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(Solved): The Market Demand Curve For A Pair Of Duopolists Is Given As P=100- Q Where Q= Q1 + Q2. The Constant...


The market demand curve for a pair of duopolists is given as P=100- Q where Q= Q1+ Q2. The constant per unit marginal cost is 0 for firm 1 and c for firm 2 where c is some number. Find the equilibrium price, quantity and profit for each firm in the Bertrand model as a function of c

a. Equilibrium price equals P=0. Equilibrium quantity is Q1=Q2=10 with both earning Π1=Π2=0. Which one is correct?

---C= 0 OR C>0

b. Firm 2 produces zero Q2=0 and earns Π2= 0. Firm 1 charges P=c and produces Q1=100-c earning Π1=100 c – c2

Which one is correct?

---C= 0 OR C>0

Is C=0 or C>0 for the two questions



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Expert Answer


Profit = (P- c) Q As given in the question the two firms are in Bertrand set up wherein firms compete over prices. So in this setup, the firms with lower price
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