A simplified economy is based on agriculture, manufacturing, and transportation.

Question

A simplified economy is based on agriculture, manufacturing, and transportation. Each unit of agricultural output requires 0.3 unit of its own output, 0.5 of manufacturing, and 0.2 unit of transportation output. Each unit of manufacturing output requires 0.3 unit of its own output, 0.1 of agricultural, and 0.4 unit of transportation output. Each unit of transportation output requires 0.4 unit of its own output, 0.2 of agricultural, and 0.1 of manufacturing output. There is demand for 95 units of agricultural, 90 units of manufacturing, and 80 units of transportation output. How many units should each segment of the economy produce?

A) Agriculture: 440; manufacturing: 555; transportation: 390

B) Agriculture: 555; manufacturing: 390; transportation: 440

C) Agriculture: 555; manufacturing: 440; transportation: 390

D) Agriculture: 390; manufacturing: 440; transportation: 555

Explanation / Answer

Given an input-output matrix A, production matrix X and demand matrix D, they are related by the matrix equation

D = X-AX

To find the production matrix, we need to solve for X,

D = (I-A)X where I is the identity

X = (I-A)-1D

So to fulfil the predicted demand, Agriculture: 365.66, manufacturing: 471.08, Transportation: 569.27

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