Question

In: Economics

Consider an industry in which all firms have constant marginal costs of 50, MC = 50,...

Consider an industry in which all firms have constant marginal costs of 50,
MC = 50, and market demand is Qd = 385 - 0.5P
(a) If there are two firms operating as Cournot duopolists, find the equilibrium price
and total quantity
(b) If there are two firms operating as Stackelberg duopolists, find the equilibrium price,
how much the leader firm produces and how much the follower firm produced?

Expert Solution

b. Assume A is sophisticated firm, B is follower firm.

A's profit function=

720Q1-2Q12-2 Q1Q2

Substitute B’s reaction function in in A’s profit function

Profit funtion= 720 Q1-2Q12-2 Q(180-.5 Q1)

=720 Q1- Q12-360 Q1

=360 Q1- Q12

Maximise

First derivative of profit function

360-2 Q1

Q1=180

Q2= 180-.5(180)

=90

P=720-2(180+90)

=180

Rahul Sunny answered 2 years ago

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