[b]Open Model: [/b]Some production consumed internally by industries, the rest is consumed by external bodies. [br][br][b]Closed Model[/b]: All of the production is consumed by industries

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

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

So far, we have two matrices:[br][br][list=1][*]We have our input-output matrix, [b]A[/b], 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, [b]X[/b], which represents the number of units of each commodity produced.[br][/*][/list][br]The matrix [b]AX[/b] gives the amount of each commodity used in the production process.[br][br]The [i]demand matrix[/i], [b]D[/b], is equal to the number of units of each commodity produced, minus the number of units used to produce these commodities. [b]D = X - AX[/b].