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 SMC_F = 4 + 0.Q,
and the marginal cost of the dominant or leading salon is MC_L = 7 +
0.1Q.

(a) Draw a figure showing D_T,
SMC_F,
MC_L, D_L, MR_T, MR_L, and the
horizontal summation of SMC_F and MC_L.

(b) Determine the best level of
output and price of hair styling for the dominant and for the smaller salons if
the large or dominant salon operates as the price leader. How many stylings
will the large salon supply per day? How many will the small salons supply
together?

(c) If the large salon forms a
centralized cartel, what would be the best level of output per day and the
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 cost by producing the
best level of output for the cartel as a whole?

(d) What would be the equilibrium
output level and price if the large salon did not exist and the small salons
operated as perfect competitors?

(e) What would be the best level
of output and price if the large salon did exist in the market but operated as
a perfect competitor, just like the small ones?