# Questions tagged [economics]

For mathematical problems arising from economics, the social science studying the production, distribution, and consumption of goods and services.

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### An oversimplified model for optimal distribution of wealth

Consider the following, overly simplified, model for determining an optimal wealth distribution for society: Let $X$ be a random variable, which will model the distribution of wealth in a society. The ...
17 views

### Can quasi-concave and monotone functions level curves that are not path-connected?

I posted this on MSE [link] and there's been no answer for the past few days. I started a bounty there and decided to post it here as well. 1. For $X = \mathbb{R}^2$, does there exist a quasi-concave ...
1 vote
50 views

### Minimising risk in dynamical systems

I have been reading the paper of Goerner and Ulancowicz - "Quantifying economic sustainability" in which it is suggested that there is a tradeoff between sustainability and efficiency. ... 169 views

### Is there a version of Arrow's theorem without unrestricted domain?

To recall Arrow's theorem: Suppose we have a finite set $X$ of voters and a finite set $Y$ of candidates. An election is a map $\phi: X \rightarrow T$ where $T$ is the space of total orderings of $Y$. ...
168 views

### Conditions for the existence of von Neumann-Morgenstern utility on a Polish space

Let $X$ be a Polish space, i.e. a separable complete metric space. Any Borel probability measure on $X$ must be locally finite, outer regular and tight. Let $\mathcal{P}(X)$ be the set of all Borel ...
1 vote
50 views

1 vote
738 views

### Simple yet interesting applications of Calculus or Linear Algebra to Economics [closed]

This is essentially a vast generalization of my previous question: Examples of separable ordinary differential equations in economics I'm giving a talk to college-level math teachers on some ...
159 views

### A categorical analogue of Debreu's independent factors theorem

Background A major question in Decision Theory is that of the cardinal meaning of a utility function. That is, given a set $X$, a utility function $u:X\rightarrow \mathbb{R}$ represents the choices ...
1k views

### On mathematical aspects of the most recent Nobel Prize in economics winners' work

Can somebody briefly introduce the mathematical aspects, in particular, those related to mathematical finance, of the three economists who were just awarded this year's Nobel Memorial Prize in ...
1 vote
469 views

### What does Arrow's theorem say about Kaldor-Hicks social welfare functions with von Neumann-Morgenstern utility? [closed]

Let $A$ be the set of all possible states of the world, let $G(A)$ be the set of all "lotteries" or "gambles", i.e. the set of all probability distributions over $A$. Now consider an individual with ...
326 views

### A kind of economic objective function in assignment

I recently thought about a concept that seems like it should come up in economics, but I don't know if there's a name for it and where people would have encountered it elsewhere: Suppose we have a ...
839 views

### Optimal auction for risk-averse seller

Consider an auction of a single unit of indivisible good. There are $n$ buyers whose values of the object is drawn independently from the uniform distribution on $[0,1]$. The buyers have interim ...
243 views

### To what equal constant in the Gibbs lemma

The Gibbs lemma is broadly used in games theory and in mathematical economics (optimal distributions of resourses, Cournot competition e.t.c.). Here it is: Lemma (Gibbs). $f_1,f_2,\ldots,f_n$ be ...
2k views

### Is there an equivalent of Heisenberg's uncertainty principle in the decision sciences ?

From memories of a quantum mechanics class and Wikipedia: In quantum mechanics, the uncertainty principle is any of a variety of mathematical inequalities asserting a fundamental limit to the ...