View Full Version : How is analysis used in grad school

01-06-2014, 07:46 PM
I just finished real analysis this past semester and am now curious how this material will be used in the setting of economics. Is it important to know certain theorems and their implications like the back of your hand ie. compactness, continuity, basic topology? If so how are these concepts applied to economic theory. Or is the reason for taking RA just to be comfortable writing and understanding proofs?

01-06-2014, 09:18 PM
Here are some applications off the top of my head:
Stochastic differential equations play an important role in financial mathematics, and a thorough grounding in analysis and measure theory is required to work with SDE's.

For a concrete result that uses topological notions, see http://cowles.econ.yale.edu/P/cd/d00b/d0076.pdf

Various fixed point theorems---facts in analysis and algebraic topology---are employed in economics as well.

Of course, it pays to be comfortable writing and reading proofs as well.

01-06-2014, 09:50 PM
Think micro theory. Micro theory is as general as you can get, so you'll need a lot of real analysis to be able to characterize things, ensure solutions exist and stuff like that. For instance, the Weierstrass theorem ensures that a solution always exists to the utility maximization problem under the assumption that u is continuous and that the set of choices is compact (i.e. because you're maximizing a continuous function over a compact set). Or the Nash theorem uses a fixed point argument to show that a Nash equlibrium always exists if the set of strategies is compact, convex and nonempty, and u is continuous. Convexity, concavity, quasi-convexity and quasi-concavity are also widely used. So yeah, it definitely helps to be familiar with some of the theorems and with this style of abstract math if you want to succeed in graduate micro theory.

More broadly, I assume some of these theorems and stuff are used in current micro theory and game theory research as well, and you can see them quite often in applied micro models as well.

01-07-2014, 12:14 AM
^Nice post but not entirely correct. Micro theory is hardly the only area where basic analysis concepts are required. Everything OP mentioned will also be seen in first year macro in most decent programs and, very likely, in first year econometrics.

For example, everything you will cover in probability theory (generally taught in first semester econometrics, or math camp) will revolve around convergence theorems, which is the theory behind why we can do anything in econometrics. And without continuity, plus the section on convergence of sequences you usually do in a first analysis class, these topics cannot be covered.

Posters here sometimes advise that you don't absolutely "need" real analysis, but they mean it only to the extent that you can try to catch up in your first year. Basic analysis concepts such as compactness and continuity absolutely have to be understood for an economics student aiming to get through a PhD program, sooner or later. Whether you might need them for your research is a different matter.

01-07-2014, 05:22 AM
After 1 quarter I definitely think I'd be overwhelmed without it.

01-09-2014, 02:58 AM
A book that covers real analysis relatively well and includes economic applications is Real Analysis with Economic Applications by Efe Ok. Maybe check that out.

01-09-2014, 06:02 AM
A book that covers real analysis relatively well and includes economic applications is Real Analysis with Economic Applications by Efe Ok. Maybe check that out.

Thanks for the info, I will definitely check it out.