Use the following information to answer the problems below:
Q1 = 500 - 10P
Q2 = 700 - 40P
Q = 1,200 - 50P
where Q1 is the quantity demanded for group 1, Q2 is the quantity demanded for group 2, and Q is the sum of the two demands for the two types of consumers. The marginal cost of serving either group is $10.
a. find out the profit-maximizing level of output and price if the company sells all of its tickets at one price.
b. find out the profit-maximizing level of output and price if it charges different prices to each group.
c. Compare the level of profits under part (a) and (b) above.
d. What condition or conditions would need to hold for the firm to be able to charge a different price to each group?