In Bayonne, New Jersey, there is a large beauty salon and a number of smaller ones. The total demand function for hair styling per day is Q=180-10P, where P is in dollars. The marginal cost function of all the small salons together is SMCf=4+0.1Q, and the marginal cost function on the dominant or leading salon is MCL=7+0.1Q.
If the large salon forms a centralized cartel, what would be the best level of output per day and price? How much will be supplied by the dominant salon and by all the small salons together if the cartel wants to minimize the total costs of producing the best level of output for the cartel as a whole?