First, (And I hope this clears up confusion rather than add to it), I like to re-arrange the equation such that P is a function of Q. (When you graph a demand function, you always put P on the y-axis, Q on the x-axis). Re-arranging terms in your demand function. P=500-Qd. Total Revenue is P*Q = 500Q - Q^2. So, marginal revenue is MR=500-2Qd.
a) always always always. MC=MR.
So, 500-2Qd = 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 (P-MC)/P or (275-50)/275 = .8182
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?
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