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.
Market Demand Equation - Price Elasticity
1. A market consists of two individuals. Their demand equations are Q1 = 16-4P and Q2 = 20-2P respectively.
a. What is the market demand equation?
b. At a price of $2, what is the point price elasticity for each person and for the market?