Question

A simple economy consists of two industries: agriculture and manufacturing. The production of 1 unit of agricultural products requires the consumption of 0.2 unit of agricultural products and 0.3 unit of manufactured goods. The production of 1 unit of manufactured goods requires the consumption of 0.4 unit of agricultural products and 0.3 unit of manufactured goods. (a) Find the total output of goods needed to satisfy a consumer demand for $100 million worth of agricultural products and $160 million worth of manufactured goods. (Round your answers to one decimal place.) agricultural products $ million manufactured goods $ million (b) Find the value of the goods consumed in the internal process of production in order to meet the gross output. (Round your answers to one decimal place.) agricultural products $ million manufactured goods $ million

Answer 1

Solution:

1. Let the total output of agricultural and manufactured goods required be denoted by x and y, respectively.

Then, if 1 unit of agriculture good requires 0.2 unit of agricultural good and 1 unit of manufactured good requires 0.4 units of agricultural good, total requirement of agricultural good by both industries is

0.2*x + 0.4*y ; as if 1 unit of agricultural good requires 0.2 units of its own good, then x units would require 0.2*x units of its own. Furthermore, the amount of production left after being utilized as inputs, should be enough to sustain consumer demand. So, we have input demand + consumer demand = total production

0.2*x + 0.4*y + 100 = x

Or 0.8*x - 0.4*y = 100 ...(*)

Similarly, for manufactured good we have:

0.3*x + 0.3*y + 160 = y

And so, -0.3*x + 0.7*y =160 ... (**)

Solving the above two equations simultaneously, we get values of x and y:

From (*), we have y = 2x - 250

Substituting this in (**), -0.3x + 0.7(2x - 250) = 160

-0.3x + 1.4x - 175 = 160

x = $304.54 million

And y = 2*304.54 - 250 = $359.08 million

Value of goods consumed in internal process = gross output - consumer demand

So, for agricultural goods, this value = 304.54 - 100 = $204.54 million

And for manufactured goods, this value = 359.08 - 160 = $199.08 million