Suppose that production of 1 unit of mining requires 3/5 unit of mining, 1/5 uni

Question

Suppose that production of 1 unit of mining requires 3/5 unit of mining, 1/5 unit of manufacturing, and 1/5 unit of communication. To produce 1 unit of manufacturing requires 1/5 unit of mining, 2/5 unit of manufacturing, and 2/5 unit of communication. To produce 1 unit of communication requires 0 unit of mining, 3/5 unit of manufacturing, and 2/5 unit of communicaiton. Find the ratio of the three commodities in the closed model.

The ratio is _____ units of mining to every 6 units of manufacturing and ____ units of communication.

Explanation / Answer

Let a = units of mining, b = units of manufacturing and c = units of communication. The following three equations can be written by using three unknowns

a = 3/5a + 1/5b + 1/5c ---- (i)

b = 1/5a + 2/5b + 2/5c ---- (ii)

c = 3/5b + 2/5c ---- (iii)

solving the third equation we get

3/5c = 3/5b hence (c=b)

putting in the seccond equation we get

b = a

Hence the solution is trivial (i,e, all of them are zero) or a=b=c

Hence the ratio is a:b:c = 1:1:1

Hence the correct answer is

The ratio is 6 units of mining to every 6 units of manufacturing and 6 units of communication.

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