Suppose a primitive economy consists of two industries, farm products and farm machinery. Suppose also that its technology matrix is If surpluses of 97 units of farm products and 18 units of farm machinery are desired, find the gross production of each industry.

Question

Suppose a primitive economy consists of two industries, farm products and farm machinery. Suppose also that its technology matrix is ​  If surpluses of 97 units of farm products and 18 units of farm machinery are desired, find the gross production of each industry.
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Quizplus · Accepted Answer

To solve this question, we need to use the inverse of the technology matrix to find the levels of production required for the desired surpluses. 
The inverse of the matrix is:
0.189 -0.053
-0.211 0.242

Multiplying this by the desired surpluses gives:
(0.189)(97) + (-0.053)(18) = 17.985
(-0.211)(97) + (0.242)(18) = 37.215

Therefore, the gross production of farm products is:
97 + 17.985 = 114.985, which we can round to 115 units

And the gross production of farm machinery is:
18 + 37.215 = 55.215, which we can round to 55 units

So, the best choice is D, with a gross production of 205 units of farm product and 55 units of farm machinery.

Suppose a Primitive Economy Consists of Two Industries, Farm Products