A sporting goods store has estimated the demand curve for a popular brand of running shoes as a function of price. Use the diagram to answer the questions that follow.

Question

a. Calculate demand elasticity using the midpoint formula between points A and B, between points C and D, and between points E and F.
b. If the store currently charges a price of $50, then increases that price to $60, what happens to total revenue from shoe sales (calculate P × Q before and after the price change)? Repeat the exercise for initial prices being decreased to $40 and $20, respectively.
c. Explain why the answers to a. can be used to predict the answers to b.
(Principles of Microeconomics, 9th Edition. Pearson Learning Solutions 9.9).
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Answer 1

a. The demand elasticity between points A and B is -2.5, between points C and D is -1.25, and between points E and F is -0.5.

b. If the store currently charges a price of $50, then increases that price to $60, total revenue from shoe sales decreases from $750 to $600. If the initial price is decreased to $40, total revenue increases from $750 to $900. If the initial price is decreased to $20, total revenue increases from $750 to $1500.

c. The answers to a. can be used to predict the answers to b. because the elasticity of demand measures the responsiveness of quantity demanded to changes in price. A higher elasticity of demand indicates that a change in price will have a greater effect on the quantity demanded, and vice versa. Therefore, if the elasticity of demand is high, then a decrease in price will lead to an increase in total revenue, and an increase in price will lead to a decrease in total revenue.