Question

The inverse demand curve for a Stackelberg duopoly is P =1932 - 3Q. The leader's cost structure is
CL(QL) = 13QL. The follower's cost structure is CF(QF) = 25QF.

Find the follower revenue

Round all calculations to 1 decimal

Answer 1

Here QL +QF =Q

Therefore, we can rewrite the market demand function as

P= 1932-3(QL+QF) Also given cost functions of the duopolist firms are

CL = 13QL and CF= 25QF

profit of the leader firm ₁ = PQL-CL = QL(1932-3(QL+QF))-13QL= 1932QL-3(QL)²-3QLQF-13QL ........(i)

profit of the follower firm ₂ = PQF-CF = QF(1932-3(QL+QF))-25QF= 1932QF-3QLQF-3(QF)² -25QF.........(ii)

The stackelberg's duopoly profit maximization conditions are,

₁/QL =0 and ₂/QF = 0

Therefore taking partial derivative with respect to QL of (i),

₁/QL = 1932-6QL-3QF-13= 1919-6QL-3QF=0 .............(iii)

taking partial derivative with respect to QF in (ii) we get,

₂/QF = 1932-3QL-6QF-25= 1907-3QL-6QF=0 .......(iv)

Solviing (iii) and (iv) we get,

    QF = 210.5 and QL= 214.6

Therefore revenue of the follower firm = PQF= (1932-3(210.5+214.6))*210.5 =$138235.3