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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2answers
59 views

Creating indices

Is there a "proper" formula for creating indices? I need to compute series of numbers into a KPI that can be tracked over time. Example dataset is like this: ...
1
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2answers
277 views

Maximum feasible output of a company

Imagine, I have following model. There is a company X, which produces one unit of final output from 0.2 units of input A and 0.8 units of input B. Inputs A and B are bought from respective ...
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3answers
145 views

My brothers share from income.

My brother is driving a limo with his partner who told him that they will go 50-50 on income and also 50-50 on gas. So if my brother earns \$1000 by spending \$200 on gas, what will be my brothers ...
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2answers
341 views

Game theory: Nash equilibrium in asymetric payoff matrix

I have a utility function describing the desirability of an outcome state. I weigh the expected utility with the probability of the outcome state occuring. I find the expected utility of an action, a, ...
-2
votes
1answer
61 views

Need to know how to inteprete an inequality

Pls have a look at this: http://imgur.com/FRfoP This is a screenshot of my lecture notes, from economics. I know that the LHS refers to the utility the agent thinks she will get if she consumes ...
2
votes
0answers
71 views

Constructing and understanding stock-flow model

Suppose that $\textbf{x} = A\textbf{x} + B\dot{\textbf{x}}$ where $\textbf{x}$ is vector of economic output level, $A$ is input-output matrix, $B$ is stock-flow matrix. The system represents ...
1
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1answer
58 views

Price mechanism question (economics)

There are two goods in the market $X1$ and $X2$ and both of their prices are positive. If an agent's utility function is given as: Q1 = amount of X1 agent buys, Q2 = amount of X2 agent buys, $u = Q1 + ...
0
votes
1answer
44 views

Clarification of equations regarding capital switching and dated labor

Then, using this example (and further discussion), Samuelson demonstrates that it is impossible to define the relative "roundaboutness" of the two techniques as in this example, contrary to ...
1
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1answer
79 views

Why is profit of all firms zero in long-term?

I heard that profit of all firms in long-term becomes zero. But I am not convinced of why it is like that. Can anyone explain this mathematically?
1
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1answer
145 views

Input-output economics and stability of general equilibrium

Here, I will start with a simple expression for an input–output system with $x(t)$ representing the vector of outputs and $A$ the input–output matrix. Then, the simplest possible linear ...
1
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1answer
112 views

Mathematics behind Incentive Design

I was working on an Applied Math project on allocation and I had an interesting idea about extending it to providing incentives to different "players" in the allocation process. But I am clueless ...
1
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1answer
132 views

vickery auction question(second-price auction)

The question is as follow, Alice and Bob would both like to own the same manuscript. The manuscript is worth 5 million to Alice and worth 3 million to Bob. The present owner of the manuscript ...
2
votes
1answer
140 views

Stability of a system that has (Jacobian-like) matrix with eigenvalue of less than 1 that has $x$ as non-eigenvector

This is about general equilibrium: Suppose that $x(t)$ represents outputs of all sectors and parts of the whole economy - represented as matrix. How outputs evolve to $x(t+1)$ is ...
0
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1answer
200 views

subgame perfect nash equilibrium for war of attrition

the question is as follow: suppose that two players are playing war of attrition, that means both of them could choose either to fight or quit, if either one of them quit, the game ends, and if ...
1
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2answers
3k views

cournot competition with N-firms

The question is as follow: Here is how we can think of N-firm Cournot competition. Assume all the firms have the same marginal cost C > 0. Firm 1 chooses Q1, Firm 2 chooses Q2, and so on. The market ...
1
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1answer
149 views

Cournot-game problem

I'm so stuck with an exercise about Cournot game and was hoping if someone could help me out here. Would appreciate all the help. This is the exercise: Consider the market for Blue Turtle (a new ...
2
votes
1answer
157 views

Applied Math for economics question: mostly algebra help

I am teaching myself the calulus component necessary to get thorugh an econ based stats and applied math class. My algebra is killing me please help - the practive problem is given $y = –x^3 + 7x – ...
0
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1answer
90 views

question on T period bargaining(alternating offers).

the following question is a kind of Rubinstein bargaining model: 2 players, A and B, have 100dollars to divide between them. They agree to spend T days negotiating over this division. The first day, ...
6
votes
1answer
120 views

How many dollars does it take to be rich?

This is probably a dumb economics question since I don't know anything about that subject beyond a few buzzwords (but I do know a little math). I'm trying to figure out how many dollars it takes to ...
1
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1answer
700 views

Eigenvalues of matrix and stability

This is about general equilibrium: Suppose that $x(t)$ represents outputs of all sectors and parts of the whole economy - represented as matrix. How outputs evolve to $x(t+1)$ is determined by the ...
2
votes
0answers
108 views

Optimal strategy in a VCG auction with partial collusion?

Suppose you control the bid prices in a multiple-item VCG auction for a partial coalition of bidders. Each bidder is only allowed to win one item out of the set of multiple items, which are all ...
1
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1answer
104 views

Find the real exchange rate

If the nominal exchange rate increases by 5%, while domestic inflation is 2% and foreign inflation is 3% then the real exchange rate changed by?
1
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1answer
194 views

Question on mixed nash equilibrium!

The question is as follows: Think of the Golden Ball game. Now player 1 is money-minded and jealous, and player 2 is very good-hearted, so the payoff matrix is follows: ...
1
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1answer
322 views

Arrow-Debreu model of general equilibrium having many equilibria

I am just beginning to study some stuffs outside introductory/sophomore(?) micro/macroeconomics. And I met with a stuff called Arrow-Debreu model. The question is, 1) What would be the proof that ...
1
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1answer
85 views

Understanding revenue and profit math stuffs in labor theory of value

In http://wrongarithmetic.wordpress.com/2010/08/22/keen-i/, it talks about how economists Steve Keen's argument against Labor Theory of Value (LTV) is wrong. What I do not get is from This ...
0
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0answers
402 views

Net Present Value Calculation for Construction Project with Initial Capital

I'm having real trouble working out how to do the following question because of the initial capital that the company has at the start of the project, meaning that they can delay taking out a loan ...
0
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1answer
104 views

long run equilibrium problem

Suppose the market for schools in a small town is of perfect competition. The market demand for school seats, $y$, is given by $y(p)$. The long run average cost function for each school is given by ...
1
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1answer
88 views

Net Present Worth Calculation (Economic Equivalence)

I'm currently doing some work involving net present worth analyses, and I'm really struggling with calculations that involve interest and inflation, such as the question below. I feel that if anyone ...
0
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1answer
83 views

Interpreting an integral/ probability

Think of two iid random variables $x$ and $y$ with density $f$ and CDF $F$ and a constant $c$. What could the qualitative meaning of the following expression be? ...
0
votes
1answer
1k views

Can someone explain what plim is?

In my Introductory Econometrics class we discussed a concept of "plim" or "probability limit. I'm not sure what this means though and my professor doesn't explain it well at all. Can someone tell me ...
1
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1answer
1k views

Properties of first degree homogeneous functions

This is a math question, even if it may seem an economics one. I'll try to explain all the economics in this question. I've got the following production function, where $Y$ is the product, $L$ is the ...
1
vote
2answers
284 views

Absolute value and sign of an elasticity

In my microeconomics book, I read that when we have $1+\dfrac{1}{\eta}$ where $\eta$ is an elasticity coefficient, we can write $1-\dfrac{ 1}{|\eta|}$ "to avoid ambiguities stemming from the negative ...
1
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1answer
29 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 ...
0
votes
1answer
47 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 ...
0
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1answer
135 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 ...
0
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1answer
497 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 ...
1
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1answer
55 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
votes
1answer
131 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 ...
0
votes
1answer
62 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 ...
2
votes
1answer
92 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 ...
1
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1answer
59 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
votes
1answer
67 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
votes
1answer
137 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 ...
0
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0answers
109 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
98 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
334 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
104 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 ...
4
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2answers
263 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
146 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 ...