# Is calculus ever useful in business?

I mean does it ever allow you to do things like predict the growth of the market?
How useful is it for analysing data?

Generally speaking, does calculus have any use as a tool in business?

How about in the economy as a whole?

IANAMathematician but if you Google “calculus business applications” you get hundreds of hits for college class syllabuses on exactly that topic so yes…it would seem there is quite a call for calculus in the business world. Some applications are, "…supply and demand curves, cost functions, revenue and profit functions, market euilibrium, taxation, and elasticity. " (Source: http://itech.pjc.edu/mpetrusk/mac2233/ )

Yes, it can be enormously useful. Go and learn it.

Usually not for business because most “business” is people of moderate intelligence and ability pushing papers and numbers around and making deals.

One exception that I can think of is if you are doing very high level financial modeling like traders use. Pricing options with Black-Scholes models and so on.

Seriously?
Are you talking from experience or what?

Not just financial modeling. Modeling any and all parts of your business at a sophisticated level can call for calculus and other higher mathematics. Marketing, churn, product success, etc…

I’m not sure about serious, no-kidding-around calculus, but a lot of the economics I’ve studied seems to be based on ‘calculus for dummies’ (IE, breaking the original curve up into a series at regular intervals, which makes it easy to work out the value of the differential on a similar basis.)

Every time an economist talks about ‘marginal’ something… (marginal cost, marginal revenue, marginal utility, marginal efficiency, marginal productivity, marginal returns, marginal propensity to such-and-such, marginal profit, marginal value, marginal rate of this-and-the-other, probably some more that I couldn’t find before I quit googling,) they’re talking about a crude, first-order derivative of whatever-it-is, based on the smallest natural unit that they can think of.

Hope this helps.

I work as an actuarial analyst in the insurance business, and calculus and calculus-based probability are the foundation of everything we do. (You can’t get a job in this field unless you understand calculus.) The severity of insurance claims tend to follow mathematical distributions, and to predict the cost of such claims you need to be able to integrate the distributions.

According to my father, who’s a market analyst,

a) It is both useful and necessary when creating models
b) Software takes care of it for him.

Of course, you have to understand why it’s applied that way, and so it’s a good idea to know how to do it yourself–but if there were ever a major breakdown such that he could not find a computer to do the dirty work for him, I suspect he’d have more important things to worry about.

The classic example we were taught in high school calculus was calculating compound interest. That and how far apart dots on a balloon got when you were blowing it up.

But aren’t you essentially an applied mathematician who works for an insurance company? How would a sales manager use calculus? I can see how consumer trends and demographics could be mathematically modeled in great detail, but with so much riding on imprecise factors such as consumer sentiment or investor perceptions, how is it worth the effort of building a model?

Mathematics need not be rigorous to be useful. If somebody is intuitive about higher math they will think in a completely different manner from somebody who isn’t. The models their brain on the fly that we call “perspective” and “ideas” will be in general a lot better and a lot more useful, making it seem as if the person has more knack for business.

A sales manager need to be at least well versed in integration, derivation and appropriate calculus-based statistics for things like sales contracts, understanding and analyzing past sales data, efficient sales distribution.

Perhaps. But the fact that an insurance company needs “applied mathematicians”, and can’t price its product properly or determine its profits without them, is an example of calculus as a “tool in business”.

(Our training, by the way, includes a fair amount of marketing and economics in addition to applied math–it’s a perfect example of the synergies between business and math.)

They probably wouldn’t–at least not directly–because they would hire a person with a different set of skills for that job. But indirectly, everything they sell is designed and priced with our input.

Some firms do attempt to capture such things with econometric modeling–for example, projecting future values of a time series as a function of previous terms, or regressing nebulous variables against better understood variables. The results can be either very useful or very bogus, but I haven’t worked in the field so I don’t know which is more common.

No and only a little. Those are statistical problems. Of course, the methods used to solve statistical problems depend on a lot of calculus.

This happens to be what I do for a living. Most of my results are pretty good, but alas, some of them are crap.

I do not have to take derivatives or integrals as part of my job, so no, I do not have to use calculus to solve actual problems. However, the intuition of calculus is critical to successful model specification. Also, I frequently have to make use of mathematical reference books to write statistics code. It is futile to read econometric references without knowing calculus. If I didn’t turn to the texts, I would never be able to expand my toolbox.

I once encountered a real case of calculus being used for business. Years ago the software company I worked for sent me to Chicago to help a customer that happened to be a large investment bank. One morning, as I was waiting to talk to an executive, I noticed that the whiteboard in someone’s cubicle was covered with partial differential equations. “Oh, look,” I said, “partial differential equations!”

Without saying a word, the guy in the cubicle got up and erased the whiteboard.

I assume the equations had to do with market analysis. In any case, they were obviously supposed to be secret. The guy needn’t have worried, since I didn’t know what any of the variables stood for.

Can you expand on this any? How does the calculus training change how they think in a way that would be advantageous to someone in business?

And if you want to calculate continuously compounded interest, you have to solve a differential equation.

Which is why most banks don’t do continuous compounding these days, I suppose.

It’s difficult to elaborate on this, since it would probably take years of research and studies, but what I was referring to are numerous things like Mean Value Theorem, that gives you the intuition of how cotinuous numbers shall behave.

For example, you are presented with a report that has a graph and some figures. With a calculus education, you would know the significance of slope (rate of change) and the integral (aggregate ___), and applying things like MVT you would know things about the rate of change. You would also know how to combine it with other graphs in a meaningful fashion, how to eyeball performance, etc.

Another example is that a manager not versed in calculus might look at a monthly sales report performance graph that happens to have equal starting and ending values and see a “plateau” (slope = 0), then you might see that as a problem. With calculus you see that as an inevitability (Rolle’s theorem).