Question: consider an inverse demand curve p 30 q...
Consider an (inverse) demand curve P = 30 - Q. And a total cost curve of C(Q) = 12Q.
Two firms (Firm A and Firm B) competing in this market. They simultaneously decide on the price of the product in a typical Bertrand fashion while producing an identical product. Both firms face the same cost function: C(qA) = 12qA and C(qB) = 12qB, where qA is the output of Firm A and qB is the output of Firm B.
(i) What will be the Bertrand-Nash equilibrium price (pB) chosen by each firm? Explain.
(ii) What is the equilibrium quantity (qB) sold by each firm and the total market output (QN)?
(iii) What, if any, is the dead-weight loss in this case?