Question 3 The market demand for ABC is Q(P) = 10 - P. Firm XYZ is one of the firms producing ABC. XYZ's cost function is given by TC(Q) = 2Q. There are four other firms that also produce ABC, they all have the same cost function: TC(q) = 3q 2q^2 .

A. Suppose all five firms behave competitively. Compute the (competitive) equilibrium price and the quantities produced by these firms.

B. Suppose firm XYZ it makes no sense to produce 8 units of output as in the equilibrium of part A, and therefore decides to behave like a dominant firm: Firm XYZ now takes into account that the market price is going to depend on its own output decisions: If it produces a little bit less than then the market price will go up. The other four firms continue to behave competitively: they take the market price as given. Compute how much profit firm XYZ is going to make if it produces

I. 7 units of output.

II. 6 units of output.

III. 5 units of output.

IV. 4 units of output.

Help: As we discussed in lecture on Nov 8 the price in the dominant firm market is determined by the following "supply equals demand" condition: Q^o + S^F (P) = Q_D(P). Here Q^o is the output the dominant firm chooses to produce, S^F (P) is the total supply function of all firms that behave competitively, and Q_D(P) is the market demand.