A concert is scheduled to perform at a theater with seating capacity 80. All tickets for this concert are to be sold in advance at a single uniform price per seat. Because too many empty seats can make the concert less enjoyable, the demand curve for the performance has the following form:
Q=100-P for Q<56
Q=100-P +1/2(Q-56) for 56

The owner of the theater sets the price for concert tickets, and pays all costs. These costs, including the concert's fee, can be expressed as a constant marginal cost of $ c per ticket.

a) Graph the demand curve for this concert, and the associated marginal revenue curve. Show and explain your derivation.

b) if c=0, what price and quantity should the owner choose?

c) Find the critical value of c (call it c*)that determines whether the owner will set the price so as to get an audience that fills more than 70% of the arena. Explain intuitively how the owner's profit-maximizing decision depends on whether c is above or below c*.

d) If the owner currently sets the level of Q at 55, what must be the value of c be? Explain

e) Suppose that consumer preferences change in such a way that demand is now equal to:

Q=100-P for Q<56
Q=100-P +(Q-56) for 56How does the owner's profit maximizing decision change as the level of c changes?