Questions tagged [economics]
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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Stochastic differential equations in economathematics [closed]
Prove that the stock price, governed by the binomial tree, converges to the stock prices of black scholes model.
What kind of assumptions should be made?
Are they unique?
...
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The Method of Quantiles
I am reading a book about quantile regression and at some point, they come to the method of quantiles, which is pretty much like the beloved method of moments. The case is that I do not understand the ...
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How to solve this post? [closed]
How long does it take to download a two-hour HD movie
from the iTunes store? According to Apple’s technical support
site, support.apple.com/en-us/HT201587, downloading such
a movie using a 15 Mbit/s ...
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Using Beta distribution in a profit maximization problem - replacing e in a system of equations that we'd already solved
I'm working on an economic model that we've already solved using 1-e^(-Investment) as the probability of a stochastic process.
Doing this we get lovely, simple derivatives for our decision rules (ex. ...
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Help understanding notation used in a problem
Can someone help me understand the notation used here? I can't seem to figure out the meaning behind what comes after the "if condition".
If Adeline chooses $T$
\begin{equation}
U_i=v\min\{...
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2
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Economics maximization problem linear activity
Consider the vectors:
$a_1 = \begin{pmatrix} 0 \\ -1 \\ 1 \\0 \end{pmatrix}, a_2 = \begin{pmatrix} 0 \\ 0 \\ -1 \\1 \end{pmatrix}, a_3 = \begin{pmatrix} 2 \\ 0 \\ 0 \\ 1\end{pmatrix}$
Find a single ...
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How to measure the affection of 2 variables on time dimension?
As the title, if in case you have 2 time series sequences A = $[a_{t}, a_{t-1},..., a_{t-n}]$ and B = $[b_{t}, b_{t-1},..., b_{t-n}]$, given $m$ steps back to history $(m<n)$ and assume we have ...
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Are there interior solutions to this constrained optimization problem?
I am getting some confusing results solving this problem:
$$\max_{c_0\geq 0, c_1\geq 0} \ R(1-c_0) [p t_1 + (1-p) c_1^{-\lambda} t_2] \\ s.t. \ c_0+c_1 \leq 1$$
where $\lambda>1$, $R>0$, $p$ is ...
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Proving hemicontinuity.
In my Mathematics for Economics course, we have started studying hemicontinuity. The concept is very clear to me, the problem is that I cannot understand how to prove it. Here is an example, from the ...
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1
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Utility in case one good is Bad and other is Good
I have a question
Suppose there are $2$ goods, $X$ and $Y$ where, $X$ is Good good, $Y$ is Bad good
Now Can the Utility be
1.) $U = x-y$
2.) $U = \frac{x}{y}$
3.) $U = \frac{\ln x}{y}$
They all are ...
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How does the Pareto distribution represent the 80-20 rule?
According to the current Wikipedia article:
The Pareto principle or "80-20 rule" stating that 80% of outcomes are
due to 20% of causes was named in honour of Pareto, but the concepts
are ...
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0
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Finding the growth rate of a variable $Y=4K^{2/3}N^{1/3}$ with respect to $K$ and $N$ simultaneously. [closed]
I took the natural log on both sides, and have an intuitive sense that I have to differentiate now but I cannot understand how.
The question is $Y = 4K^{2/3}N^{1/3}$ and find growth rate of $Y$ ...
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1
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Computing the optimal price from an auction with uniform distributed values
If I sell an item with value uniformly distributed between $0$ and $500$, and I value this item at $200$, then what is the ideal price to try to sell the item for? Note that once I set a price, I ...
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Corollary of the Frisch-Waugh Theorem
Consider the following linear regression model:
$$y=X \beta + \epsilon = X_1 \beta_1 + X_2 \beta_2 + \epsilon $$
Where we have $n$ obsevations and $k$ variables, and hence $X$ is a matrix $nk$, and $...
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Representing Submodular Functions As Maxima of Additive Functions
According to this paper, "every submodular function can be represented as a maximum of additive valuations." It gives an algebraic description as well, but I am having trouble internalizing ...
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1
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Sen's $\gamma$ and $\alpha$ imply rationalizability of choice
I need the proof or a reference for the proof that Sen's $\gamma$ and $\alpha$ imply rationalizability of choice (iff?).
Moreover, on Rubinstein's notes, rationalizability can be shown by Sen's $\...
CommunityBot
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Homogeneous of degree one functions that are a monotonic transformation of an additively separable function
Let $n>1$, and let $f:\mathbb{R}^n_{\ge 0}\rightarrow\mathbb{R}_{\ge 0}$ be continuously differentiable, concave, and homogeneous of degree one. Here, homogeneity of degree one means that for all $...
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How does one write the equation for a logit model, and then the odds ratio, with multiple explanatory variables?
I see logit equations always written with a single dependent variable, however I am running a logit model which outputs the coefficients for three explanatory variables (X1, X2, and X3) with respect ...
CommunityBot
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1
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Intuition behind the Compensating Variation!
In Economics, we can calculate the compensating variation (CV), which (to my understanding) is the amount of money we would need to give back to a consumer to keep them at the same level of Utility ...
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The expectation of the product of an estimator with its transpose
I hope you are well. I have a problem that it seems to be really easy but I just don't know how to find the solution.
So, this is the question ; I have to compute E(Ŷ'Ŷ). For that, I have some ...
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Representation of an indicator variable conditional on means
I am just starting out with math in uni for my research so this is a really simple question. I calculated the fraction of number of school enrollments during a policy period from 1991 to 1993 over the ...
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Finding Nash Equilibria and Best Response in a Strange Game
Consider a two-player game where Player 1 chooses a strategy $x_1=[1,3]$ and Player 2 chooses $x_2=[0,2]$ Let the payoff functions for P1 and P2 be $u_1(x_1,x_2)=\min\{x_1,x_2\}$ and $u_2(x_2,x_1)=\...
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Minimization of the Pollution Problem
I study Economic Analysis.I came accross the following minimization problem
I tried to show that M is quasiconcave but i failed.
I tried using the definition of quasiconcavity or using the min ...
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Distribution of linear combination of normally distributed 2-way censored variable
Consider a censored model with the latent variable given by
$$y^*=\beta_0+\beta_1 x+u,$$
and the dependent variable given by
$$
y =
\begin{cases} \displaystyle
0, & y^* \le 0 \\
y^*, & 0 < ...
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2
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A Basic Question of Continuous Time Macroeconomic Model (Variation of Constant to Solve an ODE)
I am going through the continuous time macro slides by Ben Moll (link is: https://benjaminmoll.com/wp-content/uploads/2019/07/Lecture2_ECO521.pdf), when deriving New keynesian model in continuous time,...
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Kuhn Tucker condition is sufficient for a global optimum?
$L$ is the variable and $s,r$ are parameters. The question asks to solve $max_{L\geq0}rf(L)-wL$ where $f(L)$ is twice continuously differentiable, strictly increasing and strictly concave. Then how ...
CommunityBot
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Inflation Calculations Skewed by low prices.
I am currently calculating inflation metrics for a retail store. I am simply using their POS data, to calculate the Year-Over-Year price change of each item.
I then weight this on the sales, sum it up,...
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What are some common distributions assumed for approximating a demand curve?
A demand curve is a function $d(p)$ such that at price $p$ the demand for the good is given by $d(p)$. This means that you are making a sales of $p\cdot d(p)$ at price $p$. For typical goods, demand ...
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Is there any book "economics for mathematicians"? [closed]
If you search economics book there are plenty of them on the market. We may say the say about "mathematics for economists" or "application of mathematics in economics". But I've ...
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A put option and a call option with identical exercise price are both marketable or neither is.
I am doing Exercise 1.13 in Introduction to Mathematical Finance: Discrete Time Models by Pliska.
Exercise 1.13 Suppose the interest rate $r$ is a scalar, and let $c$ and $p$ denote the prices of a ...
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How do I normalize/standardize a data set to a certain set value (not average, not min, not max)?
I know the formulas for standardizing, normalizing, and mean normalizing (if we take the wikipedia's definition for these terms). What I want to do is to normalize to a set value. For example, if I ...
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Engineering Economics Question: Uniform series present worth question
The cost of a fence that can detect poacher intrusion into a National Wildlife Preserve is $3.3 million per mile. If the effective life of the fence is 10 years, determine the equivalent annual cost ...
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Present Worth with Salvage Value
I would like to know how to consider the "Salvage Value" in the following question while calculating the present and future values.
here is the question:
We are planning to build a new bridge. ...
CommunityBot
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How can elasticity of $f(x)$ be expressed as a percentage change in $f(x)$ per $1$% change in $x$?
In answering the above question, we took the formula of elasticity:
$El_xf(x) = (x/f(x))*(∂f(x)/∂x)$
We can transform it in the following way:
$El_xf(x) = (∂f(x)/f(x))*(∂x/x)$
Now at this point, the ...
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1
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0.35 log points to percentage
What is 0.35 log points in percentages? I have no knowledge of this subject at all. From what I've gathered, it should be Percentage change = (e^log points - 1) * 100, so 42%. Is this correct?
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Cournot competition: profit maximizer vs. market share maximizer
Today during an informal conversation with an established business researcher, I learned such a fact:
In the classical Cournot competition model, if one player is a
profit-maximizer, the other is ...
CommunityBot
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Equilibrium interest rate
There are two countries in the whole world: Bolivia and Peru.
The aggregated investements in Bolivia is $I^B$ And in Peru they are $I^P$ (They are both exogenous).
The savings for Bolivia, where $B,b &...
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Need help identifying what sort of differential equation this is
I'm reading an economics paper, and have stumbled upon this differential equation system:
$\dot x = -\beta xy^\alpha$
$\dot y = \beta xy^\alpha - \frac{1}{\sigma}y$
I haven't taken any classes on ...
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Core vs. Strong Core in Housing Allocation Games
I am presently reviewing the course notes for my Game Theory course, and I'm struggling with the concepts of the core vs. the strong core. In the notes, we have three players, with preferences ...
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Trying to find why solutions to both maximization and minimization problems exist before even solving it [closed]
There is a problem which I have been thinking about but can't come to a conclusion. And Final exam is tomorrow:
enter image description here
My attempt: To find solutions to both maximization and ...
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Why is the GST for the wholesaler based on the marked price? We don't know if that is the cost price.
The price of a sewing machine is Rs.40000.The wholesaler allows a discount of 10% on it to the shopkeeper. The shopkeeper sells the sewing machine to a customer at a discount of 5% on the marked price....
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Taylor Expansion for the Return averaged over k periods? [closed]
this is my first question here. I need help to understand the Taylor Expansion which gives the (2.2.5) equation (see the pictures). Thanks
(pictures from: Schmidt - Quantitative Finance for Physicists....
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Regression relation to casual relationship
If the correlation coefficient of two variables is 0, can there still be a causal effect between them? And can the causal relationship between these two variables be studied by regression analysis?
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Many questions about a loss distribution
Long question, but mostly set up:
I'm trying to understand the capital requirements formulas of Basel III. They come from the Merton-Vasicek model for the value of a company's assets. Assume we have $...
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Pairwise majority voting and Arrow's axioms
The following is a question on Arrow's theorem with a pairwise majority decision. The bits I was unsure about was (bi) (is the 4th condition satisfied?) and also is (bii) correct? Thanks for your help
...
CommunityBot
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Definition of transition density
Sorry if this is a basic question but I have a hard time grasping the definition of transition density in a financial setting.
From what I understand, transition density is the expected (future) value ...
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How do you allocate based on historical outcomes when these can be both positive and negative?
I would like to allocate an expected yearly return based on the monthly outcomes of last year. However, these monthly outcomes can be both positive and negative.
For example (year 3 in the image), the ...
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Expected utility
The figure below describes John's preferences over lotteries for three prizes- $1, $2, and $3, where p1 is the probability of winning $1, and p3 is the probability of winning $3. Assume that John is ...
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Derivation of index decomposition analysis
I’m currently reading a paper on index decomposition. The paper is here for reference : https://www.sciencedirect.com/science/article/pii/S0140988315001772
The paper is setting out how it has gone ...
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What does it mean to "solve forward/backward" a differential equation?
I know what it means to solve forward/backward difference equations. What I have not been able to wrap my head around is how that formally makes sense in continuous time. To make things concrete, here ...
