Question

"An economy is based on three sectorsdashagriculture​, ​manufacturing, and services. For each unit of​ output, agriculture requires inputs of 0.20 unit from​ agriculture, 0.40 unit from​ manufacturing, and 0.20 unit from services. For each unit of​ output, manufacturing requires inputs of 0.30 unit from​ agriculture, 0.20 unit from​ manufacturing, and 0.20 unit from services. For each unit of​ output, services requires 0.20 unit from​ agriculture, 0.30 unit from​ manufacturing, and 0.30 unit from services. Determine the production levels needed to satisfy a final demand of 0 units for​ agriculture, 40 units for​ manufacturing, and 0 units for services. The production level needed from the agricultural sector is 40.00 units."

Answer 1

Required Production to fullfil a Demand for 40 industry units

Agriculture 54.4

Industry 83.2

Services 51.2

Step-by-step explanation:

Input Agricuilture Industrial Service

Agriculture 0.2 0.3 0.2

Industrial 0.4 0.2 0.3

Service 0.2 0.2 0.3

We require X input to generate a demand of 0 agriculture 40 industry and 0 services

The previous matrix will be the input we solve for the output

Output Agricuilture Industrial Service

Agriculture 0.8 -0.7 -0.8

Industrial -0.6 0.8 -0.7

Service -0.8 -0.8 0.7

We now reverse the matrix using excel:

Output Agricuilture Industrial Service

Agriculture 2 1.36 0.96

Industrial 1 2.08 0.88

Service 1 1.28 2.08

Now we multiply this by our desired outcome of

0

40

0

Agriculture 54.4

Industry 83.2

Services 51.2