-1
votes
0answers
40 views

Appendix question about $v_i = \frac{p_ix_i}{\sum_{j=1}^{n}p_jx_j}$

Can someone please explain to me how the authors (web.mit.edu/asuman/www/documents/aggregate-fluctuations.pdf‎) solve for $v_i = \frac{p_ix_i}{\sum_{j=1}^{n}p_jx_j}$? They are skipping a lot of steps ...
1
vote
0answers
65 views

Solving the General Equilibrium with $4$ equations and $4$ unknowns

I have to solve four equations to solve the equlilibrium prices for the two countries: $\frac{2p_1}{w_1} + \frac{p_1}{w_2}= \frac{48w_1^2 + 4p_1^2+p_2^2}{8p_1w_1}+ ...
1
vote
1answer
28 views

When do $Y$ and $r$ increase in the given economy?

This question is from "Mathematics for Economists" by Simon and Blume. IS curve: $[1-c_1(1-t_1)-a_0]Y+(a+c_2)r=c_0-c_1t+I^*+G$LM curve: $mY-hr=M_s-M^*$ The parameters $c_1$,$t_1$ and $a_0$ are ...
2
votes
0answers
71 views

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 ...
1
vote
1answer
79 views

Why is profit of all firms zero in long-term?

I heard that profit of all firms in long-term becomes zero. But I am not convinced of why it is like that. Can anyone explain this mathematically?
1
vote
1answer
145 views

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 ...
2
votes
1answer
141 views

Stability of a system that has (Jacobian-like) matrix with eigenvalue of less than 1 that has $x$ as non-eigenvector

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 ...
1
vote
1answer
704 views

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 ...
1
vote
0answers
122 views

Democratic central planning model

I want to model following situation: 1) There is a number of representatives of social groups (e. g. political parties). 2) Each of them devises an economic plan for the next year (N+1, N being ...
5
votes
1answer
2k views

Understanding the Leontief inverse

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 ...
10
votes
5answers
2k views

Motivating linear algebra for economics students?

I'm a tutor for the introductory linear algebra course at my school; this course is required for most upper division economics classes, so a lot of my tutees are economics majors. This is a typical ...
1
vote
1answer
262 views

Find a price vector p for various prices of industries.

( 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 = ...