# Tagged Questions

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### Follow-up on solution to markov process equation

I asked a question here about solving a system related to an absorbing markov chain. I now have a variation where there are $m$ types (of student, job seeker, etc) each of which applies to ...
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### Matrix Operation

Let $x$ be a $n \times 1$ vector whose jth element is $x_j$. Show that $A = xx^{T}/x^{T}x$ and $B = I_n - A$ are symmetric idempotent matrices. Note that $x^Tx$ is a scalar (real number)
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### Game theory: Nash equilibrium in asymetric payoff matrix

I have a utility function describing the desirability of an outcome state. I weigh the expected utility with the probability of the outcome state occuring. I find the expected utility of an action, a, ...
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### Constructing and understanding stock-flow model

Suppose that $\textbf{x} = A\textbf{x} + B\dot{\textbf{x}}$ where $\textbf{x}$ is vector of economic output level, $A$ is input-output matrix, $B$ is stock-flow matrix. The system represents ...
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### Input-output economics and stability of general equilibrium

Here, I will start with a simple expression for an input–output system with $x(t)$ representing the vector of outputs and $A$ the input–output matrix. Then, the simplest possible linear ...
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### Eigenvalues of matrix and stability

This is about general equilibrium: Suppose that $x(t)$ represents outputs of all sectors and parts of the whole economy - represented as matrix. How outputs evolve to $x(t+1)$ is determined by the ...
What I remember from economics about input/output analysis is that it basically analyses the interdependencies between business sectors and demand. If we use matrices we have $A$ as the input-output ...
( Leontief input-output model ) Suppose that three industries are interrelated so that their outputs are used as inputs by themselves, according to the $3 \times 3$ consumption matrix A = ...