The demand function for a Rolling Stones concert is D = 200, 000 −10, 000p. The Rolling Stones' manager
sets the ticket prices so as to max- imise revenue. The SkyDome, where the concert is to be held, holds 100,000 spectators.
a) Write down the inverse demand function.
b) Write expressions for total revenue and marginal revenue as a function of the number of tickets sold.
c) Graph the inverse demand function and the marginal revenue function. Also draw a line representing the capacity of the SkyDome.
d) What price will generate the maximum revenue? What quantity will be sold at this price?
e) At this quantity, what is marginal revenue? At this quantity, what is the price elasticity of demand? Will the SkyDome be full?
f) Imagine now that the demand curve for tickets shifts upward. The new demand function is q(p) = 300, 000 − 10, 000p. What is the new inverse demand function?
g) Jot down an expression for marginal revenue as a function of output. In your graph, draw the new demand function and the new marginal revenue function.
h) Ignoring stadium capacity, what price would generate maximum rev- enue? What quantity would be sold at this price?
i) As you noticed above, the quantity that would maximize total rev- enue given the new higher demand curve is greater than the capacity of the stadium. Clever though the manager is, he cannot sell seats he hasn't got. He notices that his marginal revenue is positive for any number of seats he sells up to the capacity of the stadium. Therefore, in order to maximize his revenue, how many tickets should he sell and at what price?
j) When he does this, what is his marginal revenue from selling an extra ticket? What is the elasticity of demand for tickets at this price quantity combination?