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This is essentially a vast generalization of my previous question: Examples of separable ordinary differential equations in economics

I'm giving a talk to college-level math teachers on some applications of mathematics to Economics. My main goal is to try to convince them is that it's possible to integrate examples and methods from economics that are both elegant and lead to real economic insight into Calculus and Linear Algebra courses. I'm probably going to skip the Leontief input-output model, as well as very basic game theory and present- and future-value calculations, since I think those are all pretty standard. I want to keep the scope of the talk manageable, so I'm going to steer clear of any statistical methods.

I'm definitely going to talk about the Keynesian multiplier, the interpretation of Lagrange multipliers as shadow prices, and about how one can use implicit differentiation to determine the incidence of taxes on supplier and consumer.

My question is the following: does anyone have any suggestions for other topics?

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  • $\begingroup$ I've deleted your final sentence, because I'm afraid it could have led to question closure. $\endgroup$
    – Daniel Moskovich
    Commented Sep 28, 2014 at 0:56
  • $\begingroup$ If you are specifically asking about applications of calculus and linear algebra, that's a fine question, but it's not about research level mathematics. You should ask on MSE or ask economists. Also, look up elasticity. $\endgroup$
    – Douglas Zare
    Commented Sep 28, 2014 at 2:03
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    $\begingroup$ I would have voted to migrate to MathematicsEducators.SE, but this is not available (yet?). I strongly advise you to ask your question there, it will probably be well-received and will fit much better than here. $\endgroup$
    – Benoît Kloeckner
    Commented Sep 28, 2014 at 9:45
  • $\begingroup$ @Daniel: thanks very much. It was meant to be flippant, but I can see why MO would have a zero-tolerance policy on offers of rewards. $\endgroup$
    – Gordon Craig
    Commented Oct 2, 2014 at 9:59
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    $\begingroup$ @Douglas: Although the question certainly isn't research-level, neither was my previous question in the same vein, although I understand that with a growing number of users, MO might need to become stricter. My goal in asking it here instead of MSE, was to get the opinions of people with experience teaching mathematics at the University/College level, who are most likely to be found here. $\endgroup$
    – Gordon Craig
    Commented Oct 3, 2014 at 1:05

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My personal favourite example is bond duration, which also gives insight into the meaning of a derivative.

The derivative of a function $f$ measures the sensitivity of $f(x)$ to a change in its input $x$. Functions whose derivatives are smaller are closer to being constant, so changing $x$ doesn't change $f(x)$ much, and vice versa.

The price of a bond is a function of its yield. The modified duration of a bond whose present value is $1$ is (minus) the first derivative of the bond price. It's one of the most important measures for bonds, because it tells you just what you would like to know when you buy a bond- namely how much interest rate risk you are taking on by buying it.

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  • $\begingroup$ Thanks very much. That's exactly what I was looking for; the Mathematics gives some insight into the Economics, but also vice-versa, as regards the meaning of the derivative. $\endgroup$
    – Gordon Craig
    Commented Oct 3, 2014 at 1:12
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One possible application of linear algebra to economics, which has been well established is its applicability to labour costs, and the production cost function. The input output function uses a linear algebra formulation, and the production functions' elasticity with respect labour is well studied. Profit models follow from these formulations, and have follow well established economic principles. The number of variables, in the production function, and so on depending upon the model, determine the production functions' elasticity.

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  • $\begingroup$ Thanks very much. I'll definitely look into that. I think most of my audience will be familiar with price elasticities, so it would be nice to introduce elasticities with respect to labor. $\endgroup$
    – Gordon Craig
    Commented Oct 3, 2014 at 1:16

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