Question #70537

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).

Expert's answer

P1 = $5, P2 = $3, Q1 = 60, Q2 = 180 Nachos Supreme appetizers per day. Beverage sales: Q1 = 30, Q2 = 150 units per day.

A. The arc price elasticity of demand for Nachos Supreme appetizers is:

Ed = (180 - 60)/(3 - 5)*(3 + 5)/(180 + 60) = -120/2*8/240 = -2, so demand is elastic.

B. The arc cross-price elasticity of demand between beverage sales and appetizer

prices is:

Ed = (150 - 30)/(3 - 5)*(3 + 5)/(150 + 30) = -120/2*8/180 = -2.66, so the products are complements.

C. If we expect an additional appetizer price decrease to $2.50, then it would cause appetizer and beverage revenues to rise, because the demand for appetizer is elastic and the goods are complements.

A. The arc price elasticity of demand for Nachos Supreme appetizers is:

Ed = (180 - 60)/(3 - 5)*(3 + 5)/(180 + 60) = -120/2*8/240 = -2, so demand is elastic.

B. The arc cross-price elasticity of demand between beverage sales and appetizer

prices is:

Ed = (150 - 30)/(3 - 5)*(3 + 5)/(150 + 30) = -120/2*8/180 = -2.66, so the products are complements.

C. If we expect an additional appetizer price decrease to $2.50, then it would cause appetizer and beverage revenues to rise, because the demand for appetizer is elastic and the goods are complements.

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