"Suppose now that a second firm enters the market. Let Q1 be the output of the first firm, yours, and Q2 the output level of the second firm. Market demand is now given by Q1 + Q2 = 53 - P or inverse demand can be expressed as P = 53 - Q1 - Q2. Also assume the second firm has adopted the same technology as you and thus has the same costs (both in total and per unit) as you. As in the Cournot model, with simultaneous choices of Qi, each firm chooses its profit maximizing level of output on the assumption that its competitor's output is fixed at its' profit maximizing level.
b. Find each firm's "reaction function" or "reaction curve," the statement that expresses a firm's desired output in terms of its competitor's output [i.e., Q1 = f(Q2) and Q2 = f(Q1)].
c. Calculate the Cournot equilibrium, the levels of each firm's output at which each firm is doing as well as it can.