For questions regarding the mathematical analysis of economic models and problems. This includes questions about the formulation or solution of models from microeconomics or macroeconomics.

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2
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1answer
123 views

Generalized Mechanism Design, Stanley Reiter diagram and Vickrey Auction

I am trying to learn this new topic, Mechanism Design and stumbled upon the "Stanley Reiter" diagram (see the top-right side on the page). I have also learned that the Second Price Sealed Bid ...
9
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1answer
382 views

Modelling risk when market making

I'm interested in learning about algorithmic trading, particularly in bitcoin. Looking at this chart, I can see that I could simultaneously offer a bid that was slightly higher than the highest ...
0
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1answer
64 views

ordinary least square regression

i have a question and i'm confused with the concepts. Pls aid Consider the estimation of the population mean in the model: $Y_i = \beta + U_i$ for $i = 1,2,3$. Assume that $E(U_1) = E(U_2) = E(U_3) = ...
3
votes
1answer
160 views

Mistake in Wikipedia article on St Petersburg paradox?

I suspect that there is a mistake in the Wikipedia article on the St Petersburg paradox, and I would like to see if I am right before modifying the article. In the section "Solving the paradox", the ...
1
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2answers
57 views

How to derive duration of unemployment?

The average monthly flow out of unemployment pool of $7.0$ million people each month is $3.1$ million. Put another way, the proportion of unemployed leaving unemployment equals $\frac{3.1}{7.0}$ or ...
2
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1answer
913 views

questions on information set definition

The definition of "information set" is An information set is a set of decision nodes, all belonging to the same player, over which that player cannot distinguish. ...
2
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1answer
80 views

Counting in Arrow's theorem

I seem to be really confused with the counting system in Arrow's theorem. Can I have a simple explanation how they determine the outcome? I can't determine the outcome using rules from my notes. It ...
1
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1answer
37 views

When do $Y$ and $r$ increase in the given economy?

This question is from "Mathematics for Economists" by Simon and Blume. IS curve: $[1-c_1(1-t_1)-a_0]Y+(a+c_2)r=c_0-c_1t+I^*+G$LM curve: $mY-hr=M_s-M^*$ The parameters $c_1$,$t_1$ and $a_0$ are ...
2
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2answers
105 views

Why not n=2 in Arrow's theorem

Why in the statement of Arrow's impossibility theorem we omit the case n=2? I will appreciate it if you can explain it in easy words. I'm by no means an expert in the area (I think it's very much ...
2
votes
2answers
262 views

Ideas about an Ordinary Differential Equations research work (University level)

Good afternoon to everyone, I need some ideas about a Ordinary Differential Equations research work. It is for the ODE subject that I am doing at my Mathematics degree in my University. They asked me ...
2
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1answer
89 views

Use Roy's Theorem to prove that …

I have an advanced microeconomics theory related question: Use Roy's theorem to prove that $s_i(p,y)= -\frac{\partial v(p,y)}{\partial lnp_i}/\frac{\partial v(p,y)}{\partial lny}$. This question has ...
0
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1answer
70 views

Density income and Total Income.

Suppose that the density income function is $f(r) = a*exp(r^2)$ with $r \in(0; 10)$ (hundred thousand euros) and $a=exp(10)-1$. Assume that the total number of people in this economy is 1 million. ...
0
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1answer
154 views

Alternatives to Monte-Carlo simulation

Imagine I have a model of economy of a region, which consists of several companies, importers and population. Let's assume that all local companies in question produce food and agricultural ...
3
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2answers
206 views

Functions minimized at the median of their arguments

I am doing research on problems of location of a public facility on a network which lead me to the following question. Is there an interesting way to characterize the class of functions $f : ...
0
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1answer
94 views

Production function (economy)

A company produces one good using two factors of production factors. If $x$ and $y$ denotes the units of the factors used by the company, the technology function is given by $F(x; y) = xy^2$. In the ...
3
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2answers
191 views

Substituting total derivative d for partial derivative \partial

In economic models it seems to be commonplace to substitute a total derivative derived from one equation, say $\frac{d k}{d \tau}$, for the partial derivative derived from another equation, say ...
0
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1answer
60 views

Statistical inference and t-stats?

I have this linear regression model with an intercept(b0) and 3 variables(b1,b2,b3). Then they drop b2 and b3 and they give a new regression line with a new b0 and b1 and consequently new standard ...
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2answers
119 views

Using derivative to estimate change overestimates change between two states

I have a profit function in which revenue is given by the state of a variable y at each point in time t: R=y[t]-y[t]^2 and costs depend on the change in y from the previous state so that large changes ...
1
vote
1answer
101 views

Properties of concave,two-parameter function

I already showed that the function $\psi(\mu,\sigma)=\mathbb{E}U(X)$ is concave in $(\mu,\sigma)$, where $X$ is normally distributed with mean $\mu$ and variance $\sigma^2$. $U$ is a nice concave ...
0
votes
2answers
52 views

Average and aggregate values with a distribution function

I'm reading an economics paper and I'm trying to understand if a statement made by the author is an assumption or the consequence of a previous definition. The part I don't understand is the ...
0
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1answer
74 views

Statistics - Covariance and variance question

Please fill in the intermediate steps $$\sum_{i=1}^nx_i(x_i-\bar x)=\sum_{i=1}^n(x_i-\bar x)^2$$ and $$\sum_{i=1}^nx_i(y_i-\bar y)=\sum_{i=1}^n(x_i-\bar x)(y_i-\bar y)$$
0
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1answer
527 views

Total differential Economics Application

Suppose we have a revenue function: $R= P*Y$ where $P=$ price and $Y=$ output and is a function of $P$ and $C$, $Y= Y(P,C)$. How could we write the total differential of $R$ with respect to $P$ and ...
2
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2answers
1k views

derivative with respect to $\log(x)$

I have a dynamic equation, $$ \frac{\dot{k}}{k} = s k^{\alpha - 1} + \delta + n$$ Where $\dot{k}/k$ is the capital growth rate as a function of savings $s$, capital $k$, capital depreciation rate ...
3
votes
1answer
104 views

Constraining estimated linear regression coefficients over several regressions

I'm trying to run a series of simultaneous linear regressions, and I want to constrain the regression coefficients. For the standard ordinary least squares regression, the specification of the ...
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0answers
70 views

what is a connection between two simple yet important economics and math formula: elasticity

what makes it interesing to define them in mathematics? what is a connection between two simple yet important economics and math formula: elasticity? Something interesting to read: ...
0
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1answer
56 views

Very simple question about trace

In MSE in econometrics, $$\mathrm{MSE}=E\| \hat{\theta}-\theta \|^2$ $=E(\hat{\theta}-\theta)'(\hat{\theta}-\theta)$$ ...
2
votes
1answer
106 views

Reformulation of the Weak Axiom of Revealed Preference

This question about foundations of mathematical economics. Let $X$ be some set, $\mathcal{B}\subset 2^{X}$ and $C:\mathcal{B}\rightarrow 2^{X}$ such that for all $B\in\mathcal{B}$ we have 1) ...
1
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2answers
188 views

How do you call $\succsim$?

actually, I study economics, not math. As some of you may know, there is a sign for comparing goods: $\succsim$. My professor read $x\succsim y$ like "x is at least as good as y". I asked her if ...
1
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1answer
128 views

Two traders don't trust each other; what transactional equation optimises reward and minimises risk?

Years ago while on a Wikipedia browsing binge, I read a maths article about how two (or more) mistrusting parties can reach an transactional equilibrium, but I've wracked my brain and I can't remember ...
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0answers
62 views

$\frac{\partial}{\partial\theta}\phi'\mu+\frac{\alpha\phi'\Sigma\phi}{2}=0$

Ok, I am working on a problem that consists of the following: I am looking to solve the portfolio choice optimization problem (maximizing utility with a known utility function) in the case where all ...
1
vote
1answer
52 views

Integration of a sum of production functions

I'm reading an economics paper in which technical knowledge at time t ($A_t$) is the function of past production ($y_{i,t-1}$) for each individual and the learning done by one individual affects the ...
4
votes
2answers
332 views

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

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
1answer
280 views

How can a social welfare function be a linear combination of von Neumann-Morgenstern utility functions?

The von Neumann-Morgenstern axioms were an attempt to characterize rational decision-making in the presence of risk. The von Neumann-Morgenstern utility theorem says that if someone is vNM-rational, ...
4
votes
1answer
109 views

Shapley value: an alternative representation

It is my belief that the more common representation of the Shapley value is given by $$ \phi_i(v)=\sum_{S\subseteq N-i} \frac{|S|!(|N|-|S|-1)!}{|N|!}(v(S\cup\{i\})-v(S)) $$ where $v \in ...
0
votes
2answers
92 views

Matrix Operation

Let $x$ be a $n \times 1$ vector whose jth element is $x_j$. Show that $A = xx^{T}/x^{T}x$ and $B = I_n - A$ are symmetric idempotent matrices. Note that $x^Tx$ is a scalar (real number)
1
vote
1answer
281 views

SPNE of infinitely repeated game

Let $G$ be a game with finitely many players and $\underline{v}= (\underline{v}_i)$ be the minmax payoff profile. Denote by $G_{\infty}(\delta)$ the infinitely repeated game whose stage game is $G$ ...
2
votes
2answers
234 views

The 10.4 Problem on Benassy's *Macroeconomic Theory*

This a repost. In my first try at the problem here I was not very clear with my question and I was also troubled by my lack of knowledge of MathJax. And I probably lost the attention of you guys while ...
0
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1answer
269 views

What is the definition of the slope of a linear function in the context of economic graphs?

I only ask this because of the fact that economists tend to plot the dependent variable on the horizontal axis and the independent variable on the vertical, which is opposite to the "normal" way of ...
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0answers
109 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
vote
0answers
109 views

Math model - constrain GDP given different growth rates of industries

ideas needed to model national GDP given different sector growth rates subject to some contraints Given: GDP equations for $n$ industries depend on growth rates and time i.e. $g(r_1,t), g(r_2, t), ...
0
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1answer
267 views

Mathematical Economics - Utility maximization

I am thankful to any hints: What I have: Simple log-utility form: $u = \log c_1 + \beta \log c_2$ Budget constraints: $c_1 + s \leq w$ $c_2 \leq R\; s$ Problem: For utility maximization: $s = ...
0
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1answer
84 views

Portfolio which replicates given payoff

Consider the following payoff function: $$p(S_T) = \begin{cases} 0 & \text{if } S_{T} \leq 70 \\ S_{T}-70 & \text{if } S_{T} \in (70; 100] \\ -S_{T}+120 & \text{if } S_{T} \in (100; 120] ...
0
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1answer
46 views

How to determine the MU in economics?

I currently have a table like so: Hours spent on Activity X | Total Utility 120 220 300 360 396 412 I know that Marginal Utility is calculated use slope formulate (delta Y / ...
0
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3answers
299 views

Arrow impossibility theorem and social choice.

I have read the Arrow impossibility theorem in Foundations of Mathematical Economics(Michael Carter). It is just too difficult to understand. So, does Arrow'theorem mean that there is always a ...
3
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2answers
311 views

Exercise in Mechanism Design

I found an exercise with solution in the field of Mechanism Design. The problem is I don't understand the solution. Exercise. Use the characterization of incentive compatible direct-revelation ...
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2answers
1k views

What is the equation representing a constant elasticity of 1?

I'm reading the chapter in my textbook about the price elasticity of demand, and it was pointed out that most demand curves do not represent a constant elasticity of demand - even linear curves like ...
0
votes
1answer
159 views

$\log(0,05)$ is minus, but $\log(0,04999\ldots)$ is plus?

How is this calculated, and why is this? We're calculating fixed-rate mortgage, with following formular: $$ n = 1-\frac{\log(\frac{L\cdot x}{y})}{\log(1+x)} $$ Where: $L$ is the loan size, $x$ is ...
2
votes
1answer
227 views

generalized method of moments and the case when solving linear regression with two error conditions

So, I am slowly getting introduced to generalized method of moments (GMM), but I am getting confused over some issues, and this is one of them: I heard that GMM solves the problem that an estimator ...
0
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0answers
39 views

How to Taylor expand $\ln{1-\exp{-i_t}}$ around i?

my question here is how to Taylor expand around $i$ $\ln{(1-\exp{(-i_t)})}$ to the first order? $i_t$ is a time series variable, $i$ is its steady state. Could anyone show me how to expand it ...
1
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0answers
53 views

How is “index” at an Walrasian equilibrium proved? (in relation to Hopf-Poincare theorem)

So, the index of an (Walrasian/general equilibrium) equilibrium point is determined as the sign of $(-1)^{L-1} \times \det M$ where $M$ is a matrix and $M_{ij} = \frac{\partial{Z_i}}{\partial {p_j}}$, ...