Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [economics]

For questions regarding the mathematical analysis of economic models and problems. This includes questions about the theory and application of the formulation or solution of models from microeconomic theory, macroeconomics, and econometrics.

For questions regarding the mathematical analysis of economic models and problems. This includes questions about the theory and application of the formulation or solution of models from microeconomic theory, macroeconomics, and econometrics.

1613 questions
35
votes
4 answers

What exactly does it mean for a function to be "well-behaved"?

Often in my studies (economics) the assumption of a "well-behaved" function will be invoked. I don't exactly know what that entails (I think twice continuously differentiability is one of the requirements), nor do I know why this is necessary…
Vivi
  • 1,509
23
votes
1 answer

Pure mathematics in our society

Is there some book or essay which deals with the sociological and economical justification of doing and funding pure mathematics? I'm looking for a modern version of Hardy's A Mathematician's Apology, but if possible from a non-mathematician's point…
Martin Brandenburg
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16
votes
1 answer

An algorithm for arbitrage in currency exchange

I found a really interesting problem on currency exchange rates and I wanted to hear people's opinions. If we are given some coins $c_1, c_2, \dots, c_n$ and an array $R$ that keeps the selling price, where $R[i,j]$ is the selling price of one unit…
tasmer_k
  • 177
15
votes
1 answer

Equilibrium existence proof

Problem: Let $J$ be an integer and let $I$ be an integer multiple of $J$. Let ${\cal I}= \lbrace 1,2,\ldots, I\rbrace$ and ${\cal J}= \lbrace 1,2,\ldots, J\rbrace$. The set $X_{I,J}$ of all $\frac{I}{J}$-subsets of $\cal I$ contains exactly…
Shane
  • 1,325
15
votes
3 answers

Can someone explain Cremer-Mclean's astonishing result in auction theory?

In mechanism design/auction theory, there is a famous result by Cremer and Mclean that if agents'/bidders' valuations are even slightly correlated, then all the surplus can be extracted by the principal/auctioneer. This is what makes auction theory…
Zermelo
14
votes
4 answers

Understanding the Leontief inverse

What I remember from economics about input/output analysis is that it basically analyses the interdependencies between business sectors and demand. If we use matrices we have $A$ as the input-output matrix, $I$ as an identity matrix and $d$ as final…
Seb
  • 241
12
votes
6 answers

Motivating linear algebra for economics students?

I'm a tutor for the introductory linear algebra course at my school; this course is required for most upper division economics classes, so a lot of my tutees are economics majors. This is a typical linear algebra course that focuses on things like…
Elliott
  • 4,244
12
votes
1 answer

A (mathematically) sound investment strategy

It is common wisdom in the investment community that a long-term investor saving for his future would do well to invest in high-risk/high-return assets when he is young, slowly switching his portfolio over to low-risk/low-return assets as he grows…
Chris Taylor
  • 29,755
12
votes
2 answers

Finding mixed Nash equilibria in continuous games

I'm taking my first (graduate-level) game theory class. I understand how to find Nash equilibria in simple games, such as those given in finite tables, and can see (usually) how to find the mixed equilibria in those cases. However, most of our…
Hanmyo
  • 322
11
votes
1 answer

What is Lévy measure? Why is it needed, and what is $(1\wedge|x^2|)$?

A Borel measure $\nu$ on $\mathbb{R}$ is called a Lévy measure if $\nu({0})=0$ and $\int_\mathbb{R}(1\wedge|x^2|) \, \nu(dx) < \infty .$…
bounce
  • 211
11
votes
1 answer

Gibbard–Satterthwaite Theorem versus Arrow Theorem

Arrow Theorem is a very classical result in social choice theory, stating very roughly that any reasonable voting procedure is either dictatorial or subject to tactical voting. More precisely, there is a set of voters, and a set of at least 3…
Jakub Konieczny
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11
votes
4 answers

Is vector geometry useful within economics?

I'm going to be taking a semester of math after my bachelor's in economics before I go on to do a master's, and one of the mandatory courses in that semester is linear algebra with a focus on vector geometry. This is how they describe it: The…
Chisq
  • 361
11
votes
1 answer

Can someone explain what plim is?

In my Introductory Econometrics class we discussed a concept of "plim" or "probability limit. I'm not sure what this means though and my professor doesn't explain it well at all. Can someone tell me what this is if you have heard of it? It seems to…
TheHopefulActuary
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  • 81
10
votes
1 answer

Modelling risk when market making

I'm interested in learning about algorithmic trading, particularly in bitcoin. Looking at this chart, I can see that I could simultaneously offer a bid that was slightly higher than the highest bid, and an ask that was slightly lower than the…
Tom Busby
  • 159
10
votes
1 answer

How to minimize game night transactions?

Me and a number of friends occasionally met up and play some game (often pool or some card game) and play for small stakes to give the game a little extra spice. After each round we jot down the results of the round to keep tally of who owes who how…
erikxiv
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