College Math Teaching

March 25, 2014

An example for “business calculus”

Filed under: applied mathematics, calculus, economics — Tags: , , — collegemathteaching @ 10:49 pm

Consider this article by Paul Krugman which contains this graph and this text:

032114krugman1-blog480

On one side we have a hypothetical but I think realistic Phillips curve, in which the rate of inflation depends on output and the relationship gets steep at high levels of utilization. On the other we have an aggregate demand curve that depends positively on expected inflation, because this reduces real interest rates at the zero lower bound. I’ve drawn the picture so that if the central bank announces a 2 percent inflation target, the actual rate of inflation will fall short of 2 percent, even if everyone believes the bank’s promise – which they won’t do for very long.

So you see my problem. Suppose that the economy really needs a 4 percent inflation target, but the central bank says, “That seems kind of radical, so let’s be more cautious and only do 2 percent.” This sounds prudent – but may actually guarantee failure.

The purpose: you can see the Philips curve (which relates unemployment to inflation: the higher the inflation, the lower the unemployment) and a linear-like (ok an affine) demand curve. You can see the concepts of derivative and concavity as being central to the analysis; that might be useful for these types of students to see.

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