Questions tagged [linear-algebra]
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12
questions
0
votes
1answer
26 views
Derive the growth rate of an equation
I have the following equation:
$$\mu =\left [s_{\pi }-v(s_{\pi }-s_{W})+\zeta \right ]$$
And I have to derive its growth rate, which is:
$$\dot \mu =-\frac{v}{\mu } (s_{\pi }-s_{W})\dot v$$
Do ...
0
votes
1answer
23 views
Hep with total differentiation of an AD function [closed]
Is there anyone who can help me with a total differentiation exercize. I am starting with the following formula for AD:
$$x=\mu ^{-1}(g+i+e)$$
Where $\mu$ is the Keynesian multiplier.
And have to ...
6
votes
1answer
90 views
Econ Intuition for Jacobian inverse in demand system
Consider the following simple linear demand system (in vector notation) with n different products
Demand: $\quad\mathbf{q=B\left(a-p\right)}$
Inverse demand: $\quad\mathbf{p=a-B^{-1}q}$
where $\...
0
votes
1answer
229 views
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 ...
0
votes
1answer
180 views
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 $M_{X}=I-X(X^{T}X)^{-1}$.
...
3
votes
1answer
149 views
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 ...
2
votes
0answers
83 views
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 ...
3
votes
2answers
137 views
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 ...
3
votes
1answer
347 views
When gradient of utility function is a zero vector
In Advanced Microeconomic theory by Jehle and Reny is said that if $\mathbf{x^*}$ is a solution to the following maximization problem $\max_{\mathbf{x} \in \mathbb{R}_+^n} u(\mathbf{x}) $ subject to $...
1
vote
0answers
479 views
Short Run vs Long Run Cost Functions
Let $z_a$ and $z_b$ are two vectors of inputs. $z_a$ is variable in both long run and short run however $z_b$ is only variable in long run.
Now let's suppose that the price of one of the inputs in ...
6
votes
3answers
234 views
How to deal with a singular Leontiev inverted matrix?
I am currently studying and experimenting the input-output methodology. It is a 1930's method based on national accountings that allows to measure the interindustry flow of good and services.
...
3
votes
1answer
55 views
How can I write a conditional expectation of finite state markov process in matrix notation
NOTE: This question is related to the econometric method explored in the following two questions:
Multiplicative factorization of stochastic growth time series--solving for an eigenfunction/...
