Questions tagged [mathematical-economics]

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

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526 views

How can I model my problems with math?

I want to ask a question about mathematical economics. When I read an article about economics, I see lots of mathematical equations. I can solve them without any help. But I can't create my own ...
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1answer
75 views

Leontief input output model with column sum greater than 1

In a linear algebra textbook I came across the following question (not included in the answer key): Consider an open economy with a consumption matrix \begin{equation} C = \begin{...
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3answers
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Auction with one buyer and multiple sellers

In the standard auction model, there are one seller and multiple buyers, the bidders are the buyers. Consider now an auction with one buyer and multiple sellers, where the bidders are the sellers. ...
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1answer
37 views

How can I know whether a good is inferior or normal? I can't determine elasticity with this?

I just need to make sense out of elasticities and how to determine if a good is normal or inferior. I have determined by $X_1$ which is in the form $m/p_1 - p_1/p_2$, that I should just take the ...
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2answers
139 views

When do prices not exist?

Often we employ the use of the separating hyperplane theorem to prove existence of price vectors, when discussing infinite economies this proof is substituted for proving existence of linear ...
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3answers
570 views

Derivative of definite integrals - how did MWG arrived at this result? Microeconomics

For a wage as a function of profit: $w(\pi)$ and profit $\pi \in [\pi_{min},\pi_{max}]$, the owner of a company sets the minimum wage to satisfy the following condition: obs $e = \{e_l, e_h\}$ but in ...
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30 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
78 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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0answers
45 views

are binary vectors and modular arithmetic important in economics? [closed]

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
56 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
69 views

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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0answers
22 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
100 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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0answers
31 views

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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0answers
50 views

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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21 views

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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2answers
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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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18 views

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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23 views

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
45 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
59 views

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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2answers
60 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
44 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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52 views

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: $x(t)$: ...
2
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1answer
39 views

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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0answers
54 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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1answer
122 views

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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0answers
64 views

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) ...
5
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1answer
87 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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0answers
116 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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0answers
73 views

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 ...
5
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1answer
578 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
258 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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0answers
56 views

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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1answer
148 views

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
52 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 ...
2
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1answer
51 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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2answers
111 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
70 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
30 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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0answers
24 views

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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0answers
25 views

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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22 views

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
87 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
86 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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53 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
41 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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2answers
171 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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101 views

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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