Philadelphia is the home of the cheesesteak, and the two most popular cheeseteak
ID: 3182101 • Letter: P
Question
Philadelphia is the home of the cheesesteak, and the two most popular cheeseteak restaurants, Pat’s and Geno’s, are bitter rivals located across the street from each other. (For simplicity, assume that these are the only two places that serve an ”authentic” Philly cheesesteak.) Both restaurants have very loyal customer bases. According to market research, 80% of the customers who purchased a Pat’s cheesesteak this month will continue to eat at Pat’s next month; consequently, 20% of the customers who purchased a Pat’s cheesesteak will instead walk across the street and eat at Geno’s next month. Meanwhile, 70% of the customers who purchased a Geno’s cheesesteak this month will continue to eat at Geno’s next month.
Assume that, in the current month (March), 55% of cheesesteak eaters went to Pat’s.
(a) What are the predicted market shares for the two restaurants in May? (b) What are the equilibrium market shares for the two restaurants?
Explanation / Answer
(a) In the month of March, 55% of Cheesesteak eaters went to Pat's so 45 % must have went to Geno's restaurent.
so APril customer percentage base
For Pat's = 0.8 * 55 + 0.3 * 45 = 57.5
FOr geno's = 0.7 * 45 + 0.2 * 55 = 42.5
FOr May Customer percentage base
For Pat's = 0.8 * 57.5 + 0.3 * 42.5 = 58.75
FOr geno's = 0.7 * 42.5 + 0.2 * 57.5 = 41.25
(b) Equilibrium market share. Let say for given month the market share of Pat's is Xn % and for Geno's 100 - Xn %
so for equilbrium Customer percentage base
FOr Pat's Xn+1 = 0.8*Xn + 0.3 * ( 1- Xn ) = 0.5 Xn + 0.3
for equilibrium phase Xn+1 = Xn = Xeq.
Xeq. = 0.5 Xeq. + 0.3
0.5 Xeq. = 0.3
Xeq. = 0.3/0.5 = 60 %
so in equilibrium, Pet's market share would be 60 % and for Geno's, it would be 40%