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The demand curve for a monopolist is Qd = 500 - P and the marginal revenue function is MR = 500 - 2P. The monoploist has a cons...Asked 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?
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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Answered by
economyst
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
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
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