Microeconomics: Introduction
A. Mathematics. Here you learn the relationship between the graph of a function, the graph of
its slope (its "marginal"), and the graph of its average. This material is tested on Exam 1
because it is crucial that you understand it before lectures on Topic F begin.
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although it actually starts at 40. Later on in the video I correct that mistake. Also, the
methods we have to find the marginal are only approximations. (An exact method would
require us to know the precise functional form of the relationship, which we do not know.)
I first use 2-hour-long intervals to approximate the marginal; later, I use tangent lines.
These approximations do not agree closely with each other in this example. In
this PDF file, I show both approximations of the marginal, and specify more about where
each comes from. In this class, we will mostly use the tangent-line approximation, which
would be exact if we could draw a precise tangent line (which we can't). Furthermore,
most of the graphs in the rest of this course will not have any numbers on their axes,
so the tangent-line approximation will be the only one that can be used. Economists have
to be able to deal with general shapes that have no numbers, because we often have little
idea of what the right numbers are (since we usually can't run controlled experiments to
measure things).
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viii) Examples inspired by the Theory of the Firm. There is no video for this topic; instead,
study the first two pages of the "Class Handouts" to understand how the lines for
averages and marginals (the bottom graphs) were derived from the totals (the top
graphs).
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its marginal.
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its marginal and its average. After watching this video, practice with the first two pages of
the "Class Handouts," trying go from their "average" and "marginal" graphs to their
"total" graphs.
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