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If the inverse market demand function facing a duopoly is P=a-bQ.
1.) What are the Cournot equilibrium quantities if the marginal cost of Firm 1 is m and that of Firm 2 is: m+x; where x>0
2.) Which firm produces more and which has the higher profit?
Assume now that Firm 1 has a constant marginal cost of 1 and Firm 2 has a constant marginal cost of 2. The new market demand is: Q = 15 – P
3.) Solve for the Cournot equilibrium price, quantities, profits and consumer surplus
4.) If the firms merge and produce at the lower marginal cost, how do the equilibrium values change?
Suppose the identical duopoly firms have constant marginal cost of R10 per unit. Firm 1 faces a demand function of: q1=100-2p1+p2where q1 is Firm 1’s output, p1is Firm 1’s price and p2is Firm 2’s price. Similarly, the demand Firm2 faces is q2= 100 – 2p2+p1
5) Solve for the Bertrand Equilibrium
6.) If Firm 1’s marginal cost changes to R30 and that of Firm 2 to R10, what are the new equilibrium values?

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