Questions tagged [mathematical-economics]
The application of mathematical methods to represent theories and analyze problems in economics.
639
questions
2
votes
1answer
48 views
homothetic functions in economics
Are there any results in economics that require function to be homothetic? The textbook I am using (Essential Mathematics for Economic Analysis) says that function is homothetic when " $f(x)=f(y)$...
1
vote
1answer
30 views
Would some help me fill in missing steps from a textbook exercise left for the reader
Question: Suppose $C_t=(1-s)Y_t-\lambda G_t$ where $s>\sigma$ as in the basic Solow model.
Out of the government expenditure , proportion $\phi$ is invested in public capital formation. Hence we ...
0
votes
2answers
40 views
Can we model risk with only probability?
Sorry for the confusion! I am adding an example to see if it helps:
For example, consider a gamble A, with payoffs {a,b,c,d}, whose probability of each payoff being realized is equal (so 25% each); ...
1
vote
1answer
26 views
Would someone be able to help me solve capital per capita in the steady state (check my work)
Question: Suppose $C_t=(1-s)Y_t$ where $s>\sigma$ as in the basic Solow model. Solve for capital per capita in the steady state.
$Y_t=K^{\alpha}_tL^{1-\alpha}_t$
$Y_t=C_t+I_t+G_t$
$K_{t+1}=I_t+(1-\...
1
vote
1answer
19 views
Are there any analysis of what is the net benefit of NASA program to US economy?
I am looking for some study that tries to calculate whether the NASA program on a net basis benefits the US economy. The program is very expensive, but it generates lots of patents, research, jobs and ...
0
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0answers
23 views
Can someone help me prove that the CES function is also a Cobb-Douglass function [duplicate]
I would like some assistance with a problem that I have showing a CES function is also a Cobb-Douglass utility function.
Question: we have a CES function: $Y=A[\alpha K^{((1-\sigma)/\sigma))}+(1-\...
0
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2answers
68 views
How to find $\phi$, that denotes the correlation of signals among informed traders?
Since I do not have an answer on Quantitative Finance in my question I cross-post here the problem to tag some other categories
The following assumptions are part of the paper of Back, Chao and ...
5
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0answers
79 views
Certainty equivalence when the utility is semi-continuous instead of continuous
Let $U:\mathbb R^2\to\mathbb R$ be a utility function.
If $U$ is strictly increasing and continuous, then it is well known that for any $(x_1,x_2)$ there exists a certainty $(c,c)$ such that $$U(x_1,...
0
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1answer
28 views
Find equilibrium price using excess demand function
Consider an economy with two agents. There are two goods, x and y. Agents' preferences are Leontif ones as follows:
$u_1(x,y)=\min(x,4y)$ and $u_2(x,y)=\min(x,y)$.
Initial endowment for 1 is (2,4), ...
0
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0answers
22 views
What are the values of the Laffer curve for Argentina?
According to this article, (spanish only)
Argentine companies pay 106% of taxes for their revenues
Supposedly the Laffer curve is different from country to country. Which are the tax rate values at ...
0
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1answer
30 views
What are the advantages of using demand systems estimation? How is this different from individual demand estimation for product?
I am unable to understand how is demand systems estimation is different from simple demand equation estimation. What's the best resource for getting a history line of demand systems?
0
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1answer
26 views
Slope vs elasticity of demand function - Is it the same thing?
Do the slope of a linear demand function and the elastisicy of demand coincide when we use specific preferences for pricing. As a paradigm, if we consider the case of CARA normal preferences, by ...
0
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1answer
21 views
Economic and Statistical Significance Of Coefficient
I want to know If I am comprehending these terms correctly
Summarizing the difference between economic and statistical significance of coefficients (Describing the terms, process of assessing each ...
1
vote
0answers
19 views
Why does the following approximation hold?
In Essential Mathematics for Economic Analysis, on page 426 there is a model on gains from search where profit function is given as:
$$\pi (t) = [p^0 -p(t)]x^0 -wt$$
$t$ is time, $p$ price, $x$ ...
2
votes
0answers
43 views
Recursive Models of dynamic linear economics (Hansen / Sargent, 2014) - optimal linear regulator problem / solution of bellman equation p. 34 ff
The optimal linear regulator problem according to Hansen/Sargent, 2014, Recursive models of dynamic linear economies, on page 34 ff. is stated as follows:
$-E\sum_{t=0}^{\infty}\beta^t[x_t' R x_t+u_t'...
3
votes
0answers
41 views
Why is my elasticity of substitution wrong?
I am calculating elasticity of substitution for the following production function:
$$F(K,L) = A(aK^{-\gamma}+bL^{-\gamma})^{-\mu/\gamma}$$
where $A, a, b, \mu, \gamma$ are constants. $A, a, b, > 0$,...
1
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0answers
31 views
Differential equation to calculate an investors fortune at time T
An investor has to investment opportunities. At time t his fortune has the value $v(t)$. In the first alternative he can put all his money into a bank account with interest rate $r(t) > 0$. The ...
0
votes
1answer
20 views
Price elasticity of demand of CES
Anyone would like to help me show the following ( or a book/paper reference would be a great help)
" The price elasticity of demand is equal to $\sigma$ for the demand function of CES preference,...
-1
votes
1answer
35 views
How to maximize utility using the Lagrange method [closed]
Is this solvable using the Lagrange method? If so, Does anyone know how to solve this using the Lagrange method? Utility is $a\ln x_1 + \ln x_2$. Budget constraint is $P_1x_1+P_2x_2= W$
4
votes
1answer
28 views
Homogeneous Utilities: Anything other than CES?
Does there exist any homogeneous utility function, i.e., $u(\lambda \mathbf{x}) = \lambda u(\mathbf{x})$, that is not a special case of the CES (or nested CES) family of utility functions or its ...
2
votes
1answer
192 views
The Principle of Optimality and the Bellman Equation
I endeavour to prove that a Bellman equation exists for a dynamic optimisation problem:
$\ max \Sigma\beta^s U(C_t)$
Subject to the following constraints.
$C_t + K_{t+1}= F(K_F, E_F,S_t)$
$E_t = F_E(...
2
votes
1answer
37 views
Practice question on Correspondences and maximization
We're learning about Theory of the Maximum. I tend to struggle with correspondences in this context, so I'm trying to work through some practice questions. I will start with some general notation of a ...
2
votes
1answer
104 views
what is monotonicity and strict monotonicity in preferences?
I am really confused between monotonic preferences and strictly monotonic preferences, I saw some video and read certain answer where it is mentioned that the
When preferences are monotone / weak ...
2
votes
1answer
84 views
How to calculate the ideal maintaining time of a machine?
I have a question regarding a cost calculation problem:
I have the following curve, which shows, that with increasing number of tasks without maintaining a machine, the error probability for the ...
1
vote
2answers
55 views
Elasticity of demand functions
I have some question about the elasticity of the demand functions of two different traders/consumers. Suppose that $x_1$ and $x_2$ are the elasticities of the demand functions of these agents. ...
2
votes
2answers
121 views
Extreme Value Theorem in Economics
Would appreciate some thoughts on proving the existence of a solution (a maximum) in an applied context.
Suppose the objective function is one of maximising utility:
$\max\Sigma\beta U(C_t)$
Subject ...
0
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0answers
35 views
Time series Econometrics demonstration
Hey there! Can anyone help me with this? I am able to arrive to expression (3) from (2) by using the lagged variable and make the variation from $Y_t$ and then divide to the right such that $\beta_0 = ...
2
votes
1answer
603 views
Mathematical Notations that I Never Understand While Reading Articles or Dissertations
I have some problems when I reading mathematical notations. For example:
$$\mathrm{E}_{0}\left\{\sum_{\mathrm{t}=0}^{\infty} \beta^{t}\left[\mathrm{u}\left(\mathrm{C}_{\mathrm{t}}, \mathrm{M}_{\mathrm{...
3
votes
2answers
187 views
Showing utility function gives preferences that are rational and convex
Consider a consumer with preferences relation $\succsim$ over non-negative commodities $x_1$ and $x_2$ such that their utility U = $x_1$ + $\ln(x_2)$
Are these preferences rational and are they convex/...
3
votes
2answers
520 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 ...
3
votes
1answer
58 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{...
3
votes
3answers
74 views
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. ...
0
votes
1answer
36 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 ...
2
votes
2answers
137 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 ...
5
votes
3answers
562 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 ...
0
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0answers
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(...
1
vote
2answers
74 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 ...
1
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0answers
44 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 ...
2
votes
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,...
2
votes
1answer
53 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. ...
2
votes
1answer
63 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
1
vote
0answers
20 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 ...
0
votes
1answer
89 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 ...
2
votes
0answers
29 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 ...
1
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0answers
49 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 ...
1
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0answers
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.
3
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2answers
118 views
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 ...
0
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0answers
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?
0
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0answers
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,...
2
votes
1answer
44 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 ...
