Question

Suppose an economy consists of three sectors: energy (e), manufacturing (m), and agriculture (a). sector e sells 70% of its output to m and 30% to
a. sector m sells 30% of its output to e, 50% to a, and retains the rest. sector a sells 15% of its output to e, 30% to m, and retains the rest.

Answer 1

Answer:

(1) Pe =0.3Pm + 0.15 Pa

Pm = 0.7Pe + 0.2 Pm + 0.3 Pa

Pa = 0.3 Pe + 0.5Pm +0.55 Pa

(2) The free variable Pa = 100

Explanation:

Solution

We create a table of outputs using the given percentages economy distribution

Energy         Manufacturing       agriculture     Purchased by

0                       0.3                       0.15                 energy

0.7                    0.2                       0.3                  manufacturing

0.3                    0.5                       0.55                Agriculture

Let Pe Pm, Pa represent the prices for each sector

We then create an income equation using the expenses of the table above

Now,

Pe =0.3Pm + 0.15 Pa

Pm = 0.7Pe + 0.2 Pm + 0.3 Pa

Pa = 0.3 Pe + 0.5Pm +0.55 Pa

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