PROBLEM I. Suppose that, in a market of a certain product, there is a single dom

Question

PROBLEM I. Suppose that, in a market of a certain product, there is a single dominant firm with a cost function C(Q) = cQ, where c > 0 is a constant, and the competitive fringe with a supply function Q"(p-p-150 The market demand function is given by QM(p) = 420-2p Q1. When c 130, the dominant firm's profit-maximizing quantity is (a) 72. (b) 84 (d) 105 (e) 110 Q2. When c = 130, the equilibrium market price of the product is (a) 120 (b) 130 (c) 135 (d) 150 (e) 160 Q3, when c = 130, what is the market share of the dominant firm? (Choose the closest (a) 98% (b) 90% (c) 86% (d) 82% (e) 75%

Explanation / Answer

1) Residual demand function is D = 420 - 2P - P + 150. This becomes QD = 570 - 3P. Inverse demand function is given by P = 190 - (1/3)Q. Hence MR = MC will be chosen by the dominant firm which gives the profit maximizing output of dominant firm and the price

190 - (2/3)Q = 130

This gives Q* = 90 and price P* = 160. At a price of 160, quantity supplied by fringe = 160 - 150 = 10 units. Total output is 100 units and so dominant firm produces 90% of the market. Its market share is 90%.

For the value c lying in the interval110 to 125, MR and MC will give QDOMINANT = 120 units and Price = $150. At a price of $150, fringe supply is Q = 150 - 150 = 0.

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