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Answer to Question #89694 in Microeconomics for Talha

Question #89694
If other firms in an oligopolistic industry do not respond to changes in the price of a firms product the demand curve is Q=700-50P however if other firms always match the firms price the demand curve is Q'=200-10p.
a. If firms marginal cost is 8.00 what is the profit maximizing quantity and price?
b. If firms managerial cost increases to 11.50 what will be profit maximizing quantity and price

a. If the demand curve is Q = 700 - 50P or P = 14 - 0.02Q and firms marginal cost is 8.00, then the profit maximizing quantity and price are:

MR = MC,

MR = TR' = (P×Q)' = 14 - 0.04Q = 8,

0.04Q = 6,

Q = 150 units,

P = 14 - 0.02×150 = 11.

If the demand curve is Q' = 200 - 10P or P = 20 - 0.1Q, then the profit maximizing quantity and price are:

MR = MC,

MR = TR' = (P×Q)' = 20 - 0.2Q = 8,

0.2Q = 12,

Q = 60 units,

P = 20 - 0.1×60 = 14.

b. If firms managerial cost increases to 11.50, then the profit maximizing quantity and price in first case are:

MR = MC,

MR = TR' = (P×Q)' = 14 - 0.04Q = 11.5,

0.04Q = 2.5,

Q = 62.5 units,

P = 14 - 0.02×62.5 = 12.75.

If second case the profit maximizing quantity and price are:

MR = MC,

MR = TR' = (P×Q)' = 20 - 0.2Q = 11.5,

0.2Q = 8.5,

Q = 42.5 units,

P = 20 - 0.1×42.5 = 15.75.

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