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
41 views

Microeconomics : Total revenue for unit elasticity

I recently read in my microeconomics book that when elasticity = 1, total revenue remains the same. However, I am unable to follow this. I have two questions on this concept: Question#1- ...
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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 ...
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 ...
15
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2answers
555 views

Pure mathematics in our society

Is there some book or essay which deals with the sociological and economical justification of doing and funding pure mathematics? I'm looking for a modern version of Hardy's A Mathematician's Apology, ...
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2answers
42 views

income distribution from N, min,max and mediansalary, and total compensation

My goal is to obtain a reasonable approximation of the Gini index of a company (UBS). I need to obtain an estimate of the salaries distribution from publicly available data: Nuber of employees=60205 ...
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5answers
212 views

A mathematical approach to economics

Are there books or papers where economics is formalized and studied very rigorously? I am very interested in this topic. I would preferably like free online books and/or papers, but that is not ...
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1answer
53 views

Profit Model from Ellison Glaeser 1997

Can someone help me understand the following profit maximization problem (from Ellison Glaeser 1997)? Manufacturing plants choose where to locate each of $N$ plants in one of $M$ locations. The ...
4
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1answer
96 views

Expected revenue obtained by the Vickery auction with reserve price $1/2$

I would like to prove that the expected revenue of the Vickery auction with reserve price $1/2$ is $5/12$ when there are one item and two bidders the distribution of valuations are uniformly between ...
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0answers
113 views

preference relation.

In the exercise below I need to check whether the relation below is a preference relation ( need to be transitive (if $x>y$ and $y>z$ then $x>z$) and connected ). But I cannot find an ...
2
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1answer
54 views

Compactness and existence of Pareto-efficient cake partitions

I am trying to understand a fundamental statement in the theory of cake-cutting. BACKGROUND: There is a certain "cake" $C$ (a subset of $R^n$). The cake is divided among two agents, 0 and 1. Each ...
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1answer
56 views

Counterexample in axioms of expected utility theory

This is an exercise problem. Suppose $X_1=200$ with probability $1/3$, $0$ with probability $2/3$. $X_2=200$ with probability $p$, $0$ with probability $1-p$. $X_3=200$ with probability $1-p$, ...
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1answer
40 views

Expected utility representation

I am stuck on some question on utility theory. The question is as follow: Consider $A=[0,+\infty)$, and $Q=${F-cumulative distribution function on $A: \int^{+\infty}_0 x dF(x)<\infty$}, the set of ...
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2answers
48 views

Autocorrelation and var-cov matrix

$$Y_t=\beta_1+\beta_2 X_{t2}+\dots +\beta_k X_{tk}+\epsilon_t \qquad (t=1,\dots,T)$$ $$\epsilon_t=\rho \epsilon_{t-1}+v_t, \qquad v_t \sim \mathrm{i.i.d.}(0,\sigma^2_v)$$ GLS estimation under AR(1) ...
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0answers
52 views

Finding criteria for a household financial budget falsification

I’m working on a financial problem about budget of households. Households in a state fill a form about their net budget in every year and our insurance company investigate their financial status and ...
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2answers
40 views

$\operatorname{Var}(\hat{\beta_1})=\frac{\sigma^2}{\sum(X_i-\bar{X})^2}$ : how to derive this?

$\hat{\beta_1}$ is an OLS estimator for parameter $\beta_1$: $Y_i=\beta_0+\beta_1 X_i+\epsilon_i$, So $\hat{\beta_1}=\frac{\sum(X_i-\bar{X})(Y_i-\bar{Y})}{\sum(X_i-\bar{X})^2}$ and ...
0
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1answer
81 views

Help to solve this problem, the result doesn't seem right :/ silly mistake somewhere probably

Suppose that Coke and Pepsi are the only firms producing cola. Their products are not identical, but are very close substitutes. Let $P_c$ denote the price of Coke and $P_p$ the price of Pepsi. Demand ...
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1answer
40 views

So I have the following question, dont have much info on class notes and not sure how to tackle it, any suggestions, any help?

A seller has a single item for sale (which she values at zero). There are two potential buyers. The seller decides to use the following auction format to sell the object: each bidder submits a sealed ...
0
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1answer
58 views

Conditions for a positve vector in null space

Precursor to problem: Preparing for an exam in General Equilibrium Theory. One of the important theorems is the No Arbitrage Theorem which states that for an economy with $S$ states of the world and ...
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0answers
29 views

Silly fraction question

I've got $$ MPK'=\frac{1-d}{1+r+x} $$ But I need it in the form $$ MPK'=d+r+x $$ How do I bring those up top?
1
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1answer
35 views

Horizontal product differentiation problem

It's a version of the Hotelling model (product differentiation). One firm is located at the beginning of a line between 0 to 3, one at the end of the line (so one at 0, one at 3). There are $b/2$ ...
4
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1answer
185 views

Increasing marginal product implies increasing returns to scale?

Setup Let $f(x,y)$ be twice differentiable in both $x$ and $y$. Assume $\partial f/\partial x>0,\partial f/\partial y>0$ for $x,y>0$. $f$ is said to have increasing marginal product of ...
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1answer
43 views

Utility optimization question

Having trouble with how to put this together. I have an answer key, but the individual steps I am struggling with. Two period economy with a representative consumer that maximizes the utility ...
0
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1answer
31 views

Economics question. Rehashing the basics of dealing with exponents

Struggling to put two equations together effectively again. I have my income equation: $$ y=zk^\alpha $$ And I'm trying to plug it into my marginal product of capital $$ MPK=\alpha z k^{\alpha-1} ...
1
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2answers
98 views

Third and average price auction

Third price auction: the winner is the highst bidder but this time instead of paying the second highst bid, he would pay the third highst bid. -assume there are at least 3 bidders. - Average price ...
1
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1answer
101 views

Conditional and unconditional variance in ARMA processes

How can I compute the conditional and unconditional variance of $x_t$ given its past if $\{x_t\}$ is an ARMA$(p,q)$ process. I'm literally struggling over that. Cheers
1
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1answer
123 views

Show that the least squares estimator of the slope is an unbiased estimator of the `true' slope in the model.

Under the assumptions of the classical simple linear regression model, show that the least squares estimator of the slope is an unbiased estimator of the `true' slope in the model. Anyone have any ...
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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, ...
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1answer
82 views

Game Theory in relation to economics and sociology [closed]

I know some algebra and calculus, and have been reading about Linear Programming/Game Theory. How are the models in this field, even the infinite calculus models, usable in macro economics. Even ...
0
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1answer
126 views

Von Neumann–Morgenstern independence axiom vs. Savage independence theorm

Von Neumann–Morgenstern independence axiom: Savage independence theorem: What is the difference between the two? I'm think Von Neumann is talking about the prizes (outcomes) and Savage is talking ...
0
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1answer
21 views

Deriving Stochastic Euler Equation

If a consumer has utility function \begin{equation*} u(c_t) = ac_t - \cfrac{b}{2}c_t^2 \end{equation*} and present value budget constraint \begin{equation*} \sum_{j=0}^\infty E_t[\beta^jc_{t+j}] = ...
0
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1answer
101 views

OLS slope estimate of AR(1) with autocorrelation

I've stumbled upon this question in my econometric textbook and can't work out the right answer. The question: Consider $$Y_t = B_2Y_{t-1} + u_t\\ \\ u_t = pu_{t-1} + \epsilon_t\\ $$ where $ ...
0
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1answer
29 views

Solving optimisation problem with langrangian method

I have a a question regarding a constrained optimisation problem where there are three constraints. I was wondering if should include lagrangian multipliers for each of the constraints or whether the ...
0
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2answers
19 views

Variable with an exponent variable

I'm actually dealing with an economics problem, but it seems like the math is always what messes me up. Ignoring what the variables mean, I'm trying to understand how to get from step 1 to step 2. $$ ...
0
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1answer
36 views

Price and price elasticity problem in Economics

I cannot figure out this problem, if anyone can just point me in the right direction that would be great. The price is $\$20$ and the price elasticity changes from $-2$ to $-3.$ If $\$20$ was the ...
0
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1answer
5k views

Microeconomics: Calculating Tax Revenue and Tax incidence

Australian Government has imposed a tax on Beer. Assume that the tax on Beer is $20 per unit (a unit is a carton of drinks) Assume the demand and supply functions for cartons of Beers per week are: ...
2
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1answer
146 views

Euler Equation and Marginal Rate of Substitution

I was wondering if someone could help me clarify a result from my lecture notes. I have put them as a picture. It concerns the result on the last slide (the other three slides are included as well ...
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1answer
29 views

Question about plotting indifference curves

So I am doing a last year paper on microeconomics I m asked to find pareto efficiencies , cores and so on within the edgeworth box. So what I wanna know is that whe they give me in this exercise the ...
0
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1answer
73 views

Average cost function and marginal cost function proof

I was wondering if someone could help me prove the following. Let $A(Q)$ be an average cost function and $M(Q)$ the corresponding marginal cost function. Show that if $M(Q)>A(Q)>0$ then $A(Q)$ ...
3
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3answers
195 views

The Historical Importance of Keynes' A Treatise on Probability

A visiting speaker in Economics recently happened to mention that John Maynard Keynes' A Treatise on Probability revolutionized probability theory. I have not heard any such claim before and it struck ...
4
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3answers
251 views

How practically relevant is game theory?

I usually don't care too much about the practical relevance of nice mathematics :-) But this time, as I am looking to find some areas where I can apply maths and possibly collaborate with ...
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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 ...
2
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1answer
52 views

Arrow's Impossibility Theorem Using Boolean Algebra

I am currently working on a research project which involves using Boolean matrices for the proof of Arrow's Impossibility Theorem and various other lemmas and results related to quasi ordered sets. In ...
0
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1answer
67 views

Suppose that the sequence of prices{$p_k$} converges to a limiting price $\bar p$. What must $\bar p$ be?

We let $Q_k$ denote the supply of commodity, $D_k$ the demand for the commodity, and $p_k$ the price at $k$-th time. The demand depends on the current price, $D_k = a + b p_k$ and the supply depends ...
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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 ...
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2answers
31 views

what are some typical systems of equations generating from practical problems?

I want to know some typical forms of system of equations generating from practical problems in engineering/economics/physics,etc. Some examples or research articles would be good. Specifically, I am ...
1
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1answer
73 views

We are interested in price of a commodity, traded at regular intervals. Why it is reasonable to take $a$, $c$, and $d > 0$ and $b < 0$?

We are interested in the price of a commodity which is traded at regular intervals. We let $Q_k$ denote the supply of commodity, $D_k$ the demand for the commodity, and $p_k$ the price at $k$-th time. ...
1
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1answer
62 views

How to differentiate this expression with respect to t

I don't understand how to differentiate $f(tx_1,\cdots, tx_n)$ with respect to t.
2
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3answers
224 views

Precise definition of a “game of incomplete information” (Game Theory)

Question: In game theory, what is the precise definition of a "game of incomplete information"? What I've found so far: In the standard first year graduate economics textbook on microeconomics ...
0
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1answer
277 views

Sequence of learning mathematics from basic algebra to calculus.

What would be a step by step sequence of learning mathematics from basic algebra to basic calculus? I pose this question because I am in the process of self-learning mathematics as a preparation for a ...
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1answer
71 views

Equilibrium level of income question

Question: In the 2012 tax year, Consumption= (85% of income after tax) + (Autonomous Consumption) Taxation rate= 20% Autonomous consumption= 175 million Investment= 485 million Government ...