An example of a simplified economy with just three sectors: agriculture, manufacturing, and households (that is, the sector of the economy that produceslabor) is shown in thefollowing input-output matrix:

Agriculture

Manufacturing

Households

Agriculture

.25

.40

.133

Manufacturing

.14

.12

.100

Households

.80

3.60

.133

The rows of the matrix represent the input, and the columns represent the output.The purpose of this assignment is to use input-output analysis tofind theproduction levels needed to meet a demand of 35 units of agriculture, 38 units of manufacturing, and 40 units of households.

Assignment Steps:

Step #1:Write the information in the table above as a 3x3 matrix, A.

Step #2:CalculateI - A, where I is the 3x3 Identity matrix.

Step #3: Find theinverse ofI -A.

Step #4:Write the demandmatrix, D, as a column matrix.

Step #5: Find the production matrix by calculating (I - A)-1D.

Step #6:Answerthequestions below.

a)How many units from each sector does the manufacturing sector require to produce 1 unit?

b)What production levels are needed to meet a demand of 35 units of agriculture, 38 units of manufacturing, and 40 units of households?(NOTE: see the column matrix in step #5)