# Just how much calculus is involved in the study of economics?

I'm a sophomore at a community college that is set to transfer to the University of California as an economics major. It's required that I took Calculus 1 and Calculus 2, but not Probability and Statistics – which I think is strange. In Principles of Microeconomics and Principles of Macroeconomics, I never really used any calculus, but then again, those are introductory classes.

Tldr

I am terrible at calculus, but I love economics. When I get into the more advanced classes, is calculus going to be more present? If so, then I think I might have to rethink my major.

• As much as i know, calculus could be used in the conCepts of findings marginalism (marginal cost and marginal revenue)... Nothing but how much cost it takes to produce one additional unit... I would recommend to google this topic:) Apr 8 '16 at 22:34
• Often in economics, we're looking to find the optimal choice for an economic agent, which means maximizing utility functions or minimizing cost functions. This involves taking first derivatives and solving systems of equations. I wouldn't say that the actual calculus is the hard part. Usually, the more difficult thing is figuring out how to solve problems using the mathematical tools you have Apr 8 '16 at 23:04
• The most lower-level math I've used has been partial differentials, integration by parts, infinite sums and series, and some differential equations. Nothing too crazy. I think it is more important for one to study theoretical mathematics.
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Apr 14 '17 at 23:33

Calculus is one of the most widely-used branches of mathematics in economics. Here are two (non-exhaustive) examples of important ways in which economists use calculus:

• to optimize functions. As a simple example, suppose we are thinking about a firm that must choose its price in order to maximize profit. Provided the profit function satisfies a few regularity properties (i.e. is continuous, concave, and smooth), locating the profit maximizing price amounts to identifying the price for which the profit function has zero slope (see figure below). Since we can calculate the slope by differentiating, calculus gives us the means to identify the optimal price.

• to perform 'comparative statics' analysis. In the simple problem above, the firm must choose its price to maximize profit. But often the result of this exercise will depend on a number of other factors. For example, the optimal price will probably depend upon competitive the market is, or how closely substitutable rival products are. A relevant question for economics is therefore "if I make the market more competitive, what will happen to the price?" The typical way of answering this question would be to calculate the optimal price, $p$, as a function of market competitiveness, $h$, and then compute the derivative: $p'(h)$.* Indeed, $p'(h)$ is the answer to the question "how much would $p$ change if I change $h$ a little bit?" Most types of policy involve going into a market and changing something, so the ability to predict what the effects of such a change are likely to be is very useful.

In your principles courses, you have probably seen problems that could be solved in this way, but were instead solved through some other method. almost certainly, the courses were organized like this in order to avoid making calculus a requirement. But, as the problems you tackle become more sophisticated, there comes a point at which the effort needed to learn calculus is much less than the difficulty of trying to figure out a way to do economics without calculus.

To answer your explicit question, there is lots of calculus in economics. But, to answer the implicit question in the background, I don't think you should be too worried by this because:

1. Economics involves a lot of fairly easy calculus rather than a little very hard calculus. Primarily, this means calculation of simple derivatives and the occasional bit of integration.
2. Doing economics is a great way to become good at calculus! You will get lots of exposure to simple calculus problems. That will give you lots of practice. Moreover, the problems will usually have a fairly concrete application and hopefully make calculus more interesting than trying to learn it from an abstract math book.
3. From long personal experience as a student and teacher: it is easier to become good at things you love than it is to learn to love things you are good at.

* If you are wondering why I use $h$ for competitiveness, take a look at the Herfindahl index.

If you intend to work on economic history, it could be not very useful but let's say, if you will work on macroeconomics, growth theory, you should have a good enough knowledge for optimal control theory, which could be considered as a branch of calculus of variation.

Also, probability and statistics are very useful courses if you intend to work on uncertainty, finance or macroeconomics or stochastic calculus. As a nutshell, all these are tools that economists use for doing formal economics.

There are some advices of Thomas Sargent on this topic that could be relevant for you. Here is the link ;

http://www.tomsargent.com/math_courses.html

Depends how far you intend to study. Graduate economics get rather deeply into real and functional analysis and game theory.

You should ask yourself why you want to study economics. You are probably right to drop this major if you intend to pursue a Ph.D. If you hate math, then you will hate studying economic theory. However, many students study economics and go on to become financial analysts and business consultants. Most of them do not even use basic calculus in those jobs.

If your goal is to get an economics degree to prepare yourself for a professional business career, then there is nothing to fear. You will probably have only a few economics courses that will require the use of calculus on assignments and exams. You can probably fill out the rest of your degree with intermediate economics courses (e.g. health care economics, public finance, international trade) that will use very little math.

While calculus is useful for economics, the relevant issue is that it's important knowledge whether you want to do economics or not. Any reasonable undergraduate degree should include calculus anyway. It's a fun and useful tool to think about many problems.