Questions tagged [mathematical-economics]

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

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How does this reporting correspondence is redefined?

Let $\mathcal{R}_i$ be a non-empty, finite set and define the reporting correspondence $R_i:S→2^{\mathcal{R}_i}-\{\emptyset\}$ to be a mapping from player i’s type space to the collection of subsets ...
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Lagrangians of a negative minimum function [duplicate]

if I rewrote min -f(x) s.t. g(x)<k as -max f(x) s.t. g(x)<k, what would my Lagrangian look like?
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minimisation problem as a maximisation problem for lagrangians?

if I have a problem min(-f) s.t. g<0, I can rewrite it as -max(f) s.t. g<0. In this case, if I take Lagrangians, would my lagrangian be L=f- lambda(g-0) or would I have to have a negative in ...
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Representing a Lexicographic Preference in a Natural X Natural Choice Space With Utility Function

my current thinking is i have to dis/prove two things cardinality continuity but im not sure about how it would apply since the above is a natural X natural choice space I know cardinality of ...
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What are the necessary and sufficient assumptions for indifference curves to be convex to the origin?

I thought this required (quasi-)concavity of the utility, but can this (e.g. declining MRS) occur with fewer assumptions?
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Auction Theory and Elections

Can we (is it reasonable to) apply auction theory and the various incentive compatible mechanisms to elections and guarantee cardinal voting? I am thinking specifically of VCG auctions and ...
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Perfect Bayesian Equilibium - Application to game with inconsistent beliefs / no common prior

Does the concept of a Perfect Bayesian Equilibrium apply only to incomplete games with a common prior / consistent belief? In both Bonanno's "Game Theory" and Osborne's "A Course in ...
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Is the following claim written with the right way?

I have a simple question though confusio for me. In game theory we usully write thet a strategy is a mapping from the set of types $T$ to the simplex set of actions (refering to mixed mixed strategies)...
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Does the Sonnenschein-Mantel-Debreu theorem fundamentally undermine Mises' Economic Calculation Argument?

So recently I have been thinking a lot about this fundamental question: Does the Sonnenschein-Mantel-Debreu theorem disprove the "Law of Demand"? Basically, the Sonnenschein-Mantel-Debreu ...
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Equivalence from correlated/communication equilibrium to Nash Equilibrium?

Taking into account the seminal papers of Forges and Imre Bárány, they proove a very strong result that gives an exact connection among the communication and the correlation equilibrium solution ...
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Comparison between stochastic and deterministic growth models

According to the paper "On Stochastic Models of Economic Growth" by Assaf Razin and Joseph A. Yahav, stochastic models might be more suitable because a steady state never actually exists in ...
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Proof of Saddle-Path Stablility in Ramsey-Cass-Koopmans model

I'm currently struggling to proof the saddle-path stability in the Ramsey-Cass-Koopmans model. Based on the books Introduction to Modern Economic Growth by D. Acemoglu (chapter 7 and 8) and ...
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What is the intuition behind Blackwell's Equivalence Theorem on Information Structures?

Let us suppose that we have a Bayesian game where the information structure is defined to be as $P^X=\{(X,\mathcal{X},P_\theta)\}_{\theta\in\Theta}$ where a signal generated by the information ...
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Determining a better model for for a new currency

I am in no way an economist (Just a computer programmer) and want to learn if we can use the gold standard (With improvements for using it in the Crypto domain) For example; If we have a physical ...
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1answer
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How to compare 2 different payment schedules over 20 year period

I have 2 options for a payment plan and need to calculate the total overall the best option. Both plans are over a 20 years. The total payment amount is identical in both cases but the amounts at each ...
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How to find the probability that the sample variance (given in the question below) is this low/lower when given the true population variance?

I'm not sure how to answer the question below. I have gone through worked examples and I have the answer for this question as well. However, the answer doesn't really provide any working. There are ...
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Computing an Exponential Moving Average

According to the Wikipedia page on moving averages, "This is also why sometimes an EMA is referred to as an $N$-day EMA. Despite the name suggesting there are $N$ periods, the terminology only ...
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Comparison of Inflation rate of particular product with world inflation rate

To check the price reasonableness of the purchased product by Procurement manager, I aim to compare the monthly inflation rate of purchased product with world inflation rate of that product and ...
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1answer
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Design of efficient cheap talk communication

Are there any papers about efficient cheap talk communication, where the players achieve the equilibrium payoffs of a correlated strategy as in Aumann's seminal paper? Or in case no such paper exists, ...
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1answer
55 views

Correlation device that induces a specific transition probability

Taking a look at this paper of Forges and Vida the authors define a correlation device in page $102$, that is a standard probability space $\left(\Omega,\mathcal{B},\mu\right)$, They assume that the ...
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What if Bergemann and Morris setting used mixed (or bbehavioral) actions instead of pure actions as reccomendations?

Once again, I will refer to the setting of Bergemann and Morris (2016) and write here the payoff formula of player $i$ from the perspective of the information designer. The payoff formula is the ...
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1answer
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Investigating the firm's supply function

Suppose the firm has a minimum cost function $C(\vec{w}, q)$ and sets up the following profit maximisation problem: $max_{q} \text{ } pq - C(\vec{w}, q)$. The below FOC characterises the solution: $p =...
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Pre-play, interim-play, intra-play communication games

I have a question that seems easy but I want some clarification. Suppose that we have a communication Bayesian game. The game starts when the players learn their prior infornation and after this they ...
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1answer
52 views

What is the economic intuition behind cross derivatives?

Suppose I have a utility function $u(c,l)$, where c is consumption and l is leisure. What does $u_{cl}$ mean in economic terms for example, or in general what is the economic meaning of cross ...
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Bergemann and Morris information designer and decision rule concept

Taking a look in the paper of Bergemman and Morris in 2016, they refer to the desicion rule as mapping $$\sigma:\Theta\times T\to\Delta(A)$$ The explanation to understand the notion of it is given as ...
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How do thresholded incentives influence behavior?

I'm trying to understand how incentives can change crowds in terms of their work performance. I have metrics describing said performance and I'm trying to see how introducing incentives might change ...
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1answer
63 views

Comparative statics of the Ramsey model, the effect of a change in population growth on the steady state capital-labor ratio

In Acemoglu's book "Introduction to Modern Economic Growth" there is Proposition 8.3 which states that the impact of a change in the population growth rate on the steady state capital-labour ...
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What's the origin of the naming of Euler equation in economics?

In Economics, Euler equation is: $u'(c_{t})=\beta Ru'(c_{t+1})$ What is the origin of the name of 'Euler' in this equation? I know that, in fluid dynamics, Euler equation is \begin{aligned}{D\mathbf {...
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What are good sources for the economics of patents?

I am curious about how the stimuli patents exercise, upon innovation, may be counteracted by their slow down of the dissemination of technology. Reading suggestions will be very much appreciated. My ...
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Repeated Games of Incomplete information set up and questions

The following are from the model of Jérôme Renault (Repeated Games of incomplete infomration). The preliminaries of the model Formally, a repeated game with incomplete information is given by the ...
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Perfect recall vs perfect monitoring

Following my previous previous post here, I would like to add another question. Is perfect recall the same with perfect monitoring? If not, what are their differences?
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Perfect recall assumption

When we assume that the players can recall perfectly everything about the previous stages of a game, in essence we assume that they know the history path that they followed until they reached to some ...
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How to set up the Hamiltonian for this utility maximization problem?

Consider a representative household who accumulates capitals, earns labour and capital incomes, consumes part of its incomes, buys bonds and pays taxes. The household maximizes its lifetime utility $$ ...
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Interpretation of an Interactive Dummy variable

I have the following regression, where I regress the consumption of gasoline on logarithmic variables. Meaning of the variables is: pnc=price index for cars pg=price index for gasoline, puc=price ...
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Mathematical proof of dynamic stability of equilibrium in international trade, with quantity adjustment

I am studying dynamic stability of neoclassical international equilibrium given in Giancarlo Gandolfo Economic Dynamics, but I am failing to understand an intermediate step, namely linearization of ...
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Comparative Statics: Income Effect

Much of this is setting up the problem. So if you're familiar it's likely best to start from the very bottom and work up if needed. The question is asking about the income and substitution effect. ...
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Definition of the space of a repeated game

I want to define the space of a stochastic game and it confuses me a lot, so I want someone to check please the space $\Theta$ that I define at the end and how could I define the sigma algebra of this ...
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Help with a (simple) log-linearisation

As a solution to an economic model, I end up with the following equation: $$L=\frac{\alpha f^{\epsilon}s\left [ 1-Ak(1-\alpha+\alpha f^{\epsilon}s)^{\frac{1}{\epsilon}} f^{-1} s^\frac {-1}{\epsilon}\...
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How to define a dynamic programming problem in an incomplete information game?

How can I define a problem of dynamic programming, to use the Hamilton-Jacobi-Bellman equation in order to solve the utility maximization problem of the generic agent of a dynamic game with incomplete ...
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Why are production functions linear in technology?

Economists often assume a production function of the form $ Y = A f(K, L) $, where $Y$ is output, $K$ is capital, $L$ is labour and $A$ is technology. This form of production function can describe ...
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How does this definition change when we introduce some kind of information?

In Heller et al, they use the Osborne and Rubinstein formal definition for the extensive form games with public information. However, the model can work with the same definitions in case all players ...
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1answer
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Solve for the Walrasian demand, Utility of three variables, and Convexity of Preferences?

I am given $U(x,y,z) = x^\frac{2}{3}y^\frac{1}{3} + z$. I am asked to solve the following: (i) Prove the convexity of these preferences (convex, strictly convex or neither?) (ii) Solve for the ...
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Understanding the properties of extensive form games

In Heller et al, they use the Osborne and Rubinstein formal definition for the extensive form games with public information. To some point they refer to the following two properties $P$ is a mapping ...
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2answers
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Violation of Monotonicity of preferences

Hi I am reading Jehle and Reny in my master's course and I have come across a problem in one of the exercises. My instructor herself was a bit confused when a student gave her a counter-example and ...
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1answer
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Drawing a Probability simplex

There are 3 possible payoffs - \$4, \$9 and \$36. The utility function for these payoffs is $\sqrt x $. I have to find all the lotteries preferable over getting $9 with probability 1 in a probability ...
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Constrained optimization problem written as minimax Lagrange

I am reading a note on moral hazard and it shows that a problem like $\max _{s(x)} \mathbb{E}[V(x-s(x))]$ s.t. $\mathbb{E}[U(s(x))] \geq \bar{H}+c\left(a^{*}\right)$ can be solved by setting up a ...
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Gini coefficient of output per capita across regions

The Gini coefficient is widely used to measure the concentration of income in a population. Similarly, the Gini coefficient can be used to measure the concentration of economic output or population ...
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Algorithmic game theory and decentralized exchange of information

An intresting topic that I want to understad has to do with the decentralized exchange of information among a network of agents, however there is not a specific theory to make such a mathematical ...
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Tullock Contests and Multiple Equilibria

I am reading this paper on the existence of multiple equilibria in Tullock contests. The authors state on page 3 that "The additional restriction $(5\alpha_1-\alpha_2)-(\beta_1-\beta_2)>0$ ...
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Application of vector calculus in economics

What are some relevant examples of the application of vector calculus in economics, apart from using gradients and Hessian matrices for optimization? I'm mostly referring to the topics and concepts ...

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