A simple economy consists of two industries: agriculture and manufacturing. The production of 1 unit of agricultural products requires the consumption of 0.1 unit of agricultural products and 0.1 unit of manufactured goods. The production of 1 unit of manufactured products requires the consumption of 0.1 unit of agricultural products and 0.4 unit of manufactured goods. Find the gross output of goods needed to satisfy a consumer demand for $140 million worth of agricultural products and $140 million worth of manufactured products. Round answers to the nearest tenth, if necessary.
A) $449.06 million
B) $826 million
C) $210 million
D) $328.3 million
E) $477.5 million

Question

A simple economy consists of two industries: agriculture and manufacturing. The production of 1 unit of agricultural products requires the consumption of 0.1 unit of agricultural products and 0.1 unit of manufactured goods. The production of 1 unit of manufactured products requires the consumption of 0.1 unit of agricultural products and 0.4 unit of manufactured goods. Find the gross output of goods needed to satisfy a consumer demand for $140 million worth of agricultural products and $140 million worth of manufactured products. Round answers to the nearest tenth, if necessary. ​
A) $449.06 million
B) $826 million
C) $210 million
D) $328.3 million
E) $477.5 million

Quizplus · Accepted Answer

To satisfy the consumer demand, we need to solve a system of equations that accounts for both the direct consumer demand and the inter-industry demand (the goods each industry needs from itself and the other to produce its output). Let $A$ be the gross output of agricultural products and $M$ the gross output of manufactured products needed.The equations based on the problem statement are:$$A = 0.1A + 0.1M + 140$$$$M = 0.1A + 0.4M + 140$$Solving these equations for $A$ and $M$, we find:$$0.9A - 0.1M = 140$$$$-0.1A + 0.6M = 140$$Multiplying the first equation by 6 and the second by 9 to eliminate $M$, we get:$$5.4A = 840$$$$5.4A = 1260$$Adding these equations, we find the total gross output needed ($A + M$) is approximately $449.06 million.

A Simple Economy Consists of Two Industries: Agriculture and Manufacturing