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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1answer
30 views

Economics simplification of stochastic transition of capital

I'm taking an macro-econ paper and I can't seem to work out the following simplification. Basically somehow by combining equation 4.14 and ...
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1answer
53 views

Either find an example of a differentiable downward-sloping function $p$ such that $\frac{d}{dx}[p(x)+xp'(x)]<0$

In economic models we assume that firms which face a decreasing demand curve also face a decreasing marginal revenue curve. I just realized that I wasn't sure that this is true, so I tried to prove ...
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1answer
161 views

Economic Analysis / Minimization Problem

I am studying and going through some old exams for a microeconomic analysis class. I am just looking for some clarification regarding one of the answers given. The question is as follows Suppose ...
2
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1answer
52 views

A question about infinite utility streams

At the end of Diamond's Evaluation of Infinite Utility Streams he proves a theorem (which he doesn't give a name to, but it's at the very end of the article). There is a step in which he jumps from ...
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1answer
608 views

bounding the the expected value of the maximum of two random variables

Consider two standardized random variables $x$ and $y$, and define a function $g(x,y)=E[max(x,y)]$ where $E$ is the expected value operator. My question is finding the upper and lower bounds of ...
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1answer
61 views

How do I interpret $n^*$ and $n^{**}$ in this mathematical economics statement?

The statement I'm confused about says the following: The best surplus we can get from trading $n$ objects equals $$\sum_{k=1}^n (v_k - c_k) = V(n) - C(n)$$ Any efficient trading volume thus ...
2
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1answer
139 views

Economics: two rival firms in two countries

I am currently working on a paper in macroeconomics, where I found a result that I cannot manage to understand. Since we don't have a macroeconomic site yet, and this is mostly game theory, I will ...
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1answer
63 views

what can we say about $G(.)$?

Given $c \in R$, a deterministic probability density $f(x)$ and its cumulative distribution $F(c)$, what can be said about $G(c)$ where: $G(c)=\int f(x)F\left( x+c\right) dx $ The question ...
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1answer
95 views

Non-core allocations in the 2-fold replica of an economy.

Here's the definitions I'm using, just in case. Let $E$ be the exchange economy given by agents $A,B$, starting allocations $x_A=(0,1)$, $x_B=(1,0)$ and utility functions given by $u_A=x+y$ and ...
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1answer
65 views

Differentiation passage

I am not able even after a whole hour spent on figuring this out to understand the following passage. Please, can you help me out somehow? It is part of the explanation of how a tax affect a monopoly. ...
0
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1answer
77 views

how can I compute a posterior distribution using Bayes?

This may be a silly question, but I cannot figure out a convincing (to myself) answer to it. Suppose that you want to buy a new car. Let $v$ be the value you attach to the car. Before visiting the ...
2
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1answer
153 views

How to prove that there exist a concave function and $\gamma\in[0,1]$ and some other numbers which satisfy an inequality

I'm working on an economics paper, and in the model I've made I've basically gotten myself a little bit stuck. I need to show that there exists a nondecreasing concave function $u$ and numbers $P$ and ...
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0answers
128 views

How did (economics) Taylor rule come out mathematically?

There is Taylor rule in economics that shows how to relate nominial interest rate with inflation and GDP. $i_t = \pi_t + r_t^* + a_\pi ( \pi_t - \pi_t^* ) + a_y ( y_t - \bar y_t )$ In this ...
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0answers
114 views

Trading price of 2 consumers with the same utility function

Say that two consumers, A and B, have the same utility function, just $u(x) = (x_1)^2 + (x_2)^2$ for simplicity. If consumer A has endowment $x_A = (4, 3)$, and consumer B has endowment $x_B = (3, ...
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2answers
471 views

Application of maths in economics

What are the branches of maths where we can see undoubtful connections with economics? Where can we use mathematical methods or models and apply them to analyze economic concepts?
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1answer
125 views

economics: two fully substitutable products - demand curves?!

I hope that this is the right stackexchange-site for my question, if not, please move it! sorry!!! :) So, I have a problem with a paper I've got to read for one of my classes, and I think you guys can ...
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2answers
309 views

Majoring in maths

Does majoring in mathematics with economics (with emphasis on mathematics) have good career prospects? Does anyone know something about this course?
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2answers
175 views

Economics Probability Question

You work for a small company and must decide whether to go forward with an investment project. The company will gain 5 million dollars if the project is successful, but will loose 1 million dollars if ...
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2answers
212 views

From which areas of mathematics does consumer theory in microeconomics spawn?

In my intermediate microeconomics class last year, I was rather surprised by the math involved in building consumer theory. In consumer theory you do things like define a binary relation $\succsim_a$ ...
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0answers
112 views

proof using (fixed point theorem)

I am seeking to solve for a Nash equilibrium in pure strategies $(d_2,d_2)$ involving two players, $1$ and $2$. Given that $h'(.)$ is s strictly decreasing and continuous function, $\Phi(d_1-d_2)$ ...
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2answers
62 views

Showing probable causality

After examining various correlations between longitudinal data and illustrating high correlation between one or more variables, I realized that I could only show that the data was correlated but could ...
0
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2answers
686 views

Subgame Perfect Nash Equilibrium

My homework question is summarized below: There are 7 players (say P1,P2,...,P7) trying to split 100 dollars. The game starts with P1 proposing an allocation of the 100 dollars to each ...
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1answer
60 views

Working out interest rates on a futures contract/exchange rates contract.

okay my main problem is I have to work out a $3$ month interest rate for the us dollar. The question I'm stuck on is At the end of trading on $1$ January $2012$ the dollar/pound spot exchange rate ...
5
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1answer
304 views

Olympic Badminton, or How to Design a Tournament

Hearing the recent news about disqualified Badminton players in the ongoing 2012 London Olympics got me wondering about how best to design tournaments to avoid situations where players are ...
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1answer
964 views

Finding Nash Equilibria with Calculus

The problem is summarized as: There are two players. Player 1's strategy is h. Player 2's strategy is w. Both of their ...
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1answer
1k views

Unable to find Nash equilibria in mixed strategies

Here is the strategic form game: Player 2 Left Middle Right Top 2,2 0,0 1,3 Player 1 Middle 1,3 3,0 1,0 ...
2
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1answer
471 views

Solving a Maximum Likelihood Estimation with an exponential distribution

I need someone's insight on applying a MLE for an exponential distribution. In a finance paper, I have the following: $\displaystyle d_i \sim \frac{\epsilon_i}{\lambda_i}$ where $\epsilon_i$ is ...
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2answers
132 views

Eq (4) of Bils and Klenow (2000)

I hope some of you read Economics. I was wondering if anyone can help me in deriving equation (4): $\ln A_{i}\left( t\right) =\beta\ln h_{i}\left( t\right) +\ln\bar{A}\left( t\right) ...
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1answer
1k views

How to find Pareto-improvements with maths?

I hope this is not off topic. I've got two utility functions for two different kinds of agents, A and B, and their endowments ($w_1$ and $w_2$) of the (2) goods ($x_1$ and $x_2$). The utility ...
0
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1answer
154 views

Finding competitve equilibrium(consumption rivalry)

Consider two agents (Pascal and Friedman) in a pure exchange economy with two goods and no free disposal. Pascal has a preference relation give by the utility function $$u^P(x_1^P,x_2^P)=a\ln ...
0
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1answer
64 views

Probability of a new number given a set of $n$ previous numbers?

I have a set of numbers (each one corresponding to a payment made from the same person) and I would like to assign a probability value to a new specified number given that historical data. I've ...
0
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1answer
115 views

Market optimization problem

Demand schedule: $Q_d=a_0-a_1P_d$Supply schedule: $Q_s=b_0+b_1P_s$$P_d$ and $P_s$ are prices faced by consumers and producers. $a_0,a_1,b_0,b_1$ are all positive constants, where $a_0>b_0$. The ...
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0answers
428 views

Time flow analysis and theoretical flow time

I'm working for my program for economy where I have an example I try to solve. The flow rate is 0.15 units/min and A - 1 server: flow time = 5, capacity = 0.2 B - 2 servers: flow time = 9, ...
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0answers
86 views

How to minimize game night transactions?

Me and a number of friends occasionally met up and play some game (often pool or some card game) and play for small stakes to give the game a little extra spice. After each round we jot down the ...
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1answer
231 views

Logarithmic terms

I've found a formula derivation in my international economics book, but I can't understand how it was derived. It says $ E P X = P^* IMP $ where E is the exchange rate, P is the level of national ...
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1answer
1k views

Calculating “deseasonalised sales y” when forecasting 2004Q1-2004Q2

I'm currently having difficulty calculating values for the deseasonalised sales column. How do you go about doing it for 2004Q1-2004Q2? Btw in case you are wondering: $$2004Q1$$ $$First MA = ...
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0answers
198 views

Understanding a Proof in Probability Theory

My question is pretty simple: I have two equations which are supposedly true (from a published paper) but I have no idea how to arrive at the solution myself. So it would be great if someone could a) ...
0
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1answer
491 views

Describe the Engel's curve for the optimum consumption bundle

A consumer has the utility function $u(x_1,x_2)=(x_1^a+x_2^a)^{1/a}$ where $0\neq a<1$. Her expenditure must satisfy $p_1x_1+p_2x_2=I$, where $p_i$ is the price of a good i, and I is her income. ...
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3answers
1k views

Using the definition of a concave function prove that $f(x)=4-x^2$ is concave (do not use derivative).

Let $D=[-2,2]$ and $f:D\rightarrow \mathbb{R}$ be $f(x)=4-x^2$. Sketch this function.Using the definition of a concave function prove that it is concave (do not use derivative). Attempt: ...
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2answers
231 views

summation notation for general sets

I'm working through an academic game theory paper and stumbled upon this summation notation in a proof and I'm not quite sure what it means: $$\sum\limits_{j \in M \backslash\ \{i\}}$$ There is a ...
0
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1answer
89 views

Find restrictions on $a>0$ and $b>0$ that ensure that $f(x_1,x_2)$ is concave.

Let $f:\mathbb{R}_{+}^2 \rightarrow \mathbb{R}$ be $f(x_1,x_2)=x_1^a x_2^b$ for $a>0$ and $b>0$. Find restrictions on $a>0$ and $b>0$ that ensure that $f(x_1,x_2)$ is concave. I ...
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2answers
384 views

Prove the set $M=\{x\in\mathbb{R}^2_+ \mid \alpha x_1+\gamma x_2\leq \beta\}$ is convex

Let $\alpha\gt 0$, $\gamma\gt 0$, and $\beta\gt 0$ be real numbers. Let $$M=\{x\in\mathbb{R}^2_+ \mid \alpha x_1+\gamma x_2\leq \beta\}$$ Prove $M$ is a convex set. Prove that $M$ is bounded. ...
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2answers
247 views

How can I reconcile these two different equations for “Arc Elasticity”?

Well, I've encountered a problem which seemed me like a wrong answered one so, I Google'd for the formulas of both "Arc Elasticity" and "Arc Elasticity of Demand" So far, I've found myself in some ...
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1answer
1k views

Calculating the Maximum Production Point for an Equation

I need some help on this equation: $x\;$: Output Quantity $CF\;$: Cost Function: $CF(x)=5000+100x-\frac{x^2}{24}\;\leftrightarrow\;0\leq x\leq1600$ Now, I've already noticed that it sounds a litte ...
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1answer
873 views

Expressing the sum / average of two AR(1) processes as an ARMA

I've got the following problem. I have two AR(1) processes (which are the returns on assets)- $$r_{1t} = \phi_1r_{1,t-1} + u_{1t},$$ $$r_{2t} = \phi_2r_{2,t-1} + u_{2t},$$ We have the following ...
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1answer
205 views

Nash equilibria of mixed strategies

I am given the following game to find nash equilibria in pure and mixed strategies: $\begin{pmatrix}& & Litte John &\\ & & c & w \\Big John & c & (5,3) & (4,4) \\ ...
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2answers
2k views

Cournot Nash Equilibrium Between Two Firms

Suppose we have two firms with specialized, but similar products. Suppose market demand for the two products is: $$p_1(q_1,q_2)=a-bq_1-dq_2$$ $$p_2(q_1,q_2)=a-bq_2-dq_1$$ where $d \in (-b,b)$. Suppose ...
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2answers
275 views

Portfolio Optimization Problem Without Correlation Info

I received this interesting problem from a friend today: Assume that you are a portfolio manager with $10 million to allocate to hedge funds. The due diligence team has identified the following ...
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0answers
127 views

Democratic central planning model

I want to model following situation: 1) There is a number of representatives of social groups (e. g. political parties). 2) Each of them devises an economic plan for the next year (N+1, N being ...
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0answers
164 views

economic modelling asked for

I am putting together a proposal for a system of economic exchange which links a transaction of money through a period of time, and subjective relationship evaluation between two people. How can it be ...