A firm sells some output in a perfectly competitive market, where the price is $60 per unit, and some on a market in which it has a monopoly, with a demand function p2= 100 – q2, where q2 is output in the monopoly market. Its total-cost function is C= (q1+q2)^2, where q1 is output in the competitive market. Find the profit maximizing outputs in the two markets and discuss the nature of the equilibrium.
Suppose now that the price in the competitive market falls to $10.
Find the new profit-maximizing solution, and discuss how it compares with the original.