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Results tagged with Search options user 42

The application of mathematical methods to represent theories and analyze problems in economics.

5
votes
There's the well known step-by-step guide on "How to build an economic model in your spare time" by Hal Varian. Edit Based on further clarifications made in the comments that OP's interest is in be …
answered Nov 2 '17 by Herr K.
4
votes
You may be interested in reading "Economic Models as Analogies", a 2014 article by Itzhak Gilboa, Andrew Postlewaite, Larry Samuelson and David Schmeidler, four well regarded economic theorists. They …
answered May 19 '18 by Herr K.
3
votes
Your example is the classic Allais paradox. I think the best way to see how the preference pattern $L_1\succ L_2$ and $L_3\succ L_4$ violates independence is to visualize it geometrically. Consider …
answered Apr 15 '18 by Herr K.
2
votes
In general, FOCs produce local, not necessarily global, optima. Consider \begin{equation} \max_x\;f(x)=x \sin(x) \quad\text{s.t. $x\in[0,7]$}. \end{equation} As the plot below shows, $f(x)$ has thre …
answered Feb 21 by Herr K.
2
votes
The "profit" function for consumer choice does exist; it is the Lagrangean: \begin{equation} \mathcal L(x;\lambda)=u(x)+\lambda[c-g(x)]\,, \end{equation} where utility $u(x)$ is to be maximized subje …
answered Dec 26 '17 by Herr K.
4
votes
My favorite example of real analysis' application in micro is the proof that lexicographic preference cannot be represented by any utility function. (A succinct version of the proof is given in p.43 o …
answered Jul 9 by Herr K.
7
votes
A bit late to the game, but I'm surprised no one has named the equation to calculate OLS estimates: $$ \hat\beta=(X'X)^{-1}X'y $$
answered Mar 11 '17 by Herr K.
1
vote
For game theory: Game Theory by Fudenberg and Tirole Repeated Games and Reputations : Long-Run Relationships by Mailath and Samuelson The Theory of Learning in Games by Fudenberg and Levine Evolut …
answered Jun 21 '15 by Herr K.
5
votes
The general procedure to solve for a MSNE in a 3-by-3 (or larger) game is always a bit tricky and involves some trial and error Step 1: Conjecture (i.e. guess) a subset of strategies that will be us …
answered Apr 18 '18 by Herr K.
2
votes
In Notes on the Theory of Choice (assuming this is what you refer to by "Kreps (1988)"), Kreps does not appear to mention WARP as such. But he does refer to "Houthakker's axiom" (Houthakker 1950, Econ …
answered May 14 by Herr K.
7
votes
The first order stochastic dominance relation is convex. An easy way to prove this is to use the property that a cdf $F$ FOSD another cdf $G$ if and only if $F(x)\le G(x)$ for all $x$. That is, $F$ …
answered Apr 2 by Herr K.
3
votes
(2) does not imply (1). Consider a utility function with "circular indifference curves", e.g. $u(x,y)=-(x-1)^2-(y-1)^2$. At the bliss point $(1,1)$, the function satisfies (2) but violates (1). (2) d …
answered Jun 9 by Herr K.