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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7 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 ...
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0answers
25 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 ...
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1answer
23 views

Applications of information theory in economics?

What are some direct applications of information theory in economics theory and/or finance? Any relevant articles, surveys, or book references are appreciated (especially if they are targeted to ...
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1answer
57 views

Marriage Market Proof (Alternative Proof of Rural Hospitals Theorem)

How do I get (a) + (b) + (c) $\implies$ (d) $\implies$ (e)? (a) Show that for each $m \in M$, if $\mu(m) = \emptyset$ for some stable matching $\mu$, then for the woman-optimal matching, $\mu_W$, ...
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1answer
53 views

Spotting mistake: unnecessary given condition

I have solved the following problem without using a given premise. Could someone please spot whether I have done something wrong? Suppose we have a relation $\geq$ that is transitive, but not ...
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1answer
21 views

Is there a mistake with this national income model Mik. Wisniewski Intro to Math Methods in Econ pg. 61

I can't figure out the steps to this equation for the national income model. It seems simple, but I don't see why in step 4 I don't get Y-bY+tY I thought it was a mistake in the book at first, but ...
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4answers
35 views

Can someone walk me through how this expression simplifies to y/x?

I am just wondering how this equation comes to be: it is from an economics problem involving marginal utilities. I have my two variables, $x$ and $y$. Intuitively, how does $$\frac{0.5\times ...
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0answers
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How to do an optimization using asymmetrical loss functions (LINEX) for time series. [closed]

ong time Lurker, first time asking. For a research paper, i'm required to optimize some parameters of a certain function using an asymmetrical loss function, specifically LINEX and compare it to the ...
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1answer
21 views

Confused by informal math: total differentiation

I'm reading these notes that say: total differentiation gives $$ P=a_LW+a_KR\implies dP=a_LdW+a_KdR+[Wd(a_L)+Rd(a_K)]\tag{i}. $$ Please let me explain the notation: we can think of $R,W$ and $P$ as ...
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1answer
34 views

Help with this function please.$ C=16x^2+6400$ [closed]

Can anyone help me find the $(x, y)$ coordinates of the average cost function when the slope of the tangent line is horizontal.
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0answers
8 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 ...
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2answers
22 views

How to analyze convergence of non-linear difference equation (recurrrence relations)

I've a couple of functions, such as: $Y(t+1)=2-\ln(Y(t))$ $Y(t+1)=(Y(t))^{-2}$ $Y(t+2)=e^{-Y(t)}$ and I need to analyze stability and convergence. No problem with stability, but I can't figure out ...
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1answer
18 views

Functions of 2 variables and applications to economics

Given the production function $Q := \sqrt K + L^2$, determine the optimal level of production and the relative demand of the two inputs capital $K$ and work $L$. The cost of a unit of capital ...
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0answers
28 views

quasi rationality, interesting axiom of revealed preferences

So imagine there is a notion of rationality that captures the idea of "thresholds in preference." For example, let $\mathbb{Z}$ be the integers: $\mathbb{Z} = \{\dots, -10, -9, \dots, 0, 1, 2, ...
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1answer
34 views

A simple dual problem in economics: profit v.s. cost

The setup is simple but a bit lengthy. Please bear with me. Suppose that I have a production function $F(K,L)$ that is: constant return to scale; increasing in each factor: $F_K>0$, $F_L>0$ ...
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0answers
34 views

Optimization across markets - How can I solve?

I am unsure how to solve problems involving several markets and optimizing the price across all my markets. Note: I am looking to be pointed in a specific direction of study, not a solution to the ...
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2answers
151 views

If you have two envelopes, and …

Suppose you're given two envelopes. Both envelopes have money in them, and you're told that one envelope has twice as much money as the other. Suppose you pick one of the envelopes. Should you switch ...
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1answer
35 views

Does maximizing an increasing function of two variables in more favorable conditions always increase both inputs?

Consider the problem of maximizing $\sqrt{x}y$ such that $x+y=10$. By basic calculus we can show that the maximum occurs at $x=10/3$, $y=20/3$. If we loosen the constraint to $x+y=12$ then the maximum ...
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1answer
17 views

Verifying a production set is a convex cone

This comes from a paper that I am reading: For $i=1,2$, suppose that $F_i(\cdot,\cdot)$ satisfies the assumption: $F_i(K_i,L_i)$ is defined for all $K_i\geq 0$, $L_i\geq 0$. $F_i(0,0)=0$. ...
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1answer
32 views

Statistica Significane of the Slope Coefficient

Can someone please help me with this? Consider that you are examining the relationship between the height of children and their parents. You decide to collect data from 110 college students, and ...
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0answers
45 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, ...
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0answers
27 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 ...
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1answer
52 views

Looking for resources for understanding derivation of demand from utility

I am struggling with my homework and would very much appreciate a rundown of the math or pointers to where I can find help otherwise. Quoting from the assigment: There are $n$ sectors in the ...
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1answer
38 views

Econometrics Question

Can someone please help explain this (or provide a website link). I know the answer is (a). To decide whether or not the slope coefficient is large or small, a) you should analyze the economic ...
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1answer
67 views

Matrix question: implication of $\frac{1}{n}X'X\to M$

Suppose $K$ is fixed and consider a matrix $X$ that is $n\times K$ and has full column rank. Assume that we know $$ \frac{1}{n}X'X\to M\text{ as } n\to\infty.\tag{i} $$ That is, as $n$ becomes larger, ...
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1answer
36 views

Show that $\frac{\mathrm{d^{2}}B }{\mathrm{d} A^{2}}> 0 $ if $U''<0$.

Given, $A = W_0 - L_0 + I - qI$, $B = W_0 - qI$, and $EU = p U(A) + (1-p) U(B) = k$, where $k$ is a constant. $\frac{\mathrm{d} B}{\mathrm{d} A}\bigg|_{}^{EU=k} = \frac{\frac{\partial EU }{\partial ...
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1answer
21 views

Inverse of a multivariable function following book derivation

I am trying to follow the text in the appendix, however I get stuck when I come to the part where I need to solve for q1. As Far As I can see I need to find the inverse, which I have seen examples off ...
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1answer
28 views

Scilab : simulating model of general equilibrium equations

Hi i'm new to scilab !!! I have a static general equilibrium model with 8 endogenous variable and 8 independent equations.Can anyone guide me how to do simulation of such model in scilab ? I want to ...
2
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1answer
74 views

Good economics textbooks.

I would like a suggestion for the most mathematically fun/interesting mathematical economics textbook, preferably using abstract math. I want to prove theorems to complete my economics minor. I have ...
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1answer
38 views

Lagranges multiplier to minimize function of two variables with two constraints

I have a Cobb Douglas type production function with $K$ and $L$ as inputs; $\alpha$ and $1-\alpha$ as output elasticities and $C$ as efficiency parameter. Now I have to minimize cost $=wL+rK$ w.r.t ...
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1answer
138 views

Impatience and interest rate

I'm having difficulties solving the following problem in economics. I come from a mathematical background, and it's hard for me to get some of the terms: Consider a two-period economy with a ...
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1answer
191 views

How to derive demand function from a utility function without any knowledge of Lagrange Multipliers?

How do I derive the demand function for a utility function of, say, $U(x,y)=\sqrt{11x+11y}$ for goods X and Y in terms of $P_x$, $P_y$, and income $I$, with basic mathematics (basic calculus, but no ...
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1answer
57 views

Utility function, plotting indifference curves

I know how to plot indifference curves; simply take the utility function and plot some level curves in $2D$. But how to plot a specific indifference curve, so all bundles on it are indifferent to a ...
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2answers
61 views

Cost per item. Diminishing marginal discount, if you will. (Bigger discount for first few items) Optimal number of units to buy?

The graph above shows price per unit. Say they are cupcakes. When you buy a higher quantity, you get a lower price per unit. Say it levels off like this graph. Obviously, buying 2 nets a nice ...
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0answers
23 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 ...
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1answer
27 views

Utility function and preferences?

This might be more of an economical question, but perhaps some of you might've come across it before as math is involved; A person P prefers bundle (x1,x2) over (y1,y2) if (x1*x2) > (y1*y2). What is ...
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1answer
31 views

Utility Max Problem

I have a utility function $U(x,y)=\frac{xy}{x+y}$ and a budget of $200=2x+2y, P_x=P_y=2$. But for the first 50 units of product 1 sell for 2 dollars but for "$x>50$" the price of product 1 ...
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0answers
17 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 ...
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1answer
60 views
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0answers
22 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 ...
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0answers
56 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 ...
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2answers
99 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
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 ...
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3answers
59 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
46 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
68 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
27 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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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 ...
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1answer
32 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
39 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 ...