In a homogeneous products duopoly, each firm has a marginal cost curve MC = 10 + Qi,

Question:

In a homogeneous products duopoly, each firm has a marginal cost curve MC = 10 + Qi, i = 1, 2. The market demand curve is P = 50 - Q, where Q = Q1 + Q2.
a) What are the Cournot equilibrium quantities and price in this market?
b) What would be the equilibrium price in this market if the two firms acted as a profit-maximizing cartel?
c) What would be the equilibrium price in this market if firms acted as price-taking firms?