The demand function for football tickets for a typical game at a large university is D(p) = 200,000 -10,000p. The university has a clever and avaricious athletic director who sets his ticket prices so as to maximize revenue. The university's football stadium holds 100,000 spectators.
(a) Write expressions for total revenue and marginal revenue as a function of the number of tickets sold and compute the profit-maximizing quantity of tickets. Find the marginal revenue and price elasticity of demand at this quantity. (Hint: First write down the inverse demand function, i.e. price as a function of quantity demanded).
(b) A series of winning seasons caused the demand curve for football tickets to shift upward. The new demand function is q(p) = 300,000 -10,000p. Write a new expression for marginal revenue as a function of tickets sold. Given the constraint imposed by the stadium capacity, find the price that would maximize the stadium revenue (and profit). Also find the price elasticity of demand. (Note: The marginal revenue at the maximum number of available seats is positive).