The typical demand function of match tickets of FC Barcelona is q (p) = 200.000- 10.000p. The goal of managers is to maximize their revenue. The total capacity of the stadium is 100.000 viewers.
a) Write the inverse demand function.
b) Write expressions for the Total Income (I) and the Marginal Revenue (Img) as functions of the total number of tickets sold.
c) What price will generate the most revenue? What amount of tickets will be sold at this price?
d) Selling the amount of the previous section, what is marginal revenue? What is the price elasticity of demand for tickets? Is the stadium full?
Due to the current good luck of the team, the demand for tickets has increased and has become q (p) = 300.000-10.000p.
e) What is the new inverse demand function?
f) Write an expression for marginal revenue as a function of the number of entries.
g) Ignoring stadium capacity, what price will generate the most income? How many tickets would be sold at this price?
h) Taking now into account the capacity of the stadium, how many tickets will go on sale to maximize revenue? At what price?