A monopolist faces a demand curve = 120 2 and has costs given by () = 20 + 100

5.1 Write the monopolist's profits in terms of the price it charges.

5.2 Use the derivative (w.r.t. price) to determine the monopolist's profit-maximizing price.

5.3 Now, derive the monopolist's inverse demand based on the demand equation above. Write out the monopolist's profits in terms of quantity.

5.4 Use the derivative w.r.t. Q to determine the monopolist's optimal quantity. What price does the monopoly charge?