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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= Q _{1}*+

*Q*

_{2}_{.}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
Q_{1}=Q_{2}=10 with both earning
Î _{1}=Î _{2}=0. Which one is correct?

---C= 0 OR C>0

b. Firm 2 produces zero Q_{2}=0 and earns Î _{2}=
0. Firm 1 charges P=c and produces Q_{1}=100-c earning
Î _{1}=100 c â€“ c^{2}

^{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