# Questions tagged [economics]

The economics tag has no usage guidance.

45
questions

**-5**

votes

**0**answers

24 views

### Tradeoff debt/equity Financial Problem [closed]

I am an MBA student and I'm having a hard time solving this issue, can someone please try and advise? that would be really really helpful!
Consider a firm that has 5M dollars in cash, and a face-value ...

**3**

votes

**1**answer

131 views

### Can we characterize the set of neoclassical production functions?

INTRODUCTION
The neoclassical production function is the main building block in neoclassical growth theory, and consequently the main building block of modern macroeconomic theory. Mathematically, ...

**19**

votes

**3**answers

895 views

### What is the fairest order for stage-striking (and is it the Thue-Morse sequence)?

Here's a fair-sequencing problem that doesn't quite match the usual fair-division problems. I think that, like those, the answer should also be the Thue-Morse sequence ("balanced alternation"), ...

**3**

votes

**1**answer

139 views

### Which utility functions are linearly transformed by normal perturbations?

I'll ask this question as pure economics, as pure math, and showing the translation.
Economics (micro):
Which utilities have the property that whenever $EU(X)>EU(Y)$, the same is true after ...

**3**

votes

**2**answers

892 views

### Can the sum of quasiconcave functions always be made quasiconcave?

Let $f_1,f_2$ be two smooth quasiconcave functions defined on a convex subset of $\mathbb{R}^d$.
It is known that $f_1+f_2$ is not necessarily quasiconcave.
Does there always exist monotonically ...

**7**

votes

**1**answer

360 views

### A game-theoretical question in a political economy model

My research question in a dynamic model of political competition boils down to the following conjecture. I am confident that it holds (all simulations work), but I have not been able to prove it yet. ...

**9**

votes

**0**answers

378 views

### A new $\ell_p$-metric on the hyperspace of finite sets?

Let $(X,d)$ be a metric space and $Fin(X)$ be the family of all non-empty finite subsets of $X$. For every $n\in\mathbb N$ the elements of the power $X^n$ are thought as functions $f:n\to X$ where $n:=...

**3**

votes

**1**answer

387 views

### Mathematical modelling of wealth distribution [closed]

How is the mathematics in modelling of wealth distribution developed? What kind of mathematics is used and how accurately is it able to model this economic phenomena? An example is the Bouchard Mezard ...

**9**

votes

**1**answer

1k views

### Stable marriage with contracts: is it known?

Consider the following generalization of the classical Stable Marriage Problem. The rough idea is that instead of merely specifying who marries whom, a matching now chooses a set of "marriage ...

**10**

votes

**1**answer

514 views

### An equivariant social choice in Mathematical economics

Motivated by this paper and its economics motivations, we recall that a social choice among $n$ objects is a continuous function $$f:\overbrace{M\times M\times\cdots\times M}^{\text{$n$ times}}\to ...

**2**

votes

**0**answers

136 views

### Cooperation in asymmetric Prisoners Dilemma

There are 2 players, each can choose 2 actions, a or b. The payoffs in each case are given by rules
Actions (a,a) -> payoffs (3,4)
Actions (a,b) -> payoffs (0,5)
Actions (b,a) -> payoffs (4,0)
...

**2**

votes

**3**answers

763 views

### Zero lambda, zero constraint in the complementary slackness condition of the Kuhn-Tucker problem

Complementary slackness condition in the KKT theorem states that:
$\lambda_i^*\geq0; \lambda_i^*h_i(x^*)=0 $
The usual reasoning goes like this: either constraint is clack $h_i(x^*)>0$ and then ...

**5**

votes

**1**answer

3k views

### Kalman filters and stock price prediction

Could someone be so kind as to direct me to a good source that would explain time series (more specifically) stock price prediction using Kalman filters, Extended kalman filters or particle filters. ...

**2**

votes

**1**answer

352 views

### A particular Lie algebra $L_{n}$ and (various) lie groups whose Lie algebra is isomorphic to $L_{n}$

Edit: According to the comment by @LSpice we realise the existing link to the main motivation of the question is not available. Then we search for the paper we found the following version:
https://www....

**11**

votes

**4**answers

2k views

### What are Reinert's reproaches to the Ricardo theory?

Economists accuse me in vulgarization of their science, so I'll edit the text from the very beginning to remove the inaccuracies.
Main question
I have just read the book by a norwegian economist, ...

**0**

votes

**0**answers

205 views

### Maximizing Expected Utility

I am currently trying to solve a maximization problem given by
$\max_{f(x)} \int_0^1 \int_\mathbb{R} (c-y\cdot f(x)-d\cdot (x+f(x)-b)^2) \ h(x) \ dx \ dy$.
Or in other words, I have a utility ...

**22**

votes

**2**answers

1k views

### Are symplectic methods used in (classical) Economics?

The tl;dr question is this: are economists using coordinate-free formulations in studying theory?
Borrowing from classical mechanics, the framework I have in mind for classical economics--involving ...

**-4**

votes

**1**answer

88 views

### C = NPm ≠ Σ Pi bowen scheme [closed]

I'm studyng right now economy and finance (I'm a law student, so be patient XD) and I can't figure it out what the "Σ" stands for in the "Bowen scheme".I'm italian , so it's also pretty hard to ...

**3**

votes

**2**answers

356 views

### Consistent price index

This question came out of a discussion with a colleague from economics about price indices. Here is MattF's formulation of the question which differs somehow from the original problem.
Let $Y=({\...

**1**

vote

**2**answers

698 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 ...

**1**

vote

**0**answers

141 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 ...

**1**

vote

**2**answers

445 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 ...

**-2**

votes

**1**answer

315 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 ...

**2**

votes

**1**answer

685 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 ...

**-1**

votes

**1**answer

207 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 ...

**15**

votes

**2**answers

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 ...

**-1**

votes

**1**answer

2k views

### concept of efficiency in auction theory [closed]

I have some confusions about the concept of "efficiency" in auction theory.
One interpretation is that an auction is efficient if it maximizes the social-welfare. But social-welfare is not well ...

**1**

vote

**1**answer

106 views

### Young transform reference

The Young transform of nonnegative function $f(x)$, $x \in \mathbb R^n_+$ is defined to be
$$
(\mathscr Yf)(y) = \inf \left[ \left. \frac{x_1 y_1 + \ldots + x_n y_n}{f(x)} \; \right|\; x \colon f(...

**0**

votes

**1**answer

380 views

### Market-clearing price vector in an “aggregate demand system”

I suppose this is really an economics question, but I'm posting here for want of a more appropriate forum. My question concerns an aggregate demand system in which we have $n$ variants of a product, ...

**29**

votes

**7**answers

1k views

### Concise model of modern fiat money and its non-conservation

A confession: I have never really understood the basic model of fiat money and central banking, by which a central bank controls the money supply. By the standards of someone trained in mathematics, ...

**5**

votes

**1**answer

4k views

### Examples of separable ordinary differential equations in economics

I'm currently teaching an integral calculus course for business students, and we're just about to discuss differential equations. They've worked hard, and I'd like to reward them with some economic ...

**2**

votes

**2**answers

230 views

### Equitable division of a contiguous resource

I have come across the following result regarding equitable division of a resource, which is a simple and immediate consequence of linear programming complementarity (in the infinite-dimensional case)....

**5**

votes

**1**answer

1k views

### Algebra - Decomposition of a matrix polynomial

Dear All,
This is related with a problem that I'm trying to solve on my PhD dissertation in econometrics, and I thought that some mathmatician can know the answer.
What is known about a possible ...

**0**

votes

**0**answers

155 views

### Why does the OLS estimator simplify as follows for the single regressor case?

I was reading in "A Guide to Econometrics" that given $Y = X \beta + \epsilon$, the variance covariance matrix of $\beta^\text{OLS}$ is given by $\sigma^2 (X' X)^{-1}$ where $\sigma^2$ is the variance ...

**-1**

votes

**2**answers

1k views

### Optimal tax Rate

Assume you have two countries A and B, with a tax rates $T_A$ and $T_B$. The tax is redistributed to each people equally. Hence if you live in A and you make $I$ as income then you will finally ...

**0**

votes

**1**answer

154 views

### Applications of linear fractional relationship

This may be the wrong forum, but are there any natural contexts (physics, economics, etc.) in which one might observe the relationship $y = ax/(bx+c)$ between a pair of variables $x$ and $y$? General ...

**17**

votes

**6**answers

6k views

### Reference for Mathematical Economics

I'm looking for a good introduction to basic economics from a mathematically solid(or, even better, rigorous) perspective. I know just about nothing about economics, but I've picked up bits and pieces ...

**21**

votes

**4**answers

1k views

### Fairest way to choose gifts

Suppose that a parent brings home from a trip $2n$ gifts of roughly
equal value for his/her two children. The children get to choose one
at a time which gifts they want. What is the fairest way to do ...

**-1**

votes

**2**answers

396 views

### Continuous optimization

I'm interested in the solution to the following problem:
I have initial capital $C$ which I can invest into $M$ classes of
resources, each unit of a class $m_i$ matures at time $t_i$, has a
return of ...

**15**

votes

**4**answers

2k views

### Zero-knowledge proof of positivity

If I have committed to a number x by revealing g^x mod p, can I prove that 0 < x mod (p-1) < (p-1)/2, i.e. that x is positive, without leaking any more information about x?
My bounty is ending ...

**3**

votes

**1**answer

609 views

### Is the max of two supermodular functions supermodular?

A function $f: \mathbb{R} \times \mathbb{R} \to \mathbb{R}$ is supermodular if for every $x'>x$ and $y'>y$,
$$f(x',y') + f(x,y) > f(x',y) + f(x,y').$$
Suppose $f$ and $g$ are supermodular, ...

**19**

votes

**9**answers

5k views

### General Equilibrium for Mathematicians

I've been reading up a lot on the recent financial crisis, and central to the story is the existence of general equilibrium models in economics, say, as proven by Arrow and Debreu (and MacKenzie?). ...

**8**

votes

**3**answers

1k views

### Weighted Regular Graphs

The following graph theoretic notion appeared in an economics paper entitled: "Prize competition under limited comparability, by Michele Piccione and Ran Spiegler which studies models of economics ...

**7**

votes

**17**answers

10k views

### Math Vs Social Science [closed]

What is the impact of Mathematics in social science today?. That is to say, what are the mathematics that a social scientist is using and, from the point of view of a mathematician, what are the ...

**3**

votes

**2**answers

3k views

### Something like mathoverflow in other sciences [closed]

Are the sites similar to mathoverflow in other sciences related to mathematics? statistics, computer science, physics, economics, etc?
Let me explain what I mean by "similar": those are sites devoted ...