# Questions tagged [linear-algebra]

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### Why the definition of productive economy in Leontief Open Model is such?

Note: as an inter-disciplinary question, it has its twin on Mathematics Exchange: https://math.stackexchange.com/questions/4193896/why-the-definition-of-productive-economy-in-leontief-open-model-is-...
56 views

### Understanding utility function curve and marginal rate of substitution

This example appears in a different question, but there is something I don't understand. Maybe this question is better suitated for algebra stackexchange. John’s utility function for food (f) and ...
72 views

### Regression Optimization problem under constraints

To estimate a simple linear regression: $$y = \beta_0 + \beta_1 x + \epsilon$$ I have the assumptions that a researcher $A$ can only sample individuals with a value $y < y^A$. Similarly, a ...
55 views

### How can difference equations with an infinite summation be represented in matrix form?

I have derived the microeconomic foundations of a dsge model and I've obtained the IS and NKPC. I would like to represent them in matrix form to study the system. However the problem is that both ...
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### What are the concepts in Linear Algebra that model the idea of Identification Strategy in Econometrics?

I just would like to know what concepts one should know before talking about identification strategies in econometrics. I see people studying such concepts but I'm not sure they realize (or even know) ...
49 views

### $x\sim y$ implies $x+a\sim y+a$ for any $a\geq0$ and $x,y\in\mathbb R^n$, then the preference is linear?

$x,y,a$ are vectors in $\mathbb R^n$ We say $a\geq0$ if all directions of the vector $a$ is greater or equal to zero. We want to prove (or disprove by counterexample) that: Suppose $x\sim y$ ...
31 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 ...
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### 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 ...
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### 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 ...