# Input-Output Models

- Author:
- Nicole Stripling

- Topic:
- Matrices

## Types of Models

**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.

**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**.