# Calculations using Price Elasticity of Demand

3. Using the midpoint formula, calculate elasticity for each of the following changes in demand by a household.

(see attached file for data).

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.

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#### Solution Preview

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:

a)

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

Similarly:

b) Ed = -0.65

c) Ed = -0.69

d) Ed = -1

4. ...

#### Solution Summary

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.