Answer
see explanation
Work Step by Step
Goods Services
0.2
0.7
Goods
0.8
0.3
Services
Each column refers to the fraction of output from one branch to the other $(\mathrm{s}) .$ e.g the second column says that Services sell 0.7 of its output to Goods and retains the rest 0.3 of its output to itself. Let $P_{G}$ be a price for goods be and let $P_{S}$ be a price for services. Goods spends $0.2 P_{G}+0.7 P_{S}$ and Services spends $0.8 P_{G}+0.3 P_{S} .$ To balance the income and outcome we need
$0.2 P_{G}+0.7 P_{S}=P_{G}$
$0.8 P_{G}+0.3 P_{S}=P_{S}$
Here we simply equate outcome price to income price. We rewrite these equations as follows:
$0.8 P_{G}-0.7 P_{S}=0$
$0.8 P_{G}-0.7 P_{S}=0$
It is actually the same equation with the solution $P_{G}=\frac{7}{8} P_{S}$ It follows that the prices can be chosen,e.g, as follows:
$P_{S}=8, P_{G}=7$ or
$P_{S}=80, P_{G}=70$ or
$P_{S}=40, P_{G}=35$
The only condition is that the ratio of the prices is $P_{G}: P_{S}=7: 8$
