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Questions tagged [economics]

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0
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0answers
20 views

Fairly allocating heterogenous items

I'm trying to find literature on what I'm sure is a well-understood mathematical problem, but am struggling for terminology. Let's say I have a number of items each of which is either shiny or matte, ...
19
votes
3answers
721 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"), ...
4
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1answer
125 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 ...
2
votes
1answer
304 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
1answer
356 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
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0answers
349 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
1answer
218 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 ...
8
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1answer
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 ...
1
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0answers
45 views

The restriction of convex function with gross substitutability

Let $f:\mathbb{R}^n\rightarrow \mathbb{R}\cup\{+\infty\}$ be a convex function and satisfy gross substitute property(GS&LAD): $\forall p\leq q, p\neq q, p,q\in \mathbb{R}^n$ and $x\in argminf[p]$, ...
9
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1answer
464 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
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0answers
115 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) ...
1
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3answers
428 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 ...
4
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1answer
2k 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. ...
0
votes
1answer
247 views

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

We define $$L_{n}=\{A=(a_{ij})\in M_{n}(\mathbb{R})\mid \sum_{i=1}^{n} a_{ij}=0 \;\;\;\text{for every fixed j}\}$$ This is a Lie subalgebra of $M_{n}(\mathbb{R})$. A dynamic-geometric proof for ...
11
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4answers
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
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0answers
194 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
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2answers
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
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1answer
86 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
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2answers
349 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
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2answers
659 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
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0answers
136 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
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2answers
421 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
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1answer
306 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
1answer
531 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
1answer
194 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 ...
12
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2answers
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
1answer
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
1answer
102 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
1answer
362 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
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7answers
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
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1answer
3k 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
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2answers
227 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
1answer
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
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0answers
145 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
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2answers
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
1answer
152 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 ...
14
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6answers
5k 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 ...
20
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4answers
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
2answers
388 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
4answers
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
1answer
559 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, ...
18
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9answers
4k 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
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3answers
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 ...
9
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17answers
10k views

Math Vs Social Science

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 ...
5
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2answers
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 ...