Question

8. Suppose that demand for OVO themed lint rollers is given by

? = 120 – ?.

There are only two firms that produce this coveted product, they both have cost function

?? = 60 + q? 2 , where ? = 1,2 denotes the factory.

Total production of the lint rollers is equal to output from the two firms.

a. [10 marks] Suppose the two firms compete on quantities. Find the Nash equilibrium price and output of each firm. How much profit does each firm make?

b. [15 marks] Suppose that firm 1 gets this innovative product to market faster, so it makes its output decision before firm two. Find the Stackelberg equilibrium price and output of each firm. Are their profits different than in part(a)? If so, explain why.

Answer 1

Here the market price is “P=70.71” and the individual firms production are “q1 = 180/7 = 25.71” and “q2 = 165/7 = 23.57”. So, the profit of both firm are given by.

=> A1 = P*q1 – C1 = 70.71*25.71 – 60 – (25.71)^2 = 1,817.95 – 60 – 661 = $1,096.95.

=> A2 = P*q2 – C2 = 70.71*23.57 – 60 – (23.57)^2 = 1,666.63 – 60 – 555.55 = $1,051.08.

So, here we can see that under the stackelberg model the 1^st mover gets more profit than the follower. Here because the leader know that the follower will produce using its reaction faction only. So, the leader increases its produce to get more profit and the follower choose its output according to its reaction function. So, leader gets more profit and the follower gets less profit compare to “part a”.