Question

Jessica Simpson sets up shop to sell “Buffalo Wings.” She observes that if the price drops from $3.50 per order to $2.50 per order, her daily sales rise from 300 to 500 orders.
A. What is the price elasticity of demand for Jessica’s “Buffalo wings?”

B. Which price yields the greater total revenue?

C. Jessica is considering adding a new product, widgets, to the menu. She has experimented and discovered that a 10% increase in the price of wings causes a 20% increase in the quantity of widgets sold. What is the cross elasticity of demand between widgets and wings? Are they complements or substitutes??

D. What is the difference between the price elasticity of demand and the slope of the demand curve? Are they the same concept? Are they even related concepts?

Answer 1

A. Elasticity of demand = (Change in quantity/Change in price)*(Initial price/Initial quantity)
= [(500-300)/(2.50-3.50)]*(3.50/300) = [200/(-1)]*(3.50/300) = (-200)*(3.50/300) = -2.33 = elasticity of demand

B. $2.50 yields a greater revenue. This is because demand is elastic which means that as price decreases then total revenue increases. So, revenue is higher with $2.50

C. The cross elasticity of demand between widgets and wings = Percentage change in the quantity of widgets sold/Percentage change in the price of wings = 20%/10% = 2
So, cross elasticity of demand between widgets and wings = 2
Thus, they are substitutes as cross elasticity of demand between widgets and wings is positive.

D. The price elasticity of demand is the percentage change in quantity demanded due to a percentage change in price. So, it is a relative concept as it considers relative changes. Whereas, slope of the demand curve is change in price to change in demand. So, it is an absolute concept as it considers absolute changes.
Though they are not the same concept but they are related concepts. The mathematical relationship between them is as follows:
Elasticity of demand = (1/Slope)*(Price/Quantity)
Thus, they are inversely related to each other.