Questions tagged [mathematical-economics]

The application of mathematical methods to represent theories and analyze problems in economics.

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30 views

Does Nine-dimensional Euclidean space has any use in Economics or Econometrics?

https://en.wikipedia.org/wiki/Nine-dimensional_space i am looking for any application of nine-dimensional space in economics or econometrics. Thanks !
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What is the time period I should assume for factor prices in the cost function? [closed]

I have a quick and rather urgent question. Using the method of Lagrangian multipliers I got my cost function for my Cobb Douglas function of the form AQ^(1/b) where b>1, and A was an extremely large ...
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33 views

Transversality Condition

I am reading the first section of chapter 10 of the Obstfeld and Rogoff textbook Foundations of International Economics and I have a doubt in how the transversality condition is obtained. Even though ...
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1answer
28 views

What's the special notation?

I'm studying "ALGORITHMIC AND HIGH-FREQUENCY TRADING". Page 249 of it tries to find a formula for $h(t,q)$. First, it supposes $h(t,q) = \bar\kappa log \space\omega(q,t)$ then let $\omega(t)=[\omega(...
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1answer
46 views

How to find the maximum profit in a graph?

We know the maximum profit will occur at the quantity where the gap of total revenue over total cost is largest. But how can we find such gap?
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Mathematics of Marxian Economics

I have studied some Marxian economics, and realise that Marx's writings were not very mathematical. I recently came to know of Analytical Marxism and Neo-Marxian economics. I read the Wikipedia page ...
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4answers
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Macroeconomics for Mathematicians

I'm coming from a math background (so my mind is set up for Definitions-Observation-Lemma-Proof frameworks) and looking for recommendations of a Macroeconomics textbook mainly devoted to growth models ...
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1answer
41 views

Simple General Equilibrium Model of Public Goods: Intuition?

We assume a two person economy, denoted by person A and B. Good y is an ordinary private good, and each person begins with an allocation of this good given by $ y^{A*} $ & $ y^{B*} $ respectively. ...
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Differentiability vs Continuous Differentiability

Why do optimization textbooks, as well as appendices for MWG JehleReny etc. simply state conditions in terms of continuous differentiability, even when the weaker condition of differentiability is ...
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1answer
43 views

Minimizing consumption in a single market( Partial Equilibrium)

Let there be a good X where the optimal consumption is 0; i.e the social costs for any unit provided would always be greater than the utility surplus of the market. We know that prohibiting it( ...
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22 views

Calculating elasticity between log term and non-log term

Given the following, I am asked to calculate the elasticity of wages with respect to age: $$𝑙𝑛(𝑤_𝑖)=𝛽_1+𝛽_2𝑎𝑔𝑒_i+𝛽_3𝑎𝑔𝑒^2_𝑖+𝛽_4𝑌_𝑖+𝛽_5𝑇_𝑖+𝛽_6𝑀𝑎𝑟_𝑖+𝜖_𝑖$$ How does one ...
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1answer
25 views

Calculating elasticity between terms in a regression equation

Given the following regression: $ln(w_i)=\beta_1+\beta_2age+\beta_3age_i^2+\beta_4Y_i+\beta_5T_i+\beta_6Mar_i+\epsilon_i$ I am asked to calculate the elasticity of wages with respect to age. Is the ...
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1answer
48 views

Why can utility functions be continuous, and what does this imply for marginal utility?

I am studying microeconomics at the introductory undergraduate level and two related but distinct questions are puzzling me. First, my textbooks express utility functions as continuous functions by ...
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1answer
71 views

When to use a lagrange multiplier?

I have a question in regards to the use of Lagrange multipliers in macro models. I have seen that when writing a Lagrange there are two ways to write the Lagrange multiplier: 1) Indexed or 2) ...
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1answer
35 views

Notation? Inverse of demand function

I'm looking through The Investment Decisions of Firms by S.J. Nickell, and I've come across some notation that I don't quite understand. Any clarification would be very welcome. Nickell first assumes ...
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1answer
47 views

Supply and Demand plotted on a three dimensional Cartesian coordinate system

Is it possible ? if it's possible can someone give me a reference ? Thanks !
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2answers
23 views

Is there an index, parameter, ecuation, or anything to compare the tax pressure exercised by a country in relation to others countries?

In my country we are told often that the tax pressure over the companies and people is huge, making it unbearable and being a reason bankrupting the Economy, and one of the largests in the world. We ...
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0answers
30 views

Shortcuts for elasticity of substitution

How can I find the elasticity of substitution (I know the definition) if I know the utility function $u(x,y)$? I know its increasing in $x$ and $y$, etcetera, and has everything else you want from a ...
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1answer
32 views

Equations of “rational mechanics” and general equilibrium

Vilfredo Pareto, referring to the equations that determine equilibrium, wrote: These equations do not seem new to me, they are old friends. They are the equations of rational mechanics. This ...
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1answer
18 views

Annual Fraud Recovery Over Time: Should I adjust for inflation?

I have a dataset of the total amount the U.S. Department of Justice obtained annually in settlements/judgments of government fraud cases from fiscal years 1988-2019. There's a lot of variation, but ...
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2answers
53 views

For the case of two goods, give an example of preferences that are represnted by a continuous utility function that allows for fat indifference curves

The question in the title sounds like a trick question, due to the monotonicity property that indifference curves have, such that for two goods x and y, strong monotonicity implies y > x. Possible ...
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1answer
29 views

How are low/middle/high classes defined mathematicaly?

I am only looking for mathematical references. I think this belongs to econometrics but am not sure nor where to look at it specifically. I suspect the definition is given with some kind of weighted ...
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0answers
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Linearization of the dynamic system (I did it, but I have a mistake that I cannot catch. Help me please)

I have the following dynamic system in discrete time For p is price, d is demand and s is supply. $$p_{t+1}-p_t= a(d_t-s_t)$$ $$s_{t+1}-s_t=bp_ts_t-ws_t$$ $$d_t= k-gp_t$$ I have to linearize this ...
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Determine lot size with extra constraints and EOQ formula

Given a fixed price of 250,00 dollars for the warehouse and the price of the product is 5,00 dollars per product. The order cost is 500,00 dollars but if more than 1000 products are ordered then it ...
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2answers
26 views

How do you calculate the intrinsic value or fair value of real estate?

How do you calculate the intrinsic value or fair value of real estate? I mean how do you determine that the house/commercial estate is undervalued or overvalued?
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2answers
21 views

NPV but adding last year net value?

I have found the following NPV (Net Present Value) formula: CF = unlevered cashflow i = interest rate (WACC) $$NPV = -I_0 + \frac {CF_{2019}}{(1+i)} + \frac {CF_{2020}}{(1+i)^{2}} +\frac {CF_{2021}}...
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0answers
30 views

Behavioral Dictator Game

I am doing a self study on behavioral economics and I am trying to solve behavioral version of the dictator game with following utilities for person 1 and 2. $$ u_1( \sigma_1, \sigma_2 ) = \...
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1answer
46 views

A question on the accuracy of economic forecasts

I apologise if thi's question appears dumb or boring, but I am asking it as a lay person. The context is that I am always arguing with friends that they should trust the economists view that Bexit (...
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1answer
67 views

How do we define an efficient tax in microeconomics?

I am currently working through problems to study for an upcoming exam. I am not seeking a solution per se. I am looking at the intertemporal choice model. I am looking at two periods where consumption ...
2
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2answers
29 views

Definition of covered market

I do Industrial Organization course, and I've seen the phrase "market is covered" several times in my lecture slides, however, I'm struggling to find the formal definition of "covered market" and the ...
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1answer
27 views

Interpretation of dummy variable : Random Effects Model

I am running a RE regression and I have export similarity index between two countries as the dependent variable and have a dummy variable such as share a border(=1 if countries share border, 0 ...
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0answers
31 views

Why decreasing co-state variable (over time) is Compulsory?

I have a short question. In the continuous time infinite horizon optimal control maximization problem Like $$\max \int^{\infty}_0 u(c_t)e^{-pt}dt$$ I use current hamiltonian function and I obtain ...
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39 views

What is the economic interpretation of the solution of this optimal control problem?

I have the following optimal control problem $$\max_{c_t} \int^{\infty}_0 e^{-p_it}\ln(c_t(i))dt$$ subject to $$\dot{w_t}(i)=rw_t(i) -n_ic_t(i)$$ $$w_0(i)=w_0>0$$ I have some wealthy and ...
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1answer
53 views

How to find mixed optimal strategies in this zero-sum game?

I'm trying to solve this problem from last year final exam in game theory: Consider the zero-sum game $G=(X, Y, g)$ where $X=Y=[0,1]$, and $$\forall (x,y) \in X \times Y: g(x, y)=\max \{x(1-2 y), y(...
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1answer
22 views

Is there some definition about risk sharing?

I was searching for a definition of risk sharing and I have found the following: $\underline{Definition:}$ Risk Sharing — also known as "risk distribution," risk sharing means that the premiums and ...
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2answers
33 views

What is wrong with the idea that resource depletion causes recessions? [closed]

How can you refute this theory, such that it never comes up again.
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1answer
31 views

Dimensional analysis of GDP

The GDP is sometimes given by $$ GDP=P\cdot h\cdot e \cdot F $$ Where $P$ is the Productivity, $h$ is the number of hours worked, $e$ is the employment rate and $F$ is the size of the labor force. ...
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1answer
55 views

Interpretation of $\frac{\partial }{\partial p_1}Q_1(p_1, p_2)/\frac{\partial}{\partial p_2} Q_1(p_1, p_2)$

I am interested in an economic interpretation for the ratio of partial derivatives of a demand function $Q_1(p_1, p_2)$, which is \begin{equation} t=\frac{\frac{\partial}{\partial p_1}Q_1(p_1, p_2)}{\...
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60 views

Writing constraint

A firm accumulates useful knowledge $k$ by investing in R&D activities. Specifically, if the firm invests $r > 0$ dollars into R&D, the stock of useful knowledge grows by about $2\sqrt{r}$ ...
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2answers
87 views

Can we have a Non-Reflexive Preference Relation?

I've been thinking about preferences alot recently and have been specifically thinking about the reflexivity requirement. That is: $$x \succsim x$$ Though this is apparent and obvious, I have been ...
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0answers
50 views

Finding optimal path in continuous time

I have the following optimal control problem $$\max_{c_t,l_t} \int_0^{\infty} [ln(c_t)+\theta ln(1-l_t)]e^{-pt}dt$$ st. $$\dot{k_t}=k_t^{1/2}l_t^{1/2}-c_t-\beta l_t$$ $$k_0>0$$ I do big part of ...
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2answers
38 views

How to use an instrumental variable to estimate the parameter?

I have the following linear model of log wages (w) explained using years of schooling (S), years of experience and its square $(E,E^2)$ and 3 dummy variables indicating whether the individual was ...
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0answers
78 views

Bliss point hamiltonian function

I have the following utility function $$u(c_t)=g(c_t-b)^2$$ for constants $g,b>0$ Edited: in order to be bliss utility function, It must be g is negative. But in the question g is given to be ...
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1answer
38 views

Linear Probability Model Instead of Logit in Fixed Effects Regression

In our panel data analysis we estimated a fixed effects linear probability model (LPM) instead of a fixed effects logit regression because our sample size was quite small (600 individuals) and the ...
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1answer
74 views

Present value heuristics problem

No idea if this is the right stackexchange for this, feel free to point me elsewhere! I'm teaching business calculus and one of the problems the students have is to figure out the present value of a ...
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1answer
27 views

Consumption Set in Arrow-Debreu

I'm very inexperienced in mathematical economics, so when I came across the idea of the consumption set in Arrow-Debreu, I was a little confused. So for each element x in consumption set X, what does ...
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1answer
37 views

How to show that the estimator is consistent?

$Y_i=\beta_0+\beta_1X_i+U_i$ is my regression model for an I.I.D. sample with N=1000 observations. Suppose $U_i\sim I.I.D.(0,\sigma^2)$ and Xi are also I.I.D for i=1,2,3......1000. Xi is independent ...
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1answer
50 views

How to test if the effect of one regressor entirely comes from other regressors?

I have a regression model that includes IQ test scores as the dependent variable; my own education, my father's education and my mother's education as independent variables. Suppose I want to know ...
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1answer
90 views

Linear Utility?

Consider a preference relation $\succeq$ on $X\subseteq\mathbb R^2$. If $\succeq$ satisifies: $$ \begin{align} &1.\mbox{ }(a_1,a_2)\succeq (b_1,b_2)\implies(a_1+t,a_2+s)\succeq (b_1+t,b_2+s),\...
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1answer
101 views

Dynamic programming, optimal consumption-savings (finite horizon) problem

Let $w_t$ denote a consumer's wealth at time $t$ and $c_t$, the amount she chooses to consume, so her savings exiting this time period are $w_t-c_t$. Given this savings decision, her savings $w_{t+1}$ ...

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