The company has the choice of selling tickets to its concerts or of selling CDs. Let P1 and Q1 be the price and quantity of concert tickets. Similarly, let P2 and Q2 be the number of CDs. The demand for Concerts is P1=100-12Q1+P2 and the demand for CDs is P2 = 50-3Q2+0.5P1. The marginal cost of selling a concert ticket is 0 and of selling a CD is $2.
a. What is the optimal price of a concert ticket? How many tickets are sold at the
b. What is the optimal price of a CD? How many CDs are sold at the optimal price?
Hint: Determine the two marginal revenue functions. These two along with the two demand functions will give you four equations. Solve these 4 equations for the 4 unknowns- P1, P2, Q1 and Q2.
P1xQ1 = 100Q1 - 12Q1^2 + P2Q1
MR (Concert Tickets) = 100 - 24Q1 + P2
P2 = 50-3Q2+0.5P1
P2xQ2 = 50Q2 - 3Q2^2 +0.5P1Q2
MR (CD) = 50 - 6Q2 + 0.5P1
For profit maximization MR = MC
100 - 24Q1 + P2 = ...
The solution provides excellent answer to the problem below. The expert determines the optimal price and marginal revenue functions for two demand functions.