In a market with demand Q = 2,310 − p, there are 3 identical firms, A, B and C; each with a total cost function TC(Q) = 3/2 Q^2 (with MC(Q) = 3Q, that is) Calculate the market price under each of the 6 scenarios below, (a) A, B, C collude as though they are all plants of the same single multi-plant monopoly. (b) A, B, C act as price taking perfectly competitive firms. (c) B and C act as two plants of a single multi-plant monopoly called “B+C”, which competes in quantities (Cournot competition) against A. (d) (WARNING: non-integer answer) As in (iii) above, but Firm A acts first and chooses its quantity as a leader and B+C
In a market with
(a) A, B, C collude as though they are all plants of the same single multi-plant
(b) A, B, C act as price taking
(c) B and C act as two plants of a single multi-plant monopoly called “B+C”, which competes in quantities (Cournot competition) against A.
(d) (WARNING: non-integer answer) As in (iii) above, but Firm A acts first and chooses its quantity as a leader and B+C follows (Stackelberg competition)
(e) B and C jointly form the fringe supply and A is the dominant firm as in the dominant firm model.
(f) A, B, C compete in quantities with each other (Cournot-Nash equilibrium). (HINT: Best Response equations should be symmetrical; hence there is a symmetric solution with qA = qB = qC as the Cournot-Nash equilibrium)
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