Suppose that a firm produces three outputs y1, y2 and y3 with 3 inputs z1, z2 and z3. The input-output requirements matrix is given by A below:
A = (3 1 2)
(2 5 1)
(1 1 3)
If the firm wants to produce 10 units of y1, 20 units of y2 and 10 units of y3, how much of z1, z2 and z3 will it require?
Solution
A*Z =Y
so, (3 1 2) (z1) (y1)
(2 5 1) * (z2) = (y2)
(1 1 3) (z3) (y3)
3z1 + z2 +2z3 = 10
2z2 +5z2+ z3 = 20
z1+z2+3z3 = 10
solving these equations we get
z1 = 0.96 = 1
z2 = 3.22 = 3
z3 = 1.93 = 2
.
Suppose that a firm produces three outputs y1- y2 and y3 with 3 inputs.docx
1. Suppose that a firm produces three outputs y1, y2 and y3 with 3 inputs z1, z2 and z3. The input-
output requirements matrix is given by A below:
A = (3 1 2)
(2 5 1)
(1 1 3)
If the firm wants to produce 10 units of y1, 20 units of y2 and 10 units of y3, how much of z1, z2
and z3 will it require?
Solution
A*Z =Y
so, (3 1 2) (z1) (y1)
(2 5 1) * (z2) = (y2)
(1 1 3) (z3) (y3)
3z1 + z2 +2z3 = 10
2z2 +5z2+ z3 = 20
z1+z2+3z3 = 10
solving these equations we get
z1 = 0.96 = 1
z2 = 3.22 = 3
z3 = 1.93 = 2
