# Is a strong understanding of calculus necessary to understand economics?

Does a person need a strong understanding/background in calculus to understand economics? Without understanding calculus how much of an understanding of economics can person have?
If this is the wrong forum please move.

IANAE but I have an undergraduate degree in the subject and I studied calculus in college as a computer/economics major. I saw almost no connection between calculus and economics on the college level. I would imagine that calculus would be useful (for derivatives mostly) when looking at large, multivariable statistical models but I’m sure most economists would be using computer software to simulate models when developing economic theories and formulas. I’m curious to hear other opinions though.

I think the same thing could be said about physics, so I’m going to answer that. Which is: basic, introductory stuff. But that would still probably put you ahead of the game for most. Anytime you have anything other than constant rates of change, you’re going to be dealing with something that an understanding of calculus will help. BUT. If all you wish to do is understand and be an armchair fellow, rather than actually buy a textbook and work out some sample problems, an understanding of calculus is possible, too, without going whole hog, so long as you have a really good grasp of algebra. Most econ 101 books have pretty much zero math in them, but understanding rates of change (which is what the calculus is all about) will always be beneficial in these kinds of things. I think that, without that, you’re memorizing rather than understanding.

But, YMMV, IANAE/P.

Just to follow up on myself, I think statistics is the most useful math course for someone studying and trying to understand economics. Many studies take empirical data and map it into functions with variables. If you are looking at Economics of Education you would examine things like money spent on education per district for elementary education vs. test scores. Then you would try to find the optimal amount spent vs. the point where the additional dollar spent doesn’t produce effective increases in test scores. Math is helpful in trying to figure these things out. Granted that it is near impossible to control for all of the outside factors when calculating models and applying them to the outside world, but if trickle-down economics can get the support of a presidential administration then any one of us has a chance to advance their own crazy theory.

It seems to me that a lot of cases, the general arguments supporting a theory in economics can be explained withtout recourse to maths. However, if you formally study economics, you’ll need some good basic (well…depends on what one would call basic…perhaps a college-level understanding of calculus and statistics) grasp of mathematics. Nowhere near as much as physics would require, for instance. I studied both (at a rather low level for physics, a little more deeply for economics) and it seems to me that a layman without knowledge of maths will have a much easier time getting an intuitive understanding of a theory in economy than in physics. Analyzing an economical model will require mathematics, but one doesn’t need to do such a thing to “get” the reasonning supporting the theory.

There is a lot of math rolled up in statistics, including, IIRC, a fair amount of calculus.

What exactly does the OP mean by “understand”? One can take watered-down physics and get the intuition just as well as in econ., but I question whether that really qualifies as understanding.

FTR, as an undergrad, I never took calculus and was a straight-D math student. I understood economics very, very well. It was a breeze. Then I took the core-year of a Ph.D. program in economics, and it turns out that a lot of what I understood, I didn’t understand fundamentally, for lack of a better word.

The thing to grasp is that calculus is not non-intuitive. Learning it makes it part of one’s intuition, and seeing the Tragedy of the Commons, for example, as a result of mis-matched optimizing conditions is both fundamentally accurate and intuitively understandable. This doesn’t necessarily obtain when one doesn’t use the proper math for the models to explain them.

So, I think you can go pretty far; but, you are ultimately limited in your understanding by the amount of math you know.

My daughter just graduated from the University of Chicago with a degree in economics, and they sure as hell think so. Statistics too - Econometrics is the course from hell you need to get through for your degree.

However, the behavioral economists there seem to pride themselves on not being up on their calculus, so there are specialties you can do without a lot of math, it seems.

I don’t know about undergraduate-level economics, but my roommate is getting her Ph.D in economics and I’ve had to help her on occasion with her homework problems that involve calculus and differential equations. To me the math she had to use looked fairly advanced, if you count differential equations as “advanced.” I don’t think she had to use differential equations as an undergraduate, though. I think the most she needed in college was integral calculus.

It’s nice to hear about your daughter, Voyager . I am interested in majoring in Mathematics with a specialization in economics at U of C. U of C puts a LOT of emphasis on a strong math background- just for the intro Macro and Micro Econ courses (equivalent of an Econ100/101) you need a good background in Calculus. The concentration I’m interested in is geared more for people interested in future PhD programs, but still, any Econ major’s gonna need a handful of math and Stat credits to get his Bachelor’s.

Then again, someone who just wants to know more about the Economy isn’t going to need a background in calculus. When you start to analyze graphs and such, that’s when the Calc comes in.

Absolutely not. Having said that, as someone who generally found math to be tedious, Calculus, on the other hand, was fascinating.

Differential equations are high-school level maths. Not really “advanced”…

Depends on where you go to school, mon ami.

A good economist is also very familiar with topology, which I sure didn’t learn in high school.

Integral calculus, set theory, and matrix algebra are enough to take you a fairly long way, though.

Because?

Well you would certainly need it for Ph D level Econometrics, but not to understand the theory. Of course, having a general understanding of non-linear dynamics would certainly facilitate a deeper understanding of the interrelationship of economic variables.

I daresay that if you think you understand the theory but do not know how to solve an optimization problem or solve for Bayesian perfect equilibrium, for example, you probably don’t really understand the theory all that well.

A friend of mine is an Econ PhD, and they do some nutty maths at the higher levels; I could hardly tell her thesis from advanced engineering stuff I’ve looked at, been frightened by, and ran away screaming from.

She also told me that it’s all complete bullshit, but I’ll leave that for another forum.

My high school math program only went up to integral calculus. When I wanted to take more advanced math as a senior, I had to take a university class, and even then I took linear algebra, not differential equations. Differential equations was offered at my university (UC San Diego) as a second-year course, the first-year courses being differential calculus, integral calculus, vector calculus, and linear algebra.

Differential equations is considered basic math for physicists, but I wasn’t sure whether it would be considered “advanced” for an economist. Sorry.

P.S. For clarification-- “Linear Algebra” = “Matrix Algebra.”

No, it wouldn’t be considered “advanced” for an economist.

Perhaps a side debate is required on the meaning of “understand.” The fact is that in economics one is generally working with curves, and the language of curves is, to a large degree, calculus. One can draw pictures and wave one’s hands all one wishes, but I just don’t see how one can really get it when one is translating from the language of calculus to the prosaic language of common speech or writing.

Isn’t it fair to say that if common language could handle the issues of calculus, then calculus wouldn’t be needed and might not even exist? If one takes a look at A History of Pi by Becker or Beckman, IIRC, one sees the failure of the language of geometry to handle a topic as basic as finding the area of a circle. One can say that finding the area means taking these miniscule, indeed more-or-less infinitely small, changes and adding them up, essentially slicing the circle into infinitely small pieces of pie and approximating those pie pieces as triangles and adding them all together. We could say that being able to state this from memory qualifies as “understanding,” or if we are more strict, we can say that one “understands” when one understands what it means to slice a circle into more-or-less infinitely thin pieces of pie and add them together to obtain the area of a circle. Is it possible to really understand that without really understanding the concept of limits, inter alia?

I’m friendly to the idea that math is pre-packaged (sp?) logic that we can apply to things in life (even though not all things in life seem to fit every bundle of pre-packaged logic that mathematicians come up with). Do we really understand a concept if we don’t understand the logical rules the concept follows? I’ve seen a few students in debate class fail to understand debating because they failed to understand the logical rules that guide policy debate. I’m skeptical that one can really understand the question of whether the census should sample if one doesn’t understand probability & statistics to some degree. I’m not entirely sure that one can really understand the profit function when the entire analysis is translated from math to common English. In all these things, one can probably get a long way toward truly understanding without getting the logic behind the concepts; however, I really don’t see how one can get all the way with out it.

As I hope my first post implies, I am largely in agreement with those that stress that an underlying ability to perform is the most reasonable indicator of “understanding”. However, the state of understanding is not usually a binary condition. I have found it possible for people to grasp what calculus is and how differential and integral calculus operate without being able to actually do such problems. They have a roughly conceptual understanding but no operational knowledge. I feel this roughly translates as being able to listen to a discussion well but not conduct one well. Even a conceptual grasp of the issues is more “understanding” than someone who doesn’t even have that. But unless that conceptual understanding is tempered by the humble knowledge that one really doesn’t know all that much because one is more or less completely operationally deficient, others are likely to view a person as “not understanding” because they overstep their bounds–something that contributed greatly to keeping myself out of a lot of economic debates, having been thoroughly shown how shallow my grasp of economics is, not because I am missing key concepts, but because I have no operational knowledge, and without that I am helpless to synthesize new information properly for use in a debate.

Compared to my friends, I “understand” economics pretty well. Compared to some members of this board, I do not understand it at all. But I read and try to pick up what I can, and I test my knowledge now and again in a debate. I learn more from my shortcomings than from my virtues.