Answer:
Given : Inverse demand function : P = 150 - 3Q
Marginal cost of producing at facility 1: MC1(Q1) = 6Q1
Marginal cost of producing at facility 2: MC2(Q2) = 2Q2
Here we will first find Total Revenue.
i.e. Total Revenue(T.R) = P*Q
T.R(Q) = (150 - 3Q)*Q =
Where
(a) MR = 150 - 6Q
(b) Since we know that profit maximizing condition is given as :
MR = MC
Therefore , profit maximizing condition for facility 1 is
=
Similary profit maximizing condition for facility 2 is
=
Now, evaluating these two equations. We get ;
-
Therefore, the profit maximizing level of output for facility 1 is
(c)The profit maximizing price is
P = 150 - 3Q
P = 90