Question

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?

Answer 1

If you read the input output matrix, you will see that it takes the following inputs to produce 1 unit of y1

3 of z1, 1 of z2 and 2 of z3

and similarly for y2 and y3

We can get the requirements of z1, z2 and z3 as below.

		Needs the following inputs units
	One unit of output	z1	z2	z3
	y1	3	1	2
	y2	2	5	1
	y3	1	1	3
		Needs the following inputs units
	Output needed	z1	z2	z3
y1	10	30	10	20
y2	20	40	100	20
y3	10	10	10	30
	Total inputs	80	120	70

80 units of z1, 120 of z2 and 70 of z3 are required.