Application of Leontief Input-Output Model/Production Equation

Solving the Leontief production equation for an economy of 3 sectors (x1, x2, x3) using the Leontief Input-Output Model also know as the Production Equation. An application of Linear Systems. Please Subscribe. More Math Videos to come!

Category:

Education

Tags:

• Leontief Input-Output Model
• Production Equation
• Linear Algebra
• Economics
• Matrix Algebra
• Consumption Matrix
• Matrix Operations

[invisiblebutterfly6]

Instead of doing a row reduction, couldn't you just 'post'-multiply by the inverse of (I-C)?

[TheCalculusGeek]

@invisiblebutterfly6 Yes you can, Ax=b, x = A^-1b. But this method is only practical if you have a calculator or software to help you find the inverse.

[saxiv]

Is that whole

x (1 - C) = d

The standard procedure for solving these kinds of problems?



[TheCalculusGeek]

@saxiv If you relationships between your sectors of economy are already linearly established, than yes that is the whole procedure. These problems can also be given in worded format, where you might have to establish a network diagram in order to model the linear expressions, and then you can apply the same procedure to solve them.

[HeyTerranceTV]

Thanks! This is my exact homework problem.

[Ahartwick38]

You're my hero!!!

[saadobama]

thanks man!

[shammary89]

the row to row reduction would've been helpul..everything else is understandble.

[Jullianic]

it's helpful but quite hard to read...