Two Cournot competitors, Nick Limited(Orm 1) and Junior LLC(Orm 2), face an inve
ID: 1196546 • Letter: T
Question
Two Cournot competitors, Nick Limited(Orm 1) and Junior LLC(Orm 2), face an inverse demand curve p = 400 2q in the market (q = q1 + q2). Both producers have a marginal cost of $10 per unit.
(a) What is the reaction function for Nick Limited?
(b) How many units will each Orm produce? What will be the price in the market?
(c) What if Nick Limited chooses Orst (Leader) and Junior LLC follows (Follower). How many units will each Orm produce?
(d) Will the consumers be better or worse o§ in Stackleberg compared to the Cournot competition?
Explanation / Answer
Inverse demand curve: P=400-2q
Q=q1+q2
Profit for firm 1 is Pr1=Revenue-Cost
Revenue=Pq1
=(400-2q1-2q2)q1
MR=dR/dq1=400-4q1-2q2
Profit maximisation MR=MC
400-4q1-2q2=10
Reaction function for Nick: Q1*=(390-2q2*)/4
b.
Reaction function for LLC: q2*=(390-2q1*)/4
Putting the value of q2* in reaction function of nick
4Q1*=390-195+q1*
Q1*=q2*=65
c.
when nick chooses as leader, then Firm 1 (leader) anticipates the follower’s behavior and takes it into consideration to make the strategic choice of q1:
Max Pr: MR=MC
d{400-2q1-2RF(2)}q1/dq1=10
400-4q1-195+2q1=10
Q1=97.5
Q2=RF(2)=48.75
d.
Since the quantity of goods supplied increases so consumer welfare will increase. As market is moving towards perfect competition.
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