Answer:
The revenue maximizing price will be $16.33.
Explanation:
The capacity of an athletic stadium is 105,000 people.
When the ticket price is $22, the attendance is 32,000.
When the ticket price is $16, the attendance is 50,000.
The slope of the demand curve will be
= [tex]\frac{50,000\ -\ 32,000 }{16\ -\ 22}[/tex]
= [tex]\frac{18,000}{-6}[/tex]
= -3,000
Q = -3,000p + b
At p = 16, Q = 50,000
50,000 = -3,000 (16) + b
b = 98,000
The linear equation is
Q = -3,000p + 98,000
The total revenue will be
= [tex]Price\ \times\ Quantity[/tex]
= [tex]-3,000p^2 + 98,000p[/tex]
The marginal revenue will be
= [tex]\frac{d}{dp} (TR)[/tex]
= [tex]\frac{d}{dp} (-3,000p^2 + 98,000p)[/tex]
= -6,000p + 98,000
The total revenue will be maximized when the marginal revenue is equal to zero.
-6,000p + 98,000 = 0
p = [tex]\frac{98,000}{6,000}[/tex]
p = 16.33
