The Ali Baba Co. is the only supplier of a particular type of Oriental carpet. The estimated demand for its carpets is
Q = 112,000 − 500P + 5M
where Q = number of carpets, P = price of carpets (dollars per unit), and M = consumers’ income per capita. The estimated average variable cost function for Ali Baba’s carpets is
AVC = 200 − 0.012Q + 0.000002Q2
Consumers’ income per capita is expected to be $20,000 and total fixed cost is $100,000.
a. How many carpets should the firm produce in order to maximize profit?
b. What is the profit-maximizing price of carpets?
c. What is the maximum amount of profit that the firm can earn selling carpets?
d. Answer parts a through c if consumers’ income per capita is expected to be $30,000 instead.