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The demand function for an oligopolistic market is given by the equation, Q = 275 – 4P, where Q is quantity demanded and P is price (Note: inverse demand for the dominant firm here is P = 50 - .2Q). T...

The demand function for an oligopolistic market is given by the equation, Q = 275 – 4P, where Q is quantity demanded and P is price (Note: inverse demand for the dominant firm here is P = 50 - .2Q). The industry has one dominant firm whose marginal cost function is: MC = 12 + 0.7QD, and many small firms, with a total supply function: QS = 25 + P. In equilibrium, the total output of all small firms is

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Answer #1

Demand function for the market is Q = 275 - 4P.

Supply function of fringe is Q = 25 + P.

This gives residual demand function Qd = 275 - 4P - 25 - P or Qd = 250 - 5P.

This implies inverse demand function is P = 50 - 0.2Q

and MR = 50 - 0.4Q. MC is 12 + 0.7Q.

Hence we have MR = MC or 50 - 0.4Q = 12 + 0.7Q.

This gives Q = 38/1.1 = 34.55 units and P = 50 - 0.2*34.55 = $43.09.  

Hence, total output of all small firms is Q = 25 + 43.09 = 68.09 units

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