# Questions tagged [linear-algebra]

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### Question About Stable Matrices - MWG Mathematical Appendix M.D Matrices: Negative (Semi)Definiteness and Other Properties

I am self-studying the mathematical appendix of Microeconomic Theory (MWG). They defined a stable matrix as follows: Definition$\quad$ A matrix is stable if all of its characteristic values have ...
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### Wage setting equation

I'm currently doing multiple choice questions and cant figure this question out. I keep getting 1/9 as an answer when its meant to be 10%. Any help would be great. Thanks Suppose that the mark-up of ...
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### Question About Non-Degenerated Constraint Qualification (NDCQ)

I am studying constrained optimization using Mathematics for Economists by Simon and Blume, and I have some difficulties understanding the Non-Degenerated Constraint Qualification (NDCQ). I would like ...
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### Question About Implicit Function Theorem and Comparative Statics - Mathematics for Economists by Simon and Blume Chapter 15 Exercise 32

I am studying Implicit Function Theorem and its application on comparative statics using Mathematics for Economists by Simon and Blume. Here is the question: Consider a pure exchange economy with two ...
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### Vector Visualisation of regression model vs scatter plot style

I wrote another post discussing the intuition of visualising OLS regression. I wanted to go a bit deeper here visualising the difference between a vector/matrix approach, and the non-linear algebra ...
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### Intuition of Linear Algebra visualisation for regression

Question: I want to clarify my understanding of the basics of OLS regression in matrix form. Let's assume we have 2 different independent variables $x_1$ and $x_2$. Our 'model' will be the plane that ...
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### Orthogonality of two Subspaces

Note: This is a Linear Algebra Question. I'm posting here because I find this community more helpful than maths stack! And ofc linear algebra is fundamental to econometrics, as well! Martin Anthony ...
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### 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 C = \begin{...
1 vote
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### Calculating natural rate of unemployment

I have sample data on unemployment rate in a market and am looking to calculate the natural unemployment rate. The natural unemployment rate I obtained is constant over a time period, which is not a ...
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### Calculating the elasticity of substitution between factors of production

Following the work of Lu (1967) (Full text available here!) I got stuck trying to derive the elasticity of substitution between factors. He use the formula developed by Allen, that when the production ...
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### How to utilize the projection matrix in econometrics?

When consider the following DGP : $y=X\beta^{*}+\epsilon$ where $\beta^{*}$ is a $\tilde k\times1\$ vector. Define the projection matrices: $P_{X}=X(X^{T}X)^{-1}X^{T}$ and $M_{X}=I-X(X^{T}X)^{-1}$. ...
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### Has this differential calculus inequality approach to optimizing the production possibility curve exist?

I just started micro-economics at my community college and my teacher mentioned the derivative of the PPF for two output resources. I thought about it a while and came up with this approach. Some of ...
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### Visualising eigenvectors/values

This might seem like an odd question but seeing as I haven't had any formal education in solving ratex models yet, it is something I have been thinking about a lot recently. Consider the following ...
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### Budget hyperplane in n dimensions

Take the set of all vectors $x = (x_1, \cdots, x_n)$ that are solutions to $p_1x_1 + \cdots + p_nx_n = I > 0$. Show that this set has $n-1$ dimensions. I have somehow managed to get myself ...
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