# Monopoly - Chapter Twenty-Four Monopoly Pure Monopoly A...

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Chapter Twenty-Four Monopoly

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Pure Monopoly A monopolized market has a single seller. The monopolist’s demand curve is the (downward sloping) market demand curve. So the monopolist can alter the market price by adjusting its output level.
Pure Monopoly Output Level, y \$/output unit p(y) Higher output y causes a lower market price, p(y).

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Why Monopolies? What causes monopolies? a legal fiat; e.g. US Postal Service a patent; e.g. a new drug sole ownership of a resource; e.g. a toll highway formation of a cartel; e.g. OPEC large economies of scale; e.g. local utility companies.
Pure Monopoly Suppose that the monopolist seeks to maximize its economic profit, What output level y* maximizes profit? Π ( ) ( ) ( ). y p y y c y = -

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Profit-Maximization Π ( ) ( ) ( ). y p y y c y = - At the profit-maximizing output level y* ( 29 d y dy d dy p y y dc y dy Π ( ) ( ) ( ) = - = 0 so, for y = y*, ( 29 d dy p y y dc y dy ( ) ( ) . =
y \$ R(y) = p(y)y Profit-Maximization

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\$ R(y) = p(y)y c(y) Profit-Maximization y
Profit-Maximization \$ R(y) = p(y)y c(y) y Π (y)

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Profit-Maximization \$ R(y) = p(y)y c(y) y Π (y) y*
Profit-Maximization \$ R(y) = p(y)y c(y) y Π (y) y*

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Profit-Maximization \$ R(y) = p(y)y c(y) y Π (y) y*
Profit-Maximization \$ R(y) = p(y)y c(y) y Π (y) y* At the profit-maximizing output level the slopes of the revenue and total cost curves are equal; MR(y*) = MC(y*).

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Marginal Revenue Marginal revenue is the rate-of-change of revenue as the output level y increases; ( 29 MR y d dy p y y p y y dp y dy ( ) ( ) ( ) ( ) . = = +
Marginal Revenue Marginal revenue is the rate-of-change of revenue as the output level y increases; ( 29 MR y d dy p y y p y y dp y dy ( ) ( ) ( ) ( ) . = = + dp(y)/dy is the slope of the market inverse demand function so dp(y)/dy < 0. Therefore MR y p y y dp y dy p y ( ) ( ) ( ) ( ) = + < for y > 0.

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Marginal Revenue E.g. if p(y) = a - by then R(y) = p(y)y = ay - by 2 and so MR(y) = a - 2by < a - by = p(y) for y > 0.
Marginal Revenue E.g. if p(y) = a - by then R(y) = p(y)y = ay - by 2 and so MR(y) = a - 2by < a - by = p(y) for y > 0. p(y) = a - by a y a/b MR(y) = a - 2by a/2b

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Marginal Cost Marginal cost is the rate-of-change of total cost as the output level y increases; MC y dc y dy ( ) ( ) . = E.g. if c(y) = F + α y + β y 2 then MC y y ( ) . = + α β 2
Marginal Cost F y y c(y) = F + α y + β y 2 \$ MC(y) = α + 2 β y \$/output unit α

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Profit-Maximization; An Example At the profit-maximizing output level y*, MR(y*) = MC(y*). So if p(y) = a - by and if c(y) = F + α y + β y 2 then MR y a by y MC y ( *) * * ( *) = - = + = 2 2 α β and the profit-maximizing output level is y a b * ( ) = - + α β 2 causing the market price to be p y a by a b a b ( *) * ( ) . = - = - - + α β 2
Profit-Maximization; An Example \$/output unit y MC(y) = α + 2 β y p(y) = a - by MR(y) = a - 2by a α

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Profit-Maximization; An Example \$/output unit y MC(y) = α + 2 β y p(y) = a - by MR(y) = a - 2by y a b * ( ) = - + α β 2 a α
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## This note was uploaded on 03/03/2011 for the course ECON 206 taught by Professor Ioanadan during the Spring '10 term at University of Toronto.

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Monopoly - Chapter Twenty-Four Monopoly Pure Monopoly A...

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