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does it change with the ownprice elasticity of demand? Markup Pricing p y k p y k k( *) ( *)1 11 1 1???????? ? ????????is the monopolist’s price. Markup Pricing p y k p y k k( *) ( *)1 11 1 1???????? ? ????????is the monopolist’s price. The markup is p y k k k k( *) .? ? ? ? ? ? ?? ? ?1 1 Markup Pricing p y k p y k k( *) ( *)1 11 1 1???????? ? ????????is the monopolist’s price. The markup is p y k k k k( *) .? ? ? ? ? ? ?? ? ?1 1. if ? = 3 then the markup is k/2, and if ? = 2 then the markup is k. The markup rises as the ownprice elasticity of demand rises towards 1. A Profits Tax Levied on a Monopoly ?A profits tax levied at rate t reduces profit from ?(y*) to (1t)?(y*). ?Q: How is aftertax profit, (1t)?(y*), maximized? ?A: By maximizing beforetax profit, ?(y*). ?So a profits tax has no effect on the monopolist’s choices of output level, output price, or demands for inputs. ?. the profits tax is a neutral tax. Quantity Tax Levied on a Monopolist ?A quantity tax of $t/output unit raises the marginal cost of production by $t. ?So the tax reduces the profitmaximizing output level, causes the market price to rise, and input demands to fall. ?The quantity tax is distortionary( 扭曲) . Linear Demand Curve $/output unit y MC(y) p(y) MR(y) y* p(y*) $/output unit y MC(y) p(y) MR(y) MC(y) + t t y* p(y*) Linear Demand Curve $/output unit y MC(y) p(y) MR(y) MC(y) + t t y* p(y*) yt p(yt) Linear Demand Curve $/output unit y MC(y) p(y) MR(y) MC(y) + t t y* p(y*) yt p(yt) The quantity tax causes a drop in the output level, a rise in the output’s price and a decline in demand for inputs. Linear Demand Curve ? p=aby ? MR=a2by ? With tax, MC=c+t ? Profit maximization: a2by=c+t y=(act)/2b p(y)=aby=a(act)/2 ? dp/dt=1/2 ? The monopolist passes on half of the tax. Linear Demand Curve Constant Elasticity Demand ?Can a monopolist “pass” all of a $t quantity tax to the consumers? ?Suppose the marginal cost of production is constant at $k/output unit. ?With no tax, the monopolist’s price is p y k( *) .? ?? ?1 ?The tax increases marginal cost to $(k+t)/output unit, changing the profitmaximizing price to ?The amount of the tax paid by buyers is p y k tt( ) ( ) .? ?? ??1p y p yt( ) ( *) .?Constant Elasticity Demand p y p y k t k tt( ) ( *) ( )? ? ?? ? ? ? ??? ? ? ? ?1 1 1is the amount of the tax passed on to buyers. . if ? = 2, the amount of the tax passed on is 2t. Because ? 1, ? /?1??) 1 and so the monopolist passes on to consumers more than the tax! Constant Elasticity Demand The Inefficiency of Monopoly ?A market is Pareto efficient if it achieves the maximum possible total gainstotrade. ?Otherwise a market is Pareto inefficient. The Inefficiency of Monopoly $/output unit y MC(y) p(y) ye p(ye) The efficient output level ye satisfies p(y) = MC(y). The Inefficiency of Monopoly $/output unit y MC(y) p(y) ye p(ye) The efficient output level ye satisfies p(y) = MC(y). CS The Inefficiency of Monopoly $/output unit y MC(y) p(y) ye p(ye) The efficient