4. A sporting goods store has estimated the demand curve for a popular brand of running shoes as a function of price. Use the diagram (see attached) to answer the questions that follow.
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 show sales (calculate P X 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.
3. The midpoint formula for price elasticity is:
Ed = ((P1 + P2)/(Q1 + Q2)) x ((Q2 - Q1)/(P2 - P1))
Applying this formula to the given data:
Ed = ((0.25 + 0.15)/(300 + 400)) x ((400 - 300)/(0.15 - 0.25))
Ed = (0.40/700) x (100/-0.10)
Ed = -0.57
b) Ed = -0.65
c) Ed = -0.69
d) Ed = -1
This solution shows how to use the midpoint formula to calculate price elasticity of demand. It goes on to calculate changes in a shoe store's total revenue (TR) when it changes its price, and explain how to predict the direction of change of TR when the store's elasticity at that price is known.