Answer to Question #70632 in Microeconomics for nouga

Question

If the price of a good rises by 10 percent and quantity demanded falls by 20
percent, we can predict that
please i need help and explanation for the answer

Answer 1

The question concerns the indicator that shows the extent to which the price of a good (p) influences quantity demanded (q). It’s so called “price elasticity of demand” (E(p)).
Price elasticity of demand is the relative change in quantity demanded given a one percent change in the price.
E_((p))=(∆q/q)/(∆p/p);
If the price of a good rises by 10 percent and quantity demanded falls by 20 percent the value of the price elasticity will be
E_((p))=(∆q/q)/(∆p/p)=(-0.2)/(+0.1)=-2.0.
It means that one percent change in price stipulates 2% decrease in quantity demanded by consumers, and that the demand for this good is quite elastic  |E_((p)) |>1.
We can predict that the total revenue (TR) of the firm, that produces / sells the good will decline
Let
〖TR〗_0=pq.
After the changes:
〖TR〗_1=p(1+1.1)×q(1-0.2)=1.1p×0.8q=0.88pq=0.88〖TR〗_0.
So the total revenue (TR) of the firm will decline by 12% (10.88).