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Econ501aL17

# Econ501aL17 - Monopoly Reasons for monopoly(1 patent...

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Monopoly Reasons for monopoly: (1) patent, government protec- tion, (2) ownership of a key input, (3) natural monopoly, because LRAC falls until it crosses the market demand curve. max π = p x x TC ( x ) yields the fi rst order condition p x + x dp x dx MC ( x ) = 0 . The fi rst two terms comprise marginal revenue. When a monopolist produces more output, it takes into account the fact that the price it can charge is lower. We can think of the monopolist as choosing p x or as choosing x .

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0 20 40 60 80 px 20 40 60 80 X Monopoly The monopoly quantity satis fi es MR ( x ) = MC ( x ) . The monopolist charges the price the market will pay for that quantity.
example: X d = 80 p x LRTC = 500 + 20 x. First, we convert the demand curve into an inverse de- mand, price as a function of x. p x = 80 x. Next, derive the total revenue function. TR ( x ) = (80 x ) x. Finally, set marginal revenue equal to marginal cost and solve for x. MR ( x ) = 80 2 x = 20 = MC ( x ) . x = 30 , which implies p x = 50 .

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The monopolist receives pro fi t equal to 50(30) 500 20(30) = 400 . There is a deadweight loss triangle, since the socially optimal quantity is 60, where demand and marginal cost intersect. 0
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