Question

Two firms compete as a Stackelberg duopoly. The inverse market demand they face is P = 62 − 4.5Q. The cost function for each firm is C(Q) = 8Q. The outputs of the two firms are:

Multiple Choice
QL = 48; QF = 24.
QL = 35; QF = 6.
QL = 6; QF = 3.
None of the answers is correct.

Answer 1

To determine the outputs of the two firms in a Stackelberg duopoly, we need to solve for their reaction functions. The correct outputs of the leader and follower firms in this case are QL = 6 and QF = 3.

Step-by-step explanation:

To determine the outputs of the two firms in a Stackelberg duopoly, we need to find the quantities at which the firms maximize their profits. In a Stackelberg duopoly, one firm acts as the leader and determines its output level first, while the other firm acts as the follower and adjusts its output accordingly.

To find the outputs, we need to solve for the reaction functions of the firms. The reaction function of the leader firm is obtained by setting the derivative of its profit with respect to its output equal to zero. The reaction function of the follower firm is obtained by setting the derivative of its profit with respect to its output equal to zero, taking into account the output chosen by the leader.

In this case, the reaction functions can be derived as follows:

Leader reaction function: QL = (62 - 4.5QF - 8) / (2*4.5)

Follower reaction function: QF = (62 - 4.5QL - 8) / (2*4.5)

By solving these equations simultaneously, we can find the values of QL and QF. In this case, the correct outputs are: QL = 6 and QF = 3. Therefore, the answer is QL = 6; QF = 3.