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Questions tagged [mathematical-economics]

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

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Economists Working At the Intersection of Pure Math and Economics

As a math student interested in economics I was recently reading some of the papers by Graciela Chichilnisky on social choice theory and some of her papers applying topology to other areas of ...
Throwawayaccount's user avatar
2 votes
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Berge's theorem of maximum's application to expenditure minimisation problem

Let $f:X\times A \rightarrow \mathbb{R}$ be a continuous function, and $\Gamma:A \rightrightarrows X$ be a non-empty, compact-valued and continuous correspondence, with $X$,$A$ be Euclidean Space. ...
Nonenicht's user avatar
-1 votes
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Cost Benefit of Publishing Novel Economic Result and Equations

In the course of developing various trading models, I have come across, and further developed equations that deal with predicting states of efficient markets. These may also have potential for risk ...
cronius's user avatar
2 votes
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Proof of Second Welfare Theorem with infinitely many goods

I'm trying to understand the proof of the Second Welfare Theorem and I'm still struggling with the intuition behind the use of a linear functional as a mathematical instrument in order to prove that ...
Pepus's user avatar
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About Two Methods of Computing Bayesian Equilibria

Question I want to compute the Bayesian equilibria for the following Bayesian game: With probability $p$, player 1 would be of type 1.1. With probability $1-p$, player 1 would be of type 1.2. Player ...
Beerus's user avatar
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consumption, income and utility

Question Description: Consider an economy populated by a large number of Farmers (F) and Computer Scientists (CS). Each person divides his 24-hour day into labour and leisure. If a Farmer decides to ...
ZZZ's user avatar
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1 vote
2 answers
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How to derive Fisher's equation?

Guys help me derive Fisher's equation or suggest references that have the derivation. I am looking for this relation: (1+i)=(1+r)(1+π)
user205152's user avatar
1 vote
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Parameter in calibration are not sufficient for pruposed Model. Where is the lacking data coming from?

The paper „social security reforms, capital accumulation and welfare: A notional defined contribution system vs a modified payg system“ by Lin, li Presents a model for analyzing the impact of ...
Felix Neuwirth's user avatar
2 votes
1 answer
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Question About Proof of Proposition 3.C.1 in MWG - Step 1

I have difficulties understanding the first step of the proof of Proposition 3.C.1 in MWG. Proposition 3.C.1$\quad$ Suppose that the rational preference relation $\succsim$ on $X$ is continuous. Then ...
Beerus's user avatar
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Understanding the definition of monotone

In Microeconomic Theory by Mas-Colell, Whinston, and Green, the definition of monotone preference relations is given as follows: Definition 3.B.2$\quad$ The preference relation $\succsim$ on $X$ is ...
Beerus's user avatar
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Demand aggregation with CES

I am reading the following paper by Angeletos and Lian and got stuck on equation (3). The problem is the standard optimal consumption bundle choice. Namely, aggregate consumption of "farmer" ...
Wittgenstein's Poker's user avatar
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Two candidate voting game on the unit interval ideological spectrum (game theory exercise)

(Politics game) Consider a population of voters uniformly distributed along the ideological spectrum from left $(x = 0)$ to right $(x = 1)$. Each of the candidates for a single office simultaneously ...
Oliver Queen's user avatar
1 vote
1 answer
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How To Publish a Quantitative Economics Paper Without a Degree or Affiliations

I dropped out of a physics degree and do not have a degree. After this, I somehow found myself going from writing marketing software related code to writing quantitative trading code and doing ...
cronius's user avatar
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Chan Park - Fundamentals of Engineering economics - 1st edition - Chapter 5 - Present value - 5.8

hope I could ask some help around here. I'm working with Chan S Park book Fundamentals of Engineering Economics, 1st edition. I'm in the problem 5.8, page 171. Which states: ``Your firm is considering ...
GearKnight95's user avatar
4 votes
3 answers
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What kind of utility function is needed to derive a "Backwards Bending Labor Supply Curve"

The idea of a backwards bending labor supply curve is often discussed in many introductory labor economics classes where a consumer's labor leisure decision at higher wages (due to a diminishing ...
EconJohn's user avatar
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5 votes
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Why is exponential discounting considered rational?

I have repeatedly heard a claim that only an exponential discounting is the rational one, however I've never seen the proof. Why is it so? Intuitively, we would expect exponential discount since the ...
marmistrz's user avatar
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Judge prosecutor example of Kameinica and Gentzkow

Based on Kamenica and Gentzkow example about the prosecutor and the judge. The utilities of the sender and the receiver are $v(\alpha,\omega)=\alpha$ and $u(\alpha,\omega)=-(\alpha-\omega)^2$. The ...
Oliver Queen's user avatar
1 vote
2 answers
181 views

Why this optimisation problem cannot be solved with "usual" KT conditions?

I have this optimisation problem: $$f(x, y, z) = 2xy + yz \qquad \text{subject to} \qquad \begin{cases} x+y+2z \leq 1 \\ x \geq 0, y \geq 0, z\geq 0 \end{cases}$$ I solved it with "a certain ...
Heidegger's user avatar
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2 answers
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Question About Stable Matrices - MWG Mathematical Appendix M.D Matrices: Negative (Semi)Definiteness and Other Properties

I am self-studying the mathematical appendix of Microeconomic Theory (MWG). They defined a stable matrix as follows: Definition$\quad$ A matrix is stable if all of its characteristic values have ...
Beerus's user avatar
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0 answers
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How to aggregate goods with different units of measurement to reduce the economy with a Cobb Douglas utility function?

I want to model a economy where consumers have a Cobb Douglas utility function and where X1 = goods that pay a value added TAX (VAT), and X2 = goods that are exempt from this tax. I am working with ...
Santiago Valdivieso's user avatar
1 vote
0 answers
35 views

Proof that utility function is differentiable

after a little problem (I asked my question in the answer section, apologize, all my bad for this), I repost my question here with the same message : "I'm new on economics stackexchange, and I've ...
Economos's user avatar
1 vote
1 answer
114 views

Proving an additive function is sigma additive (Measure Theory)

I'm here to kindly ask u a check about the proof of the following statement: Let $\mathcal{A}$ be an algebra and $\mu : A \rightarrow [0,\infty]$ and additive function. Then $\mu$ is $\sigma$ ...
Calogero Sortino's user avatar
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1 answer
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Confusion regarding the Slutsky equation

I'm reading Henderson and Quandt's Microeconomic Theory textbook and in the derivation process of the slutsky equation the final formula confused me a bit. The first term on the right of the equation ...
Adnan's user avatar
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1 vote
1 answer
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Intuition of two Measure theory statements

I'm struggling in getting the intuition of two statements about measure theory: Given a measure space $(X,F,\mu)$, $f \in M^+ $, where $M^+ = M^+(F) $ is the set of non negative F-measurable functions ...
Calogero Sortino's user avatar
4 votes
1 answer
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Prove: The law of demand holds if WA, Walras' law, homogeneity of degree 0, and homogeneity of degree 1 in wealth hold for Walrasian demand functions

Problem I am asked to prove the following result (MWG Exercise 2.F.5): The law of demand always holds if the walrasian demand function $x(\mathbf{p},w)$ satisfies the weak axiom of revealed ...
Beerus's user avatar
  • 471
2 votes
1 answer
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CES function: Lagrangian or Kuhn-Tucker

Let's have the following problem: $$U(\boldsymbol{x}) = \left(x_1^\rho + x_2^\rho \right)^{\frac{1}{\rho}} \qquad s.t. \qquad P_1 x_1 + P_2 x_2 \leq M$$ Is it optimal to solve this problem via pure ...
Athaeneus's user avatar
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Why did Bergemann and Morris chose a different setting with respect to Kamenica and Gentzkow only to reach to the same results?

Why did Bergemann and Morris choose a different setting with respect to Kamenica and Gentzkow only to reach to the same results? However none of both approaches seem to present the problem in a ...
Oliver Queen's user avatar
2 votes
1 answer
72 views

Suppose $A$ is a $2x2$ matrix and ${\bf x}=(x_1, x_2)$. What does "$f(Ax)$ is supermodular" mean?

Suppose $A$ is a $2x2$ matrix, e.g., $A=\begin{vmatrix} a_{11} & a_{12} \\ a_{21} & a_{22} \\ \end{vmatrix}$, and ${\bf x}=(x_1, x_2)$. Suppose $f()$ is continuous and twice differentiable. ...
opre's user avatar
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Question on Isolating The Wealth Effect in Analysis of Changes in Price-Wealth Combinations - MWG Exercise 2.F.3 Parts (e) and (f)

I am doing exercises in Chapter 2 of MWG. I feel I got completely lost in exercise 2.F.3 parts (e) and (f). $\textbf{Exercise}$ Here is the question: I have solved parts (a) to (d). In particular, I ...
Shenron's user avatar
  • 105
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2 answers
52 views

Continuous logit framework

I am reading Dupuy & Galichon (2014), which extend the estimation of matching model in Choo & Siow (2006) to continuous types. The way they build the continuous logit model is based on the ...
Alalalalaki's user avatar
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3 votes
1 answer
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Is this proof correct (measure theory)?

I'm trying to prove the following statement: I did the following proof but i donno if it makes sense: Proof of $(\Rightarrow)$ direction: Assume $\mathcal{F}$ is a $\sigma$-algebra. Assume also $\{...
Calogero Sortino's user avatar
1 vote
1 answer
58 views

Cost function from a weighted CES production function

I want to find the cost function given the CES production function: $$ Y = F(x_1,x_2) = (\lambda x_1^ \rho+(1-\lambda)x_2^\rho)^\frac{1}{\rho} $$ with $0<\rho<1$. So far I have set up the ...
fabs's user avatar
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Resources for grad level math courses

I am currently waiting on Econ PhD decisions. I thought I could use this time to start brushing up on some coursework. I wished to know if there are any resources for graduate level mathematical ...
user584534's user avatar
3 votes
1 answer
122 views

Question on The Weak Axiom of Revealed Preference and The Definition of Revealed Preference Relation

I am solving the following problem (from Exercise 2.F.3 (b) in MWG) and I got confused by the weak axiom of revealed preference and the definition of the revealed preference relation. Here is the ...
Shenron's user avatar
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1 vote
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Trouble understanding the equation that lays out the concept of prediction policy problems in Kleinberg et al. 2015

Kleinberg et al. (2015) introduce the concept of prediction policy problems, and claim to unite prediction problems and causal inference problems in a single framework. In section I of the paper, ...
Brash Equilibrium's user avatar
2 votes
1 answer
131 views

Resources for a Deep Dive into the New Keynesian / DSGE models

I would like to deep dive into new Keynesian models and DSGE models. Do you know comprehensive resources that cover both the mathematical and economic requirements?
Maurizio Marinaro's user avatar
2 votes
1 answer
99 views

MWG Exercise 2.E.5

Exercise Suppose that $x(\mathbf{p},w)$ is a demand function which is homogeneous of degree one with respect to $w$ and satisfies Walras' law and homogeneity of degree zero. Suppose also that all the ...
Shenron's user avatar
  • 105
2 votes
0 answers
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Kuhn’s equivalence theorem in game theory

I consider a game with two players in incomplete information with perfect recall and I would like to prove Kuhn’s theorem stating that for every mixed strategy $\sigma$ there exists a behavior ...
coboy's user avatar
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0 answers
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Assumption of interior solution in the Lagrangian method

Why do we need to assume an interior solution before using Lagrangian method for utility maximization problems?
Ranu Jain's user avatar
1 vote
0 answers
45 views

Help with Simulating a Time Series Process in R

I'm having difficulty expressing the following process in its most reduced form. Every time I try to simulate it with the arima.sim function, I end up with a non-stationary AR part that cannot be ...
NoNameBoyy's user avatar
1 vote
0 answers
37 views

Considering there are four different goods {w,x,y,z}, how many different relations can be defined using all goods

In this problem, you can either prefer a good to another, disprefer a good to another or be indifferent between the two goods. While I have been able to do it mechanically, I am very confused as to ...
Sasha Blain's user avatar
4 votes
1 answer
168 views

How can I apply the Hamiltonian function and Pontryagin's maximum principle in the context of Optimal Control Theory?

I am really struggling to grasp how the Hamiltonian Function and Pontryagin's Maximum Principle work in the context of Optimal Control Theory (Maths for Economics) course. I am given the following ...
astute-hoplite's user avatar
0 votes
1 answer
72 views

Can a single dummy variable be made to meet multiple criteria?

Let say I have criteria 1, 2, 3, and 4. I would like the Dummy variable to be 1 only if a certain minimum amount of criteria are met. For example, if 3 of the 4 are true, then Dummy =1. If 4 of the 4 ...
MLux's user avatar
  • 25
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Correlation Coefficient of #DIV/0!

I am trying to ask Excel to make a correlation matrix for variables that affect the Chinese exchange rate. However, since I found data with labor cost having a base year (2019), I ended up with lots ...
Nikolai's user avatar
  • 16
3 votes
1 answer
22 views

Ask about the HLT method of "Life cycle wage growth across countries"

paper :https://www.journals.uchicago.edu/doi/epdf/10.1086/696225 deaton imposes linear constraints in order to deal with the collinearity of age-period-cohort. How to implement it through stata? Why ...
Barry Alen's user avatar
1 vote
0 answers
53 views

A question in social choice and preference aggregation

Let $I = \{1, 2, 3\}$ denote the set of individuals and $X = [a, b]\subset \mathbb{R}^+$ with $a, b \in \mathbb{R}^+$ and $a < b$, be the set of alternatives. For each $i\in I$ and some $p_i\in X$ ...
Oliver Queen's user avatar
4 votes
1 answer
314 views

"Derivative" of an indicator function

I am studying a paper where I have the following indicator function: $\text{I}(i) = \mathbf{1} \{ \eta^* - \eta(\beta(i)) + u(i) > 0 \}$ where $\beta(i)$ is taken from uniform distribution $U[\chi-\...
Dario's user avatar
  • 85
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0 answers
57 views

Finding the equilibrium interest rate

Let's say there are only two countries in the entire world, Argentina and Chile, and there is free trade between them. The aggregated investments in both countries are $I^A$ and $I^C$ that are both ...
Ari Samueli's user avatar
5 votes
2 answers
266 views

Is there relationship between increasing and decreasing returns to scale and homogeneity?

According to Varian's Macroeconomic Analysis (page 15), when returns to scale are constant, production function will be homogeneous of degree 1. When he discusses increasing and decreasing returns to ...
HerrMaximus's user avatar
1 vote
0 answers
29 views

Substitutable preferences vs. gross substitutes over indivisible items

I don't really have a background in economics. I'm trying to understand the relationship between these two terms, if they are related at all. The definitions that I understand are here: Substitutable ...
AWhite's user avatar
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