking about them in an accurate and succinct fashion. Maths is obviously the best language for the job. That the same people who claim human behaviour is complex often also rail against the mathematisation of economics baffles me.

### 3 Responses to "Marshall’s maths"

An excellent post. Let me make my position clear:

I disagree with 1 because, while mathematics are a very convenient short-hand language, they are also an excellent engine of inquiry. Many insights are arrived at by defining a mathematical model and then see how it behaves, rather than necessarily having an intuitive notion of how it does so and then simply writing in short-hand math.

I disagree with 2 and 5, because the math is useful. It’s also convenient and in many cases neccesary to understand an idea.

I don’t disagree with 4, but I don’t find it necessary either. Lots of interesting work in economics is more ‘technical’ and does not readily apply to reality (only as a contituent part of more complete models), so I wouldn’t characterise all papers that do not naturally generate practical examples as useless.

Also, how come Bluematter. resides under ‘institutional economics’? (not that I mind, just curious 🙂

Thanks so much for replying and clarifying your position. It seems I wholly misinterpreted your criticism of Marshall’s quote, sorry. I took the spirit of it to be that mathematics is useful for formalising ideas and exploring models, but that we should always try to relate our results to the problem we are trying to solve. In economics that problem is something to do with scarce resources in the real world and so our models should give us come insight that we can express in English.

I do agree with most of your critiques. It reminds me of a quote which I repeat ad nauseum to those who I talk to regularly. The gist is that journal articles should either be theoretical and advance the theory or practical and explain the world. They should never be theoretically practical and explain nothing about the real world using known theory. I fear that sometimes the method of mathematical inquiry is misused to disguise the latter as a real contribution to to the literature.

As to why you’re institutional, I don’t know but I’m sure Web Master Matt will chime in at some stage 🙂

“Also, how come Bluematter. resides under ‘institutional economics’?”

Institutional is just where I’ve put things that have talked about path dependence or economic history, or seem in some way holistic. I’ve noticed that you like to mention economic history stuff so I slipped you in there – personally I think I need to work on making the economic distinctions on our blog roll clearer 😉