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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12
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0answers
322 views

Equilibrium existence proof

Problem: Let $J$ be an integer and let $I$ be an integer multiple of $J$. Let ${\cal I}= \lbrace 1,2,\ldots, I\rbrace$ and ${\cal J}= \lbrace 1,2,\ldots, J\rbrace$. The set $X_{I,J}$ of all ...
6
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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 ...
5
votes
0answers
250 views

Open Problem in Fixed Point Theory [Prize]

This open problem appeared on the bulletins of Evans Hall at Berkeley this week. I hope this doesn't violate StackExchange policy (the solution carries a $500 prize), but I thought why not re-post ...
4
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0answers
82 views

How to solve a non-homogeneous second-order linear difference equation with both a forward and a backward difference?

Quite a long title for this: I'm looking for the general solution of the following difference equation: $$ax_{t+1} -bx_t + x_{t-1} = c + u_t$$ where $a,b,c$ are real constants and $u_t$ is a bounded ...
3
votes
0answers
129 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 ...
3
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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 ...
3
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0answers
121 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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0answers
29 views

What are the most recent devopments with applying fractals to economics?

I was researching fractals for my senior mathematics presentation and discovered that one of the most recent pioneers in that section of the field was able to apply fractal mathematics to the field of ...
2
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0answers
127 views

Engineering Economics Cash Flow Diagram

I have the following question and solution below. What I don't understand is why is the 100,000 seen as savings/revenue when clearly it is coming out of pocket? Additionally, the monthly loan payment ...
2
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0answers
182 views

What is the (expected) outcome of this hybrid auction?

A certain hybrid auction can be accurately modelled as follows. There are $n$ risk-neutral, rational participants $i=1,2,\ldots,n$, and a guy called Zerro: $i=0$. Each, except Zerro, has a private ...
2
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0answers
91 views

Suggestions for projects in mathematics of finance

I am looking for computational projects related to mathematics of finance suitable for a senior level independent study for a student who has seen the green light, (or the light of the green!). I had ...
2
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0answers
83 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 ...
2
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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, $\Phi(d_1-d_2)$ ...
1
vote
0answers
25 views

A sufficient condition for a good to be normal

Context: there are $2$ goods with prices $P_1$ and $P_2$ and the decision maker has the utility function $U(C_1,C_2)$. Denote $U_j=\frac{\partial U(C_1,C_2)}{\partial C_j}$ for $j\in\{1,2\}$. A good ...
1
vote
0answers
59 views

Follow-up on solution to Markov process equation

I asked a question here about solving a system related to an absorbing Markov chain. I now have a variation where there are $m$ types (of student, job seeker, etc) each of which applies to ...
1
vote
0answers
59 views

Application of a general “Weierstrass theorem”

http://books.google.at/books?id=9OSrV73a40gC&pg=PA45&lpg=PA45 gives a general Weierstrass theorem. Are there notable applications of this theorem, say in the calculus of variations? (I could ...
1
vote
0answers
29 views

Properties of this set of functionals (mixed pairings)

(from the 4th page of http://www.math.toronto.edu/mccann/papers/econ.pdf) Let $X$ be a compact Hausdorff space, and let $\omega$ be a Borel probability measure on $X$. A Borel probability measure, ...
1
vote
0answers
22 views

Optimize profit given complete market information

Assume there are $N$ market participants (on the order of several hundred), and $M$ items (several thousand) being bought and sold on a market. For each participant/item pair, you know how many units ...
1
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0answers
32 views

Introductory book about economic models with deterministic chaos

I'm looking for introductory textbook about economic models (micro/macro/finance) which incorporate deterministic chaos. Models could be with or without random noise. By introductory I meant master ...
1
vote
0answers
67 views

Using data points and a best-fit to find a function for quantity with respect to price

So I'm taking an entrepreneurship class, and we're doing a simulation where we run a donut shop. My math is pretty strong (integral and differential calculus level), so I'm trying to use my math ...
1
vote
0answers
94 views

Solving the General Equilibrium with $4$ equations and $4$ unknowns

I have to solve four equations to solve the equlilibrium prices for the two countries: $\frac{2p_1}{w_1} + \frac{p_1}{w_2}= \frac{48w_1^2 + 4p_1^2+p_2^2}{8p_1w_1}+ ...
1
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0answers
1k views

Profit Maximization Question of a Leontief (Perfect Complements) Production Function?

This is a question from my intermediate micro economics text book. Any help is very appreciated! Given Info: Company ST (a company which offers custom travel-planning services) is a ...
1
vote
0answers
64 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: ...
1
vote
0answers
54 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
0answers
91 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
105 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), ...
1
vote
0answers
49 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 $M_{ij} = \frac{\partial{Z_i}}{\partial {p_j}}$, ...
1
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0answers
204 views

Econometrics Simultaneous equation Indirect Least Squares and Two Stage Least Squares

I still can't figure out this problem. PLEASE HELP! (1) $F_t = a_1 + a_2.C_t + a_3.P_t + e_t$ (2) $P_t = b_1 + b_2.F_t + b_3.S_t + b_4.I_t + u_t$
1
vote
0answers
63 views

Differentiation help

I recently got some lecture slides, but needed a little help understanding the maths behind them. (equations) (Working and Answer) Basically, I don't understand how to get from step (4) to (5). ...
1
vote
0answers
90 views

Game theory question- information quality maximisation, opinions of the question

I am developing a game theory question to help in deconstructing situations where information quality is comprimised and requires valuation against a set of criteria. I would be interested to know any ...
1
vote
0answers
24 views

Is there a trade model which takes in account credulity?

I have to admit I'm not to familiar with mathematical economics but, as a student in mathematics, I was trying to play a bit with a toy trade model I'm try to build over a finite population. My ...
1
vote
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, ...
1
vote
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, ...
1
vote
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 ...
1
vote
0answers
407 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. ...
0
votes
0answers
25 views

Using Mean vs Median for Rapidly Changing Data

I am writing a report on global GDP per capita trends. As many of you know, were large shifts in the growth rates of these figures before and after the Great Recession. There has been some analysis on ...
0
votes
0answers
34 views

How to compute implicit rental rate?

I come across this question in my economics textbook, however I have no idea how to compute the implicit rental rate. Marc bought a new car last year for \$10,000. He can now sell the car for ...
0
votes
0answers
29 views

Help with optimization and second-order conditions on area ):

If I wanted to enclose an area to have a total of 3000 square feet. I have two types of walls. Stone walls which cost 45 per foot. Stone walls must cover three walls. Wood walls cost 20 per foot. Wood ...
0
votes
0answers
22 views

growing number of sample

The problem I have is as following, which I would like a solution to I am a tomato seller Everyday I sell tomatoes. I also have a demand forecast for tomatoes required everyday countrywide. I§m ...
0
votes
0answers
40 views

Is this derivative of $\frac{\partial x}{\partial P}$ correct?

By IFT, let $x^* + \Phi \left (\frac{f(x)+\check{G}}{a(\hat{G}+f(x))} \right ) - 1 = 0 \equiv F$. $P=f(x)$ is a convex function, where $f'<0$, and $f''>0$. I want to find $\frac{\partial ...
0
votes
0answers
16 views

Aggregated demand function for several similar offers?

I want to generate a realistic demand function for a service, depending on the price and properties of offers. The service is passenger travel, for whatever purpose. There are several companies that ...
0
votes
0answers
40 views

A linear algebra textbook that is advanced enough as a prerequisite to read time series and econometric textbook?

A linear algebra textbook that is advanced and comprehensive enough as a prerequisite to read time series by Hamiliton and econometric by Hayashi? If possible, please also answer on which statistics ...
0
votes
0answers
18 views

Reasoning for the Shape of MRTS line

I was looking to understand better the shape of the MRTS curve (Marginal rate of technical substitutes for A production function with 2 inputs). So I know that for 2 inputs in production function they ...
0
votes
0answers
53 views

Convergence of probability

So I am getting ready for my first econometrics exam, and we have a lot of these plim (probability limits). Looking at the definition, I have that as n goes to infinity, ...
0
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0answers
33 views

The t-statistics

can someone please explain this further, or is there an equation. I know the answer is (c) The t-statistic is calculated by dividing a) the OLS estimator by its standard error. b) the slope by the ...
0
votes
0answers
37 views

Finding the competitive equilibrium in an economy with two consumers and two commodities

I am unable to solve the following problem in general equilibrium. Consider an economy with two consumers and two commodities X and Y. $X_i$ and $Y_i$ are the amounts of commodities present with ...
0
votes
0answers
20 views

Profit Maximization without an explicit functional form for f(x1, x2) - Need to infer the signs of derivatives

Consider the following 2 input, 1 output profit maximization problem: $$ \max_{y,x1,x2} \{py-w_1x_1-w_2x_2 : y=f(x_1,x_2)\} $$ where f is the producers production function, w_i>0 is the price of ...
0
votes
0answers
30 views

Project Management - PERT completion time question

The following represents a project with known activity times. All times are in weeks. Activity--Predecessor--Time A ……………………………..….4 B………………………………....3 C………………….A..…………..2 D………………….B…………...7 ...
0
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0answers
19 views

How to characterize $F(x \mid Y = y)$ satisfies $\exists ! G(\cdot)( G(x) = \int F( x \mid Y = y) dG(y))$?

$F(x \mid Y = y)$ is the conditional distibution function $P(X \leq x \mid Y =y)$. $G(x)$,$G(y)$ represent $P(X \leq x)$ and $P(Y \leq y)$. Is there a charaterization of $F(x \mid Y = y)$ such that ...
0
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0answers
45 views

How they're doing this calculation?

Consider this paper by Laura Alfaro, Sebnem Kalemli-Ozcan, and Vadym Volosovych: http://econ.sciences-po.fr/sites/default/files/file/pmartin/secondyear/restat.pdf In page 355, (actually page 9 in ...