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Featured Teaching Economics Without Calculus

  1. May 7, 2018 #1

    bhobba

    Staff: Mentor

    Just a quick question. Can you really teach economics without calculus? Reviewing it now just to refresh my memory since we have a budget being delivered tomorrow here in Aus. I have reached the point where it is proven that maximizing overall profit is different from profit per unit of whatever you are considering - you can maximize one or the other - but not necessarily both - obviously you usually want to maximize overall profit. It is easy with calculus but without it how the bejesus would you do it. And for those that studied without calculus I wonder how many even know its true?

    BTW for those interested the course I am using for review is Economics With Calculus on Edx exactly as taught at Caltec,

    Thanks
    Bill
     
    Last edited: May 7, 2018
  2. jcsd
  3. May 7, 2018 #2

    jedishrfu

    Staff: Mentor

    Well one way to solve is to ask someone who knows Calculus...

    Another way might be by numerical methods where you try to tune your parameters until you get the best result.

    A third way might be via genetic algorithms (similar to the preview idea but better organized) where you create solution vectors that you score keeping the better scored solutions after each iteration.
     
  4. May 7, 2018 #3

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    As my econ prof would tell the class, think marginal, i.e., consider what happens when you increase or decrease production by one unit.
     
  5. May 7, 2018 #4

    bhobba

    Staff: Mentor

    I think those doing more advanced Economics cant escape calculus. I certainly learnt it in Mathematical Methods Of Economics and calculus was a required perquisite. Strangely I was the only student which says a lot. Actuaries of course do it. Very in demand course as the pay is so high and job prospects so good - but without a stimulus like that it seems unloved. Advanced degrees in economics must have it - no choice. Just disappointing its not at the early level nearly everyone does at uni so they understand something every citizen should know. The economic stuff you hear certainly would, hopefully anyway, be elevated.

    Thanks
    Bill
     
  6. May 7, 2018 #5

    jedishrfu

    Staff: Mentor

    While not directly related to this question, here are some lectures using python and julia to do economics problems.

    https://lectures.quantecon.org/
     
  7. May 7, 2018 #6
    I've never had a mathematical economics course. What is the very greatest thing that calculus has ever done for economics? What tops the list as the one greatest feat and that calculus was the hero?
     
  8. May 8, 2018 #7
    My only Econ course was 101 - the intro. I remember thinking that this whole course could be taught in a few weeks if we used calculus instead of words.
     
  9. May 8, 2018 #8

    jasonRF

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    The short answer is yes, it is possible to learn basic economics without calculus. At least in the US, it is typical for introductory level courses (even those for economics majors) to use no calculus. I certainly took courses that worked that way. Would it be more efficient with calculus? Sure, but you can still learn quite a bit and get an understanding for how things work and why without calculus. A deeper understanding probably does require extra tools like calculus, statistics, etc. which is why upper division courses do require a calculus background and economics students need to learn serious probability and statistics as well.

    You can even work as an economist without using much, if any, calculus. My father was an economics professor, published regularly, and had a successful consulting business. Very little of his research and consulting required any calculus. He seemed to think that one of the primary benefits of studying economics is that you learn distinct, useful ways to formulate and analyze problems that was not just mathematics. It is a social science after all. For the types of problems he was interested in, a lot of math just wasn't required. Of course, he advised his students to take as much math as possible if they planned to go to grad school.

    jason
     
  10. May 9, 2018 #9
    I asked what the one great thing that calculus did for economics and no one answered, and that was two days of thinking time. I think that calculus isn't the first thing that comes to mind when it comes to economics.
    People don't act and chose, buy and sell, according to calculus. The criticism the calculus-economist faces is the factuality of his models. Do they represent reality?
    When calculus was introduced to the study of planetary motion, the physics immensely improved. The same thing cannot be said for economics. The calculus really didn't solve any mystery or give us any new understanding of economics.
    I don't see economics getting to be called "advanced economics" just because it loads on a bunch of advanced mathematics. I don't see economics getting called "caveman economics" just because it omits calculus. Math can make economics look like physics, but we should consider that there's a false sophistication economics can assume if it misuses or excessively uses mathematics. There are certainly alot of economic quacks with their mathematical fantasies and there is alot of institutional quack economics that goes unchallenged.
     
  11. May 10, 2018 #10
    Well, it was the first thing that came to my mind as I sat in Econ101 and heard the professor saying things like "ceteris paribus" and "elasticity of demand"

    That's pretty much the question for any model, isn't it?

    I can't really speak to any of your other points.
     
  12. May 12, 2018 #11
    At my school we had economics students taking analysis, let alone calculus. Analysis is, IMHO, the grown up version of calculus, where you rigorously prove every little piece of calculus bit by bit in very general ways starting from scratch.

    Remember the epsilon delta stuff everyone glossed over in calculus? In analysis you take that to the extreme, based on the text I have, and it makes elementary calculus look like child’s play.

    And economics students were taking that course at my school (although to be fair, I think they were first year post grads or senior undergrads).
     
  13. May 12, 2018 #12
    i just today decided to start a review of calculus with the intent of being more theoretical about it this time (at least looking at proofs, and trying to understand the logic behind the definitions and theorems). i got stuck on the epsilon and delta using definition of the limit. i'll probably take a second look at it tomorrow. it sounds like i might have trouble with analysis then if it is as you say ... that and abstract algebra are subjects i know little of but have a strong curiosity about. got to buff up on regular calc. and trig. before i get into that though!

    anyway, i have never taken an economics course and i doubt i will because of the cost, unless i can take it as a required elective. can anyone suggest books to read or textbooks that are good for getting an introduction to the subject? if i ever have time i would like to learn a little about it, out of curiosity and so i can become a more educated citizen. i do have "New Ideas From Dead Economists" and "Freakonomics" - these are the only two economics related books i have. is it a really hard subject to learn?
     
  14. May 13, 2018 #13

    bhobba

    Staff: Mentor

    I gave an example - your view of it is? ie can you explain it easily, in a few lines without calculus? I am not sure how you would explain it at all without calculus - but willing to listen to answers.

    BTW the answer is things are easier if you use calculus often only taking a couple lof lines. As an example explain optimizing some utility function without calculus? Trivial with calculus - otherwise - I have no idea.

    It's called advanced economics because it often has concepts you cant do without calculus eg how do you explain to concept of force of interest which is used in more advanced work.

    Thanks
    Bill
     
    Last edited: May 13, 2018
  15. May 13, 2018 #14

    bhobba

    Staff: Mentor

    When I did Mathematical Economics strictly speaking I would have had to do intro to Macroeconomics and Microeconomics. But my professor said you can read about it over the break - just get a calculus based book. Non calculus based books, for example, so he claimed, spend the first chapter discussing a straight line - with your background that would just be boring and of no value. The course I am currently doing does it all in 9 sections - say a section a day and its a week and a bit - I learnt it all in about 2 weeks over the break with just a couple of hours each day before doing the course at uni.

    Thanks
    Bill
     
    Last edited: May 13, 2018
  16. May 13, 2018 #15

    bhobba

    Staff: Mentor

    Discussing why you should do analysis really requires a new thread. But only as a comment it allows you to understand issues that would otherwise confuse a thinking student eg exactly how do you resolve Zeno's paradox. You sometimes see questions on this forum that Zeno's paradox is an unresolved problem. I did a math degree - most students hated it - only a few nuts like me took to it.

    Thanks
    'Bill
     
    Last edited: May 13, 2018
  17. May 13, 2018 #16

    bhobba

    Staff: Mentor

  18. May 13, 2018 #17

    bhobba

    Staff: Mentor

    The use of calculus is an understanding thing - in practice you use computer programs to do the grunt work such as give the results of some complicated model or pound out statistics. What was it, I think it was Marvin Minsky said, when asked what programming language do you use - he said - graduate student.

    Being a professor he would have access to packages like SAS, Simula etc that do the grunt work for him - it's uderstanding what they say and what implicit assumptions they make - now that's hard. He would have learnt the theory behind that understanding and that would have required calculus and advanced statistics - for which, if you do it properly requires calculus as well. But having gone beyond that he would rarely need it.

    And yes Economics is not just applied math - it significantly requires a good intuitive understanding as well. Even the course I am doing emphasized it does not matter what the math says you must subject it to the intuitive understanding you have developed - and a big part of the course is developing that understanding. Somethings however, like what I mentioned about profit per item and overall profit are not intuitive - that's when one must triple check the math to make sure its true.

    Thanks
    Bill
     
    Last edited: May 13, 2018
  19. May 13, 2018 #18
    In the universities in most European countries, only in STEM courses does calculus get taught, with the caveat that sciences stands for the physical sciences. Applied/technical mathematics students get the same calculus course as physics students (Calc I, II and III), while pure mathematics students get taught analysis as well. Computer science students and econometrics students usually only have to take Calc I with Calc II and III remaining as electives.

    All other sciences (life, social, cognitive, etc) including economics, either do not get taught calculus or get a heavily simplified version without any serious mathematical theory such as rigorous definitions about continuity, theorems, the epsilon-delta definition of the limit and so on.

    They basically get taught how to differentiate and how to integrate simple functions by doing a bunch of problems following the sum, product and chain rules; this is not unlike how high school level calculus is taught except at a higher pace. Usually this course is combined with a heavily simplified and shortened version of linear algebra as well.

    The only two semi-rigorous concepts they sometimes do get taught in this course, much earlier than physics/math students, are 1) a truncated version of Taylor expansion, wherein a function needs to be constructed based on the relevant quantities in the function given as part of a word problem, and 2) constrained optimization using Lagrangian multipliers.
     
  20. May 13, 2018 #19

    bhobba

    Staff: Mentor

    Well here in Aus it depends on the course. One course you do calculus to quite an advanced level and use it in economics and finance, and pass rigorous exams on it, is Actuarial Science.

    The typical prepatory math they take is the same as any science or math student in first year - or what godd students do if they take accelerated math at HS:
    https://handbook.unimelb.edu.au/subjects/mast10008
    https://handbook.unimelb.edu.au/subjects/mast10009

    The reason of course is those actuarial exams are both rigorous - hence the math - and tough - they really only want dedicated students.

    Thanks
    Bill
     
  21. May 13, 2018 #20
    Yeah it does, but I DID notice something cool looking at analysis (at least with the text books I own): it sometimes carries a resemblance to topology. It’s been a while since I looked at those books, but I distinctly remember an “oh my” moment when I realized that, at least in that particular case (which I regret I do not recall), it appeared the two were more or less doing the same thing.


    Edit- I think it involved a particular proof, and I think the topology relevance was related to neighborhoods, but as I said, I can’t recall. But I swear it felt like more or less a different take on the same process.
     
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