Three firms, 1, 2, and 3, produce quantities q₁, q₂ and q₃ of the same good with market demand P = 100 2Q, where Q = q₁ + q₂ + q₃ is the total market supply. The total costs of each firm are expressed as

C (q_i) = 10q_i + 0.5q_i²

If the firms are in Cournot competition:

(a) Find the Nash equilibrium quantities of the game.

(b) Find the outcome which maximises the sum of the three firms' profits subject to q1 = q2 = q3. Why can this not be sustained in Nash equilibrium?