Open Model: Some production consumed internally by industries, the rest is consumed by external bodies.
Closed Model: All of the production is consumed by industries

Input-Output Matrix

An input-output matrix describes the amount of each commodity used in the production of one unit of each commodity.
Example: Suppose an economy involves coffee, technology, and transportation.
Production of 1 unit of coffee requires 1/2 unit of technology and 1/4 unit of transportation.
Production of 1 unit of technology requires 1/4 unit of coffee and 1/4 unit of transportation.
Production of 1 unit of transportation requires 1/3 unit of coffee and 1/2 unit of technology.
Then our input-output matrix, A, will be:

Production Matrices

The Production Matrix gives the amount of each commodity produced.
Example:
Let's say we want to produce 60 units of coffee, 52 units of technology, and 48 units of transportation.
Then our production matrix will be:

Demand Matrices

So far, we have two matrices:

We have our input-output matrix, A, which represents the number of units of each commodity used to produce 1 unit of each of the commodities.

We also have our production matrix, X, which represents the number of units of each commodity produced.

The matrix AX gives the amount of each commodity used in the production process.
The demand matrix, D, is equal to the number of units of each commodity produced, minus the number of units used to produce these commodities. D = X - AX.