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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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 ...
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0answers
40 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 ...
-3
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0answers
48 views

Econometrics, OLS, economics, probability [on hold]

You have obtained a sub-sample of $1744$ individuals from the Current Population Survey (CPS) and are interested in the relationship between weekly earnings and age. The regression yielded the ...
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2answers
33 views

Simple differentiation / economics marginal cost question

This seems like a very simple question, so I'm sure I'm doing something stupid here, but I'm not quite getting my head around the following question: I have a total cost function: $C = 5x^2 +15x + ...
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0answers
14 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 ...
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3answers
51 views

Capitalization of interest

I've got quiet a strange problem but a simple one I guess. So I have a starting sum of 10 and I would like to know how many years need to pass to achieve 30000 with 32% interest applied every 2 years. ...
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1answer
40 views

Calculating the chance of something happening over and over again

I'm trying to calculate the probability, and potential cost on society, of people returning to homelessness after going through the system one, two, or several more times. Let's say that someone who ...
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1answer
54 views

Economic Applications of Game Theory

I'm currently looking at this course in economic game theory. However, when attempting this example: In this question you are asked to price a simplified version of mortgage-backed securities. ...
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1answer
21 views

Break Even Point

Suppose that x thousand units of a product will be sold when the price is p(x) = 50 - 1.25x dollars per unit and the cost of producing x thousand units is C(x) = 20x + 100 thousand dollars. a) What ...
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0answers
43 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 ...
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1answer
31 views

proof related to production functions [closed]

Prove that when the production function f(x,y) is homogeneous of degree 1, it may be written as the sum $f(x,y) = x\cdot MPx+y\cdot MP_y$, where MPx and MPy are the marginal products of x and y, ...
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1answer
23 views

Variance of OLS estimator

Iam trying to understand how the variance of the OLS estimator is calculated. here is what i have: $E[\hat{ \beta} \mid X] = \beta$ and $V(\hat{\beta} \mid X) = \sigma^2(X^TX)^{-1}$ where ...
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0answers
33 views

Cost functions in economics

A firm has two plants. One plant produces out- put according to the production function $x_1^ax_2^{1-a}$ . The other plant has a production function $x_1^bx_2^{1-b}$ . What is the cost function for ...
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1answer
47 views

Minimizing the cost of production by choosing between two options with different resource demands

Suppose that the firm has two possible activities to produce output. Activity $A$ uses $a_1$ units of good $1$ and $a_2$ units of good $2$ to produce $1$ unit of output. Activity $B$ uses $b_1$ units ...
2
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1answer
45 views

Need help explaining how the elasticity was derived [closed]

We had a lecture on calculating elasticity in microeconomics and I need help understanding how the answer was derived. I didn't quite get how we came up with the answer. My classmate said to just ...
2
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1answer
41 views

How to find the short run and long run cost functions, given the production function?

The production function of car is given by $f(x_1,x_2,x_3) = \sqrt{x_1}+\sqrt{x_2}+\sqrt{x_3}$ (assume competitive input and output markets). Find the short run cost function (let input 3 ...
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2answers
36 views

Problem understanding an implicit differentiation

Here is a general budget constraint: $p{_1}x{_1}+p_{2}x_{2}=M\Leftrightarrow \frac{p_1}{p_2}x_1+x_2=\frac{M}{p_2}\Leftrightarrow {p_{1}}'x_1+x_2=M{}'$. The main idea is that since prices are given, ...
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1answer
41 views

In Courty and Li (2000) “Sequential Screening”, what justifies the last equation in Lemma 3.2?

Regarding the article "Sequential Screening," in Review of Economic Studies, 2000 by Courty and Li: In Lemma 3.2, the last equality states that ...
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0answers
12 views

variance-covariance matrix of 2sls in homoskedasticity and heteroskedasticity

How the variance-covariance matrix of two stage least square estimate in homoskedasticity or heteroskedasticity? The answer in homoskedasticity is $\sigma^2(E[xz'](E[zz'])^{-1}E[zx'])^{-1}$ and in ...
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2answers
24 views

Rounding a real number w.r.t. a given amount of steps

Let $x$ be a real number, $x \in [0,1]$. Suppose a system can only provide a noisy signal about the value of $x$, given the granularity allowed by the system, $N \in \mathbb{N}^*$. I'm looking for an ...
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1answer
25 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
51 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 ...
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0answers
41 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 ...
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1answer
22 views

Micro Econ production functions [on hold]

Find out the MP_L, MP_K and MRTS_(L,K) for the following production functions 1. Y= A L^(1/2)k^(1/2) 2. Y = A L^(1/3) K^(2/3) 3. Y= A(L+K) 4. Y = ALK
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1answer
13 views

help finding marginal utility [duplicate]

There are two goods in the economy: X1 , X2 utility function given by $U(X_1,X_2) =X_1^{1/4}X_2^{3/4}$ Price of good 1 $(P_1) = \$2$ Price of good 2 $(P_2) = \$3$ Income $(m) = \$120$ Find out ...
13
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2answers
489 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
38 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 ...
2
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4answers
145 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
50 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
107 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
53 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
30 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
28 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
37 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
51 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
35 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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0answers
64 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 ...
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1answer
51 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
27 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?
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1answer
29 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
76 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
37 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 ...
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1answer
26 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} ...
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2answers
69 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 ...
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1answer
43 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
56 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
27 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
24 views

Calculate elasticity of demand [closed]

Calculate elasticity of demand if p=100-5q at the full levels of P&Q 1)P=90, Q=2 2)P=50, Q=10 3)P=5, Q=19 Thanks in advance.