Answer:
70 units
Explanation:
The computation of profit maximizing output level is shown below:-
Monopolist perform Marginal Revenue which equivalent to the Marginal Cost as
MR = Marginal Revenue and MC = Marginal Cost
[tex]MR = \frac{\partial TR}{\partial Q} = \frac{\partial PQ}{\partial Q} = \frac{\partial (320-0.5Q)Q}{\partial Q}[/tex]
[tex]MR = \frac{\partial (320Q -0.5Q^2)}{\partial Q}[/tex]
MR = 320 - Q
Now we will find the MC which is
[tex]MC = \frac{\partial TC}{\partial Q} =\frac{\partial (1.5Q^2 + 40Q)}{\partial Q} = 3Q + 40[/tex]
now we will put the value of which is into MR = MC
320 - Q = 3Q + 40
280 = 4Q
70 = Q
So, the profit maximizing output level is 70 units.
