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
82 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
167 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
145 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
134 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
603 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
136 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 ...
2
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2answers
269 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 $\succsim_a$ ...
2
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1answer
125 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
74 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
764 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
61 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
347 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 ...
0
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1answer
1k 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
554 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
135 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) ...
2
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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
163 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
120 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
536 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
89 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
2k 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 = ...
0
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1answer
513 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
2k 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
247 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
92 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 ...
0
votes
2answers
399 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. ...
2
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2answers
279 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
2k 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 ...
0
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1answer
1k 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
271 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) \\ ...
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 ...
0
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2answers
325 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
136 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 ...
3
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0answers
175 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 ...
4
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1answer
208 views

Is functional integration useful in theoretical economics?

Definition of functional integration here Functional integration is a collection of results in mathematics and physics where the domain of an integral is no longer a region of space, but a ...
0
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1answer
252 views

Consumer maximizing his total utility

Consumer is trying to maximize his total utility if at a certain consuming amout: a) marginal utility is equal to 0 b) marginal utility is equal to his total utility c) marginal utility divided by ...
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2answers
2k views

How to find the minimum variance portfolio?

I am doing some revision questions on my Portfolio Theory module, and have come across the following question: Consider an investor who has constructed a risky portfolio from N securities. The ...
7
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2answers
4k views

Understanding the Leontief inverse

What I remember from economics about input/output analysis is that it basically analyses the interdependencies between business sectors and demand. If we use matrices we have $A$ as the input-output ...
2
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1answer
5k views

An algorithm for arbitrage in currency exchange

I found a really interesting problem and I wanted to hear people's opinion. It has to do with currency exchange rate. If we are give some coins $c_1,c_2,\dots,c_n$ and an array $R$ that keeps the ...
2
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1answer
305 views

Application of the Factor–Price equalization theorem (Samuelson) on trade?

I'm trying to understand the factor price equalization theorem by Samuelson. I came across this graph but I don't know how to interpret it. Could anyone give me a short resume on what the graph is ...
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3answers
151 views

Problem relating convex sets and optimization

I am working on a microeconomics problem, but I have just kind of just boiled down to the following problem involving convex sets. I have a convex set of vectors in $\mathbb{R^n_+}$ of the form ...
10
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3answers
998 views

Can someone explain Cremer-Mclean's astonishing result in auction theory?

In mechanism design/auction theory, there is a famous result by Cremer and Mclean that if agents'/bidders' valuations are even slightly correlated, then all the surplus can be extracted by the ...
3
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1answer
2k views

What's the most straight-forward way to prove Walras's Law?

Walras' Law states that summation of pi Ei(p) = 0 for all pi. We define Ei(p) = xi(p) - qi(p) - Ri. What are the next steps that I should take?
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1answer
545 views

How to show that Roy's identity holds in the case of a monotonic increasing transformation?

I know that by Roy's identity, the Marshallian demand for a good (i) is $x^*_i = -\frac{V_i}{V_y}$, where $V(Y,P)$ is the indirect utility function, $V_i=\frac{\partial V}{\partial P_i}$, and ...
0
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2answers
7k views

Given supply and demand curves, and a tax, how can I find the tax burdens and revenue?

Suppose we have the following system of equations: $Q_s=-20+3P$ $Q_d=-220-5P$ $Q_s=Q_d$ Say we want to find the tax burden of the consumer, the tax burden of the firm, and the total revenue ...
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1answer
340 views

Optimization price per unit

I have no idea how to do this, I tried a lot of things but they don't make sense and I have too many variables. A manufacturer has been selling lamps at the price of \$6/lamp, and at this price ...
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2answers
402 views

What can I deduce from the graph of marginal value?

Homework problem: We have a graph of value: x coordinate number of widgets made. y coordinate value in $. For the first 5 widgets the value greatly increases to $100 and then after 5 ...