Consider the following learning-by-doing two-stage model of strategic choice. Firm 1 is an incumbent in the first period and behaves as a monopolist. In the second period firm 2 enters the market. Firm 1 has a first-period cost function of 1(q11) = 4 q11 (where qi j denotes the output of firm i in period j ), while it has a second-period cost function given by c1(q12) = (4 − 0.5q11)q12.
Firm 2’s second-period cost function is c2(q22) = 4q22. Note that industry demand in period i is given by Pi = 10 − Qi , where second-period total output is Q2 = q12 + q22.
(a) Find firm 1’s optimal, monopolist level of output in the first period (qM 11 ), without taking into account any second-period information. Also calculate its period 1 profits.
(b) Assuming that firm 1 chose q11 = qM 11 in period 1, solve for the Cournot quantity competition outputs of both firms in the second stage. Calculate firm 1’s total undiscounted profits over the two periods.
(c) Show that firm 1 can increase its total profits by altering its first-period level of output qM 11 , from the level derived in (a). [Hint: consider small changes.]
(d) Explain under the taxonomy of accommodation strategies why this is possible.