Answer to Question #145538 in Microeconomics for Vishnu

Question

Suppose favorable weather increased the supply of tomatoes so that the price of tomatoes fell from US$45 a ton to US$35 a ton and quantity sold increased from 300 tons to 420 tons. What is the value of the price elasticity of demand? Show your work.

Answer 1

Initial price $P_1= 45$

Final price $P_2= 35$

Initial quantity $Q_1= 300\;tons$

Final quantity $Q_2= 420\;tons$

Rise in quantity sold indicates rise in quantity demanded.

Arc elasticity is given as the avg percentage change in quantity demanded/avg percentage change in price.

Midpoint of $Q (Q')= \frac{Q_1+Q_2}{2} = \frac{720}{2} = 360$

Midpoint of $P (P') = \frac{P_1+ P_2}{2} = \frac{80}{2} = 40$

Avg percentage change in quantity $= \frac{Q_2- Q_1}{Q'} = \frac{120}{360} = 0.333$

Avg percentage change in price $= \frac{P_2 - P_1}{P'} = \frac{-10}{40} = -0.25$

Elasticity of demand $= \frac{0.333}{-0.25} = -1.332$

The negative sign indicates inverse relation of price and quantity.