The market demand curve in the aluminum industry is given by: Q D = 500-9P. The

Question

The market demand curve in the aluminum industry is given by:

QD = 500-9P.
The industry is dominated by a large firm with a constant marginal cost of $10 per unit. These also exists a competitive fringe of 100 firms, each of which has a marginal cost given by MC

MC = 10 + 6q,
where q is the output of a typical fringe firm.

Using the dominant firm model, derive numerically the expected market price and quantity that you predict will prevail in this market as well as the quantities produced by the dominant firm and the fringe firms. Explain carefully what you are doing.

Explanation / Answer

Let us find P and Q of dominant firm for max profit. Q = 500 - 9P => P = 500/9 - Q/9 so, R = P*Q = 500 Q/9 - Q^2/9 => MR = dR/dQ = 500/9 - 2Q/9 for max Profit, MR = MC => 500/9 - 2Q/9 = 10 =>2Q/9 = 500/9 - 10 = 410/9 => Q = 205 and P = 500/9 - 205/9 = 295/9 = 32.8 Let fringe firms have Q(F) at price P of dominant firm R = P*Q(F) = 295/9 * Q(F) MR = dR/dQ(F) = 295/9 MC = 10+6Q(F) for max profit, MR = MC => 295/9 = 10 +6Q(F) => Q(F) = (205/9)/6 = 3.8 So, prevailing market price = 32.8, Q (market) = 205 + 3.8 = 208.8 and Q (dominant) = 205 (ANSWER)

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