Question

A​ monopoly's cost function​ (C) is: C=0.2Q^3-8.0Q^2+380Q+50

where Q is output. Demand is: p=560-2Q

Determine the profit maximizing price and output for the monopolist.

The profit-maximizing output level is _ units of output.

The profit-maximizing price is _

Answer 1

A monopolist would maximize its profit at the Quantity where MR=MC

Revenue = Price*Quantity

Revenue =

Now,

and

Now lets solve for Q:

=>

we get: Q = 30 and Q=-10 as Q cant be negative so here Quantity would be 30

Now this the profit maximizing quantity. the price that the monopoly charge at this quantity would be on demand curve.

Hence P = 560-2Q = 560-2*30 = 560-60 = 500

Hence the Profit maximizing Price = 500 and Quantity = 30