To: Economyst  Can you please help me?
posted by too old .
The demand curve for a monopolist is Qd = 500  P and the marginal revenue function is MR = 500  2P. The monopoloist has a constant marginal and average total cost of $50 per unit.
a. Find the monopolist's profit maximizing output and price
b.Calculate the monopolist's profit.
c.What is the Lerner Index for this industry?

First, (And I hope this clears up confusion rather than add to it), I like to rearrange the equation such that P is a function of Q. (When you graph a demand function, you always put P on the yaxis, Q on the xaxis). Rearranging terms in your demand function. P=500Qd. Total Revenue is P*Q = 500Q  Q^2. So, marginal revenue is MR=5002Qd.
a) always always always. MC=MR.
So, 5002Qd = 50. Solve for Qd. I get Qd=225. Plug this into the demand equation. I get P=275.
b) Total profit is Qotal revenue  Total costs. So profit=(275*225)  (50*225) = $50,625
c) the Lerner index is (PMC)/P or (27550)/275 = .8182