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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Implications of axioms of expected utility theory

Axioms for Expected Utility: Let $\succ $ be a binary relation on $X$. A1. $\succ $ is asymmetric and negatively transitive. A2. Independence of Irrelevant Alternatives: If $p,q,r \in X$ and if ...
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58 views

differentiating a cost function using chain rule

How to differentiate the function (cost function) $$C(x)=V\left(\frac{px-W}{q}\right)$$ where $W,p,q$ are constants,and $W$ representing the consumer's budget or wealth. $V$ is a function of $x$. ...
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239 views

Consumer optimization problem

A customer has to decide how many of products $x$ and $y$ to buy. The price of $x$ is $2x^{1/2}$ and the price of $y$ is $4y^{1/2}$. The cost of $x$ is 10 dollars and the cost of $y$ is 5 dollars. ...
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56 views

Math / Accounting problem

I have been stuck for over an hour with the following problem. In my textbook the following is written: "Suppose, for example, that Polany Manufacturing Company enters into a long-term lease July 1 ...
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65 views

Measuring how “connected” nodes are in a network

I am an undergraduate studying economics and mathematics. I've never studied graph theory formally (only briefly in my spare time) and as such I don't have formal terms for what I'm clumsily trying to ...
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86 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}+ ...
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100 views

Maximize $ax + by + c$

Working on a problem of comparative advantage of the economist David Ricardo, I've gone into solving a more general case of that study in which I stumbled over this question : how do we maximize the ...
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270 views

why is this economics parabola sideways? switch x and y axis

Why is this "parabola" sideways? Normally, f(x)=y, would be that x is graphed horizontally, and you would write that "wage rate is a function of hours worked", which is how I would normally think ...
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42 views

Need recommendations for a function with certain properties

Not sure if this might be a strange way of posing a question, but anyway: I need a function $f(v,p,a)$ with the following properties: it is defined for $v \in [-\infty,\infty]$ it is defined for $p ...
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44 views

Confusion regarding an alleged hyperbola

While studying a chapter called price elasticity of demand in my economics course, I have been presented with something called a unit elasticity curve (some sort of a hyperbola), which has supposed ...
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61 views

A doubt about Evans and Jovanovic (1989) economic model for entrepreneurs with credit constraints

In Evans and Jovanovic (1989) you will find a model for entrepreneurs with credit constraints. The part that is important for my question follows. Here it is the production function and the income ...
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58 views

How are relative maximum problems solved?

I found this problem in an economics mathematics book self test and I really do not know how a person goes about solving a problem like this: I think there is differentiation involved but I'm just ...
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21 views

Understanding a component of an equation of finite game repetition

I have the following equation: T = total times the game is repeated t = current period delta = discount rate u_i(a_i^t...) = the state payoff to player i I'm attempting to understand the ...
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65 views

econometric transformation of variables

I would like to ask a question, which has been already asked, however I dind´t fully understand the answer and nobody replied to my edit question..maybe you can give me a arithmetic example for one ...
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41 views

econometric data

I have a quit straight forward question: I have a variable which is coal rents measured in 2009 US Dollar. I would like to set this variable in relation (ratio) to another variable which is PPP ...
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69 views

How are these maximization problems same?

This question is from Nicholson-Snyder's "Microeconomic Theory",page 200.(e-book here.) Compare$$V^*(p_1,\dots,p_n,I_1,\dots,I_m)= \max_{x_1,…,x_n} \left[U(x_1,…,x_n)\text{ such that}\sum_{i\in ...
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90 views

Leontief Models: Characterizing efficient net outputs

Given a Leontief model with $n \times n$ input-output matrix $B$, whose diagonal elements are positive and off-diagonal elements are non-positive. There is a single unit of labor available to this ...
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105 views

How CES function becomes MINIMUM function?

Let the CES utility function be $$U(x,y)=\frac{x^\delta}{\delta}+\frac{y^\delta}{\delta},$$where $\delta\leq1,\delta\neq0.$ For $\delta=-\infty$, the given function is equivalent to ...
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101 views

What is my unit of observation for this time series data set?

My professor gave us a data set to run a regression and I have a data set which lists years from 1959-2007, gross private investments (in billions of dollars), and gross private savings (in billions ...
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102 views

For a price and cost function, at what rate do the weekly sales change per week?

For a price function of $p=4000-25x$ and a cost function of $C=1800x+4500$, if the profit is increasing at a rate of $3000$ per week and the weekly sales are $x=32$ units, at what rate do the weekly ...
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2answers
47 views

Differential equation non linear first order

Can you find the solution of that equation please? I don't know how to solve it. I use it to solve a dynamic system in macroeconomics for my homework. $$\frac{dy}{dt} = y^3 + 1$$
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129 views

Nash Equilibrium in Cournot Duopoly

If you have a demand function Q1= 20 + 3/4 p2 - p1 and Q2= 20 + 3/4 p1 - p2, how does one go about solving for the Nash equilibrium if you know there are no costs? I've tried solving for Q and then ...
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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 ...
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226 views

Question related to the General equilibrium in exchange economies

I need some help in solving this question: Consider the following two-person, two-good economy. Persons $A$ and $B$ each consume two goods xylophones $(x)$ and yams $(y)$. Person $A$ enters the world ...
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155 views

Does risk aversion cause diminishing marginal utility, or vice versa?

Let $A$ be the set of possible states of the world, or possible preferences a person could have. Let $G(A)$ be the set of "gambles" or "lotteries", i.e. the set of probability distributions over $A$. ...
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74 views

distinguish homogenous and homothetic

I am not sure how to distinguish whether a function is homothetic. For example, Q1. $$ U(x,y) = a\log(x) + b\log(y), $$ Q2. $$ U(x,y) = \exp[(x^a+by^a)^3 +r] $$ I can understand that these two ...
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46 views

Math behind Keynesian Expenditure Multiplier

Take a look at this page: http://wiki.ubc.ca/Keynesian_Multiplier Why can you find out the sum of the geometric series just by dividing the mps by 1?
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1answer
96 views

Generalized Mechanism Design, Stanley Reiter diagram and Vickrey Auction

I am trying to learn this new topic, Mechanism Design and stumbled upon the "Stanley Reiter" diagram (see the top-right side on the page). I have also learned that the Second Price Sealed Bid ...
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278 views

Modelling risk when market making

I'm interested in learning about algorithmic trading, particularly in bitcoin. Looking at this chart, I can see that I could simultaneously offer a bid that was slightly higher than the highest ...
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58 views

ordinary least square regression

i have a question and i'm confused with the concepts. Pls aid Consider the estimation of the population mean in the model: $Y_i = \beta + U_i$ for $i = 1,2,3$. Assume that $E(U_1) = E(U_2) = E(U_3) = ...
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120 views

Mistake wikipedia article on St petersburg paradox?

I suspect that there is a mistake in the wikipedia article on the St petersburg paradox, and I would like to see if I am right before modifying the article. In the section "Solving the paradox", the ...
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54 views

How to derive duration of unemployment?

The average monthly flow out of unemployment pool of $7.0$ million people each month is $3.1$ million. Put another way, the proportion of unemployed leaving unemployment equals $\frac{3.1}{7.0}$ or ...
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455 views

questions on information set definition

The definition of "information set" is An information set is a set of decision nodes, all belonging to the same player, over which that player cannot distinguish. ...
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1answer
74 views

Counting in Arrow's theorem

I seem to be really confused with the counting system in Arrow's theorem. Can I have a simple explanation how they determine the outcome? I can't determine the outcome using rules from my notes. It ...
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32 views

When do $Y$ and $r$ increase in the given economy?

This question is from "Mathematics for Economists" by Simon and Blume. IS curve: $[1-c_1(1-t_1)-a_0]Y+(a+c_2)r=c_0-c_1t+I^*+G$LM curve: $mY-hr=M_s-M^*$ The parameters $c_1$,$t_1$ and $a_0$ are ...
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2answers
100 views

Why not n=2 in Arrow's theorem

Why in the statement of Arrow's impossibility theorem we omit the case n=2? I will appreciate it if you can explain it in easy words. I'm by no means an expert in the area (I think it's very much ...
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2answers
143 views

Ideas about an Ordinary Differential Equations research work (University level)

Good afternoon to everyone, I need some ideas about a Ordinary Differential Equations research work. It is for the ODE subject that I am doing at my Mathematics degree in my University. They asked me ...
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1answer
78 views

Use Roy's Theorem to prove that …

I have an advanced microeconomics theory related question: Use Roy's theorem to prove that $s_i(p,y)= -\frac{\partial v(p,y)}{\partial lnp_i}/\frac{\partial v(p,y)}{\partial lny}$. This question has ...
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214 views

Stone-Geary utility function

$$ u(C_{t})=\frac{(C_{t}-\underline{C})^{1-\sigma }-1}{1- \sigma};\sigma > 0 $$ Does anyone know how to solve the utility maximization problem here and how consumption varies depending on ...
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61 views

Density income and Total Income.

Suppose that the density income function is $f(r) = a*exp(r^2)$ with $r \in(0; 10)$ (hundred thousand euros) and $a=exp(10)-1$. Assume that the total number of people in this economy is 1 million. ...
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139 views

Alternatives to Monte-Carlo simulation

Imagine I have a model of economy of a region, which consists of several companies, importers and population. Let's assume that all local companies in question produce food and agricultural ...
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194 views

Functions minimized at the median of their arguments

I am doing research on problems of location of a public facility on a network which lead me to the following question. Is there an interesting way to characterize the class of functions $f : ...
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1answer
87 views

Production function (economy)

A company produces one good using two factors of production factors. If $x$ and $y$ denotes the units of the factors used by the company, the technology function is given by $F(x; y) = xy^2$. In the ...
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2answers
160 views

Substituting total derivative d for partial derivative \partial

In economic models it seems to be commonplace to substitute a total derivative derived from one equation, say $\frac{d k}{d \tau}$, for the partial derivative derived from another equation, say ...
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55 views

Statistical inference and t-stats?

I have this linear regression model with an intercept(b0) and 3 variables(b1,b2,b3). Then they drop b2 and b3 and they give a new regression line with a new b0 and b1 and consequently new standard ...
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94 views

Using derivative to estimate change overestimates change between two states

I have a profit function in which revenue is given by the state of a variable y at each point in time t: R=y[t]-y[t]^2 and costs depend on the change in y from the previous state so that large changes ...
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93 views

Properties of concave,two-parameter function

I already showed that the function $\psi(\mu,\sigma)=\mathbb{E}U(X)$ is concave in $(\mu,\sigma)$, where $X$ is normally distributed with mean $\mu$ and variance $\sigma^2$. $U$ is a nice concave ...
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46 views

Average and aggregate values with a distribution function

I'm reading an economics paper and I'm trying to understand if a statement made by the author is an assumption or the consequence of a previous definition. The part I don't understand is the ...
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69 views

Statistics - Covariance and variance question

Please fill in the intermediate steps $$\sum_{i=1}^nx_i(x_i-\bar x)=\sum_{i=1}^n(x_i-\bar x)^2$$ and $$\sum_{i=1}^nx_i(y_i-\bar y)=\sum_{i=1}^n(x_i-\bar x)(y_i-\bar y)$$
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243 views

Total differential Economics Application

Suppose we have a revenue function: $R= P*Y$ where $P=$ price and $Y=$ output and is a function of $P$ and $C$, $Y= Y(P,C)$. How could we write the total differential of $R$ with respect to $P$ and ...