Questions tagged [mathematical-economics]

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

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22 views

Obtain the OLS estimators of the simple model from the multiple model

I'm looking for the answer to this question: In the context of the simple regression model (two variables) we know that the estimators of OLS are given from: $\hat{\beta}_{1}=\frac{Cov(x_i.y_i)}{Var(...
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2answers
65 views

Are Price and Quantity Conjugate Variables?

I am taking a thermodynamics class. In this class one of the things that is discussed is how the partial derivatives of the internal energy with respect to extensive parameters (entropy, volume, mol ...
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are binary vectors and modular arithmetic important in economics?

I am currently taking a class in linear algebra at university as an additional elective. The course is generic and followed by students from various disciplines so it is not focused on economics. We ...
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1answer
47 views

Acemoglu - Introduction to Economic Growth - Existence of a one-to-one relation between human and physical capital

In the book the author claims that equation $(1)$ $$ f_x(x(t),y(t)) - f_y(x(t),y(t)) = a - b \hspace{10mm} (1) $$ where $f_x(\cdot)$ is the partial derivative of $f(\cdot)$ with respect to $x$ and $a,...
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1answer
47 views

Bothersome Mean/Variance Analysis

I'm currently writing my thesis in which I compare a series of ESG General Equilibrium models. I fell over this proof in Pastor, Stambaugh, Taylor Sustainable Investing in Equilibrium (2019) page 42. ...
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1answer
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HARA preferences details

I am searching for some exntensive details about HARA preferences. Where could I find some extensive details for HARA preferences? Something like a textbook or notes
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Development Accounting: Source of a country's poverty [closed]

Two economies, H and F. They both produce output using a Cobb Douglas production function that uses capital and labor. The savings rate and productivity are different across countries but constant ...
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18 views

Lorenz curve extension to 3d?

While thinking about Lorenz curves and economic inequality I wondered if you can extend Lorenz curves to Lorenz surfaces by revolving a Lorenz curve about the line of perfect equality. Would such a ...
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1answer
77 views

Tax multiplier in IS-LM model

I should consider a following modification of IS-LM model: IS curve is standard: Y = C(Y-T) + I(r) + G In LM curve the demand for money depends now on after tax income: M/P = L(r, Y-T) Price level is ...
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How does a change in the saving rate will affect the steady state growth in Neoclassical Model? [closed]

I tried to use derivatives and keep tin mind that at the steady state variables per capita increase at the rate g
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Nash in demand functions!

I am searching for some types of games that are played in linear demand functions. Altough I hear that there is a vast literatrure for games that are played in the intercept or the slope of the demand ...
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The local airport of a small town has decided to begin allowing nighttime flights in an effort to accrue more income [closed]

for d i did 40X50/100 = 20 then 20+35 = 55 and for c i did 40*35=1400 then 1400X20 = 28000 But I'm not sure if what did is correct, can anyone help?
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What are the mathematical prerequisites to understand Whinston and Green's “Microeconomic Thoery”?

I've completed my under graduation in economics where I used micro books like Nicholson and Snyder's Microeconomic Theory and Hal Varian's Intermediate Microeconomics. I am comfortable with topics ...
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What is the difference in estimation between A, B, and C? They seem very similar [closed]

This is a question in our econometrics class, and we're unsure of how to deal with the additional z2 and z3 in part B and part C.
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1answer
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How was the Cobb Douglas function derived?

In economics and econometrics, the Cobb–Douglas production function is a particular functional form of the production function, widely used to represent the technological relationship between the ...
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What is the math behind the coefficient of Absolute Risk aversion? [duplicate]

I have a good grasp of Calculus but I have never used the ratio of second and first derivatives. So, I am having a hard time understanding what it does and how?
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Violation of the transitivity axiom [duplicate]

I'm struggling to think of a way to violate the transitivity axiom. I was thinking about the following scenario: Let's say that you're voting on three different choices, A, B and C. If you pit A vs. B,...
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1answer
43 views

Question about an interpretation of the MRS

Given the marginal rate of substitution of $x$ for $y$ : $\frac{u'(x)}{u'(y)} $ I know one can interpret this as the amount of $y$ one is willing to give up for an additional unit of $x$, or the ...
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1answer
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Returns to Scale Microeconomics

Are there any production function $f(x_1,\ldots,x_n)$ that is having decreasing returns to scale, given that the marginal product in every input $i$ in the function $f$ is constant?
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1answer
37 views

What is state space representation for DSGE modeling

I'm beginning with DSGE modeling, and a mathematical representation (perhaps trivial for most of the people that are more with this topic) is the space-state state representation of a dynamical model, ...
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1answer
29 views

Proving that Marshallian demand is of the form: $x_i^*(p,I) = \hat{x}_i^*(p)I$ with certain conditions

Can I please have some feedback/help proving the following. My proof is below but I am quite uncertain as to whether my solution is efficient. Thank you. If $u(x)$ is a homothetic utility, then show ...
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Optimization in discrete time

I have made optimizations in continuous time that belong to the control theory, for example one case: $\max(\min)V[u(t)]=\int_0^Tf(t,x(t),u(t))dt$ constraint to: $\dot x=g(t,x(t),u(t))$ Where: $x(t)$: ...
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1answer
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Mankiw's version of the Cagan model - need help interpreting it

To keep the math as simple as possible, we posit a money demand function that is linear in the natural logarithms of all the variables. The money demand function is $$m_t - p_t = -\gamma(p_{t+1}-p_{t})...
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50 views

Conditional distributions in model with continuum of agents

Many economic models consider a continuum of agents, $i \in [0,1]$. Suppose these agents have characteristics $(x_i, y_i)$, which are independently distributed. Are all possible values of $(x_i,y_i) \...
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Continuous time optimization with two laws of motion (the Hamiltonian with two laws of motion)

How would we deal with a continuous time optimal control problem with two laws of motion? Suppose we have the following RCK like environment with human capital investment. $$\max_{c(t),k(t),h(t)}\int_{...
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Continuous logit models - random utility with uncountable choice set

This question is about the mathematical foundations of the continuous logit model, as derived in McFadden (1976) (https://eml.berkeley.edu/reprints/mcfadden/math_theory.pdf) and Ben-Akiva et al (1985) ...
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1answer
64 views

Current Value Hamiltonian VS Present Value Hamiltonian in Economics

I've been looking at a number of optimal control problems and have been wondering under what conditions one should use the current value Hamiltonian over the present value Hamiltonian. Does it depend ...
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100 views

Topological intuition to continuous preference relation

For a Microeconomics Course, we are going through MWG, and in the lecture we discussed the notion of a continuous preference relation. A preference relation $\succsim$ on a set $X$ is called ...
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Some questions about Kyle's model in Continuous Auctions and Insider Trading (1985)

I was trying to understand Kyle'e Theorem 1 in page $1319$ in Continuous Auctions and Insider Trading in 1985. As we can see by the proof, this factor $\beta=\frac{1}{2\lambda}$ refers to the ...
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1answer
554 views

Is there an economic interpretation of the envelope theorem?

I wonder if envelope theorem has also some hidden economic interpretation. For example, Lagrangian multiplier in economics can have interpretation of 'shadow price' which is useful economic concept. ...
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2answers
253 views

Has anybody seen anything this expression before?

Suppose that $z(\cdot)$ is the demand function of an individual (consumer/investor) and $p$ is the price of the commodity/asset demanded. Does anybody know what is the intuition behind the following ...
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Are trig functions not used in economics? [duplicate]

I noticed that many mathematics textbooks designed specifically for economics students like for example Essential Mathematics for Economic Analysis - Knut Sydsaeter / Peter Hammond / Arne Strom / ...
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To what extent does economics use Mathematical Logic?

My economics program had a class that transitions or introduces to proofs with books like Bridge to Abstract Mathematics , Reading, Writing, and Proving: A Closer Look at Mathematics or A Transition ...
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1answer
51 views

Are there some examples of theoretical models that discuss pandemics?

I am looking for some papers/references that showcase theoretical economic models that incorporate pandemics. Most work seem to be purely empirical. Does anyone know of some papers that try to model ...
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1answer
50 views

Informed traders do know the cross section of the privately known signal between each other

I am having the following setup of privately known signals and I am trying to understand an assumption. Here, I quote the setup. Consider two agents idexed by $i=\{1,2\}$ and each one observes some ...
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108 views

How can I build a fixed point theorem argument in pure strategies?

To begin with, I am recalling the Banach Fixed Point Theorem. Let $(X,d)$ be a non-empty complete metric space with a contraction mapping $T:X\to X$. Then $T$ admits a unique fixed-point $x^*$ in $X$ ...
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1answer
62 views

Find a perfect Bayesian equilibrium

Each of two sellers, $1$ and $2$ owns one indivisible object that a buyer would like to buy. The two objects are identical. The buyer´s valuation depends on the number of objects he gets. The ...
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1answer
29 views

What is the probability of an unemployed worker receiving no job offer during a time period?

we are currently covering one sided search models and I had a question for you all. I kind of understand the raw calculus behind finding the probability of a job offer over a time interval h, but what ...
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Simplex Lp interpretation of dual problem´s solution

I am wondering whether my interpretation of my simplex dual problem result is correct. The primal problem is: ...
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Solving a HJB with additional constraints on control and state variables

I am trying to solve a Hamiltonian-Jacobi-Bellman equation with additional constraints on the state and control variables, but I am a bit confused on how to do that. In Intrilligator 2002, it is ...
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Numerical Backward Induction Optimal portfolio choice

I am currently considering a simple life-cycle problem. We consider a market with equity risk only, which follows a geometric Brownian motion. We seek to maximize the terminal wealth of a CRRA utility ...
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1answer
77 views

Game theory and differential equations

Does anybody know, any (advanced/classic) textbook that combines game theory with differential equations in mathematical economics. Specifically, I an interested in asymmetric information problems.
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1answer
61 views

Generalizing demand for perfect substitutes utility function

I have the utility function: $U(x_1,...,x_n)=a_0+\sum_{i=1}^{n}a_ix_i\;\;\;\;\;\;\;\;\;a_j\in\mathbb{R}_+ \;\;\forall j=\{0,...,n\}$ (maybe $a_0$ could be zero) $\sum_{i=1}^{n}a_i\in (0,K)\;\;\;$ ...
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50 views

How to optimize this dynamical system? Needing guidelines

I'm trying to solve a growth model, where the author indicates is a dynamical system. I want to ask if someone would help me with some guidelines of how to optimize this, I've been trying to solve it ...
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1answer
37 views

How to determine a corner solution? Growth Model

I'm working on a paper called "Fertility clubs and economic growth" of Ahituv and MOav (linked below) and arrived at this point: The paper shows three optimal conditions respect to ...
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165 views

Solving a HJB with a probability to transit to a new state

I am trying to solve the problem of a firm facing the possibility of a future tax, in continuous time. The firm maximizes $V(k)=\int_{t=0}^{\infty}e^{-rt} \pi_t dt$ with $\pi_t=f(k_t)-i_t$ and $\dot{k}...
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how to calculate Leontief demand functions from first order conditions of a CES function when sigma tends to 0?

This question is NOT about how to approximate a CES function to a leontief function. Knowing that: $i= good (\begin{array}{*{20}{c}} {1}&{or}&{2} \end{array})$ $j= firm (\begin{array}{*{20}{c}}...
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4answers
116 views

What are good advanced textbooks to learn mathematics for economist?

I am looking for books or other sources that focus on math that is above bachelor level (i.e. above just simple calculus). I am not looking for a specialized text for some field but just general ...
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26 views

How to choose the autocorrelation type ? MA(q)^2 or AR(1)

I have heteroskedastic and serrialy correlated (autocorrelated) panel data. I want to test it with both dynamic and static models. For the dynamic test, I use GMM and the results of GMM is parallel to ...
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1answer
64 views

Interpretation of $x c '(x)$

Consider a cost function that is continuous, differentiable and (possibly) convex: $c(x):\mathbb{R}^+\to \mathbb{R}$. I was wondering if there is a "common" way to interpret the expression: $...

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