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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107 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
368 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
82 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
230 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
874 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
169 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
459 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
774 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
221 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
86 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
377 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
218 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
854 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
695 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
168 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
244 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
122 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
156 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 ...
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1answer
174 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 ...
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1answer
189 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 ...
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1answer
2k 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 ...
3
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1answer
3k 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
252 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 ...
2
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3answers
127 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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2answers
665 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
970 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
377 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 ...
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2answers
4k 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
215 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 ...
3
votes
1answer
401 views

Nash equilibrium question

(Hotelling’s voting model) Consider a population of voters uniformly distributed along the ideological spectrum from left (x = 0) to right (x = 1). There are two candidates i = 1,2 for a single office ...
2
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1answer
69 views

Incomplete “round trip” of taking a minimum, then a maximum, from a positively skewed distribution

Let's say you have a distribution that is either symmetric or positively skewed (and defined over 0-1). Call it F. Then, you find the distribution of the minimum of n>1 draws from F. Call it Fmin. ...
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1answer
839 views

Proof involving a convex set

So, the problem is actually from a microeconomics class. The problem is this: If preferences are represented by a utility function $u(x,y)=xy$, show that these preferences are convex. Now in case ...
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1answer
203 views

Economic optimisation problem

Here is the question: Consider a car-owning consumer with utility function $$u (x) = x_1x_2 + x_3 (x_4)^2 ,$$ where $x_1$ denotes food consumed, $x_2$ denotes alcohol consumed, $x_3$ denotes kms of ...
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1answer
2k views

How do I graph this budget constraint?

How do I graph the following conditions? We are in two good life, spinach and sprouts, spinach on x axis, sprouts on y axis. If you consume 10 or less servings of spinach, you pay \$5 for each. Above ...
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1answer
197 views

Economics formula

This is an economics question, but if I can get the correct answer to this formula I can answer the question. Any help is appreciated, thanks! If the demand $Q_x^d$ for a product given the price ...
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3answers
552 views

Economics supply and demand question

If the market demand for shoes is given by $QD = 10000-250P$ and the supply is $QS = 5000$, what is the equilibrium price of shoes? How many pairs of shoes will be sold? Thanks in advance.
2
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1answer
526 views

Statistics with overlapping periods

I've been having a lot of discussions about finance recently in which people will point to some results using overlapping time periods and claim a high degree of statistical significance. For ...
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5answers
2k views

Motivating linear algebra for economics students?

I'm a tutor for the introductory linear algebra course at my school; this course is required for most upper division economics classes, so a lot of my tutees are economics majors. This is a typical ...
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2answers
402 views

Engineering Economics - Annual Cost Question

My question is as follows: 1.) An earth compactor costs $38,000 and has an economic life of 9 years. However, the purchaser needs it for only 1 project that will be completed in 3 years. At the end ...
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0answers
116 views

Optimal tax rate

Suppose you have two countries A and B, with a tax rate $T_A$ and $T_B$, respectively. The tax is redistributed to all people equally. Hence if you live in A and you make $I$ as income then you will ...
2
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1answer
350 views

Production Function

Yes.. I know this is a math forums but there is no economics.stackexchange.com :(. Since this is also a math problem, I thought I'd post it here. Please help. An undeveloped economy produces goods ...
10
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1answer
368 views

A (mathematically) sound investment strategy

It is common wisdom in the investment community that a long-term investor saving for his future would do well to invest in high-risk/high-return assets when he is young, slowly switching his portfolio ...
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0answers
383 views

Maximizing two codependant profit equations for Bertrand Model Oligopolies

For this problem I was given the Fixed Cost, Marginal cost, and demand curves for two firms (x and y). So far, from this information I derived the profit (π) function for each firm. ...
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2answers
436 views

Finding best response function with probabilities (BR) given a normal-matrix representation of the game

We are given players 1, 2 and their respective strategies (U, M, D for player 1, L, C, R for player 2) and the corresponding pay-offs through the following table: $\begin{matrix} 1|2 & L & C ...
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1answer
147 views

Optimizing Group Spending

I have always thought that groups of individuals that spend more money(as opposed to save) have more money in the long run. My reasoning is that if a particular group spends money, then each dollar ...
1
vote
1answer
272 views

Find a price vector p for various prices of industries.

( Leontief input-output model ) Suppose that three industries are interrelated so that their outputs are used as inputs by themselves, according to the $3 \times 3$ consumption matrix A = ...
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1answer
154 views

Normal distribution probability

just a quick question dealing with probability. The annual returns on stocks and treasury bonds over the next 12 months are uncertain. Suppose that these returns can be described by normal ...
5
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1answer
227 views

Measure of value of resources in a competitive game

Let we have a competitive survival game in which a player has choice between different resources to earn. The question here is which resource should he prefer to maximize the chance of survival. I ...