1. For each of these monopolists, find the profit maximizing price
Solution
Profit maximization rule is
MR = MC. where
MR = d(TR) / dQ [TR = Total Revenue = P x Q}
(a) Q = 100 - 4P,
So P = (100 - Q) / 4
TR = P x Q = Q x (100 - Q) / 4
MR = 25 - 0.5Q
So 25 - 0.5Q = 10
Solving, Q = 30 & P = 17.5
(b) Q = 40 - 0.5P
or P = 80 - 2Q
TR = P x Q = Q x (80 - 2Q)
So MR = 80 - 4Q
So 80 - 4Q = 16
Solving, Q = 16 & P = 48
(c) Q = 1 / P4
Or, P = Q1/4
So TR = Q5/4
MR = 5Q1/4
So, 5Q1/4 = 3
Solving, Q = 0.1296 & P = 0.60