An economy is based on two sectors,agriculture and manufacturing.Production of a dollar's worth of agriculture requires an input of $0.40 from agriculture and $0.10 from manufacturing.Production of a dollar's worth of manufacturing requires an input of $0.20 from agriculture and $0.30 from manufacturing.Find the output for each sector that is needed to satisfy a final demand of $16 billion for agriculture and $32 billion for manufacturing.
A) $44 billion agriculture, $52 billion manufacturing
B) $36 billion agriculture, $56 billion manufacturing
C) $56 billion agriculture, $36 billion manufacturing
D) $52 billion agriculture, $44 billion manufacturing

Question

Quizplus · Accepted Answer

To solve this, we can set up equations based on the input-output model. Let $A$ be the total output needed for agriculture and $M$ for manufacturing. The equations based on the given information are:$$A = 0.4A + 0.1M + 16$$$$M = 0.2A + 0.3M + 32$$Solving these equations simultaneously gives us $A = 44$ billion and $M = 52$ billion, which corresponds to choice A.

An Economy Is Based on Two Sectors,agriculture and Manufacturing