Firm A operates on two markets, M and D. Firm A is a monopolist on market M. However, on market D, firm A faces a competitor, firm B. Competition on market D takes the form of Cournot competition. Firm B operates only on market D. If a total quantity of q is offered on any particular market then the price on that market is D(q)-q whenever q ? [0,1] (and D(q) if q>1). The firms have identical cost functions. Specifically, a firm that produces a total quantity of q across the markets on which it is active incurs total costs of c(q)^2. Note that marginal costs are not constant. Let qb denote firm B's quantity on market D. Similarly, let qa denote firm A's quantity on market D. Finally, let qm denote firm A's quantity on market M. Note that firm A's action is a pair (qa,qm), since it has to decide how much to sell on both market D and market M. Firm A's total production is thus qa+qm. Assume that 0 = qa, qb, qm =1.
a) Derive the two firms' best response functions. Verify that if firm A responds to qb by selling on both markets (i.e. qa>0 and qm>0) then marginal revenues are the same on both markets. Explain the intuition.
b) For any qb, determine on which market firm A responds by selling the larger quantity. Explain the economic intuition. How do qa and qm change as qb changes? Explain the intuition
c) Is there a Nash equilibrium in which firm A is not active on market D (i.e. qa=0)? Prove and explain your answer.
d) Derive a Nash equilibrium in which firm A is active on both markets. Which firm produces more on market D? Carefully explain the economic intuition. Which firm produces more in total? Explain the intuition.