Question

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

Answer 1

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.