Answer to Question #194268 in Microeconomics for Fadzai Mawoyo

Question

Fadzi's demand curve for food is Q=10-2p. Her price elasticity of demand for food at price P*equals -2/3. How much is P*?

Answer 1

The demand curve of Fadzi's food is as follows:

 Q=10-2p (Given)

The price elasticity of Fadzi's food = -2/3 (Given)

Now substitute these values in the formula of price elasticity of demand to obtain a value of price:

$Q=10-2P\\\frac{dQ}{dP}=-2\\e_d=\frac{(dQ_f)P}{(dP)Q_f}\\\frac{-2}{3}=-2\times\times\frac{P}{10-2P}\\-2(10-2P)=-6P\\10-2P=3P\\-2P-3P=-10\\-5P=-10\\P=\frac{-10}{-5}\\P=2$

Thus P* will be $2.