Answer to Question #70461 in Microeconomics for Ariba

Question

Kitty Russell’s Longbranch Cafe in Sausalito recently reduced Nachos Supreme appetizer prices
from $5 to $3 for afternoon “early bird” customers and enjoyed a resulting increase in sales
from 60 to 180 orders per day. Beverage sales also increased from 30 to 150 units per day.
A. Calculate the arc price elasticity of demand for Nachos Supreme appetizers.
B. Calculate the arc cross-price elasticity of demand between beverage sales and appetizer
prices.
C. Holding all else equal, would you expect an additional appetizer price decrease to $2.50
to cause both appetizer and beverage revenues to rise? Explain
Hint: For Arc use average price (P1+ P2/2) and quantity as average quantity (Q1+Q2/2).

Answer 1

A. Calculate the arc price elasticity of demand for Nachos Supreme appetizers.
Answer
Price elasticity of demand for Nachos Supreme appetizers. = Percentage change in Quantity demand / Percentage change in price
Percentage change in Quantity demanded of Nachos Supreme appetizers = (180-60)/ (180+60)/2
Percentage change in Quantity demanded of Nachos Supreme appetizers =1
Percentage change in Price = (3-5)/(3+5)/2 = -0.5
Price elasticity of demand for Nachos Supreme appetizers = 1/-0.5 = -2

B. Calculate the arc cross-price elasticity of demand between beverage sales and appetizer
prices.
Answer
Cross-price elasticity of demand between beverage sales and appetizer = Percentage change in Quantity of beverage sale / Percentage change in price of appetizer
Percentage change in Quantity of beverage sale = (150-30)/(150+30)/2 = 1.33
Percentage change in price of appetizer = (3-5)/(3+5)/2 = -0.5
Cross-price elasticity of demand between beverage sales and appetizer = 1.33/ -0.5 = -2.66
C. Holding all else equal, would you expect an additional appetizer price decrease to $2.50 to cause both appetizer and beverage revenues to rise? Explain
Answer
Yes , decreasing price to $2.50 would increase revenues for both appetizer and beverage, because both appetizer and beverage has elastic demand and price decrease would leads to much greater increase in quantity sold and hence total revenue will rise for both.

Hint: For Arc use average price (P1+ P2/2) and quantity as average quantity (Q1+Q2/2).