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Monopoly 垄断 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. $/output unit p(y) Higher output y causes a lower market price, p(y). Output Level, y 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. Suppose that the monopolist seeks to maximize its economic profit, ( y) p( y)y c( y). What output level y* maximizes profit? ( y) p( y)y c( y). At the profit-maximizing output level y* d( y) d dc( y) 0 p( y)y dy dy dy so, for y = y*, d dc( y) . p( y)y dy dy At the profit-maximizing output level the slopes of the revenue and total cost curves are equal; MR(y*) = MC(y*). In a monopoly market, P>MR, how to prove? Marginal revenue is the rate-of-change of revenue as the output level y increases; d dp( y) MR( y) . p( y)y p( y) y dy dy dp(y)/dy is the slope of the market inverse demand function so dp(y)/dy < 0. Therefore dp( y) MR( y) p( y) y p( y) dy for y > 0. E.g. if p(y) = a - by then R(y) = p(y)y = ay - by2 and so MR(y) = a - 2by < a - by = p(y) for y > 0. E.g. if p(y) = a - by then R(y) = p(y)y = ay - by2 and so MR(y) = a - 2by < a - by = p(y) for y > 0. a p(y) = a - by a/2b a/b y MR(y) = a - 2by Marginal cost is the rate-of-change of total cost as the output level y increases; dc( y) MC( y) . dy E.g. if c(y) = F + ay + by2 then MC( y) a 2by. $ c(y) = F + ay + by2 F $/output unit y MC(y) = a + 2by a y At the profit-maximizing output level y*, MR(y*) = MC(y*). So if p(y) = a - by and if c(y) = F + ay + by2 then MR( y*) a 2by* a 2by* MC( y*) and the profit-maximizing output level is aa y* 2(b b ) causing the market price to be aa p( y*) a by* a b . 2(b b ) $/output unit a p(y) = a - by MC(y) = a + 2by a y MR(y) = a - 2by $/output unit a p(y) = a - by MC(y) = a + 2by a y* aa 2(b b ) y MR(y) = a - 2by $/output unit a p(y) = a - by p( y*) aa ab 2(b b ) MC(y) = a + 2by a y* aa 2(b b ) y MR(y) = a - 2by Proposition: A monopolist will never choose to operate where the demand curve is inelastic. Q: How to prove it? d dp( y) MR( y) p( y)y p( y) y dy dy y dp( y) p( y) 1 . p( y) dy d dp( y) MR( y) p( y)y p( y) y dy dy y dp( y) p( y) 1 . p( y) dy Own-price elasticity of demand is p( y) dy 1 so MR( y) p( y) 1 . y dp( y) 1 MR( y) p( y) 1 . Suppose the monopolist’s marginal cost of production is constant, at $k/output unit. For a profit-maximum 1 MR( y*) p( y*) 1 k which is k p( y*) . 1 1 p( y*) k 1 1 . •E.g. if = -3 then p(y*) = 3k/2, •and if = -2 then p(y*) = 2k. •So as rises towards -1 the monopolist alters its output level to make the market price of its product to rise. 1 Notice that, since MR ( y*) p( y*)1 k , 1 1 p( y*) 1 0 1 0 1 1 1. That is, So a profit-maximizing monopolist always selects an output level for which market demand is own-price elastic. Markup pricing: Output price is the marginal cost of production plus a “markup.” How big is a monopolist’s markup and how does it change with the own-price elasticity of demand? 1 p( y*) 1 k k p( y*) 1 1 1 k is the monopolist’s price. The markup is k k p( y*) k k . 1 1 •E.g. if = -3 then the markup is k/2, •and if = -2 then the markup is k. •The markup rises as the own-price elasticity of demand rises towards -1. Two kinds of taxes: ---Profit tax ---Quantity tax A profits tax levied at rate t reduces profit from (y*) to (1-t)(y*). Q: How is after-tax profit, (1-t)(y*), maximized? A: By maximizing before-tax profit, (y*). So a profits tax has no effect on the monopolist’s choices of output level, output price, or demands for inputs. I.e. the profits tax is a neutral tax (中性税). A quantity tax of $t/output unit raises the marginal cost of production by $t. So the tax reduces the profit-maximizing output level, causes the market price to rise, and input demands to fall. The quantity tax is distortionary（扭曲）. $/output unit p(y) p(y*) MC(y) y y* MR(y) $/output unit p(y) MC(y) + t p(y*) t MC(y) y y* MR(y) $/output unit p(y) p(yt) p(y*) MC(y) + t t MC(y) y yt y* MR(y) $/output unit p(y) p(yt) p(y*) The quantity tax causes a drop in the output level, a rise in the output’s price and a decline in demand for inputs. MC(y) + t t MC(y) y yt y* MR(y) p=a-by MR=a-2by With tax, MC=c+t Profit maximization: a-2by=c+t y=(a-c-t)/2b p(y)=a-by=a-(a-c-t)/2 dp/dt=1/2 The monopolist passes on half of the tax. 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 k p( y*) . 1 The tax increases marginal cost to $(k+t)/output unit, changing the profit-maximizing price to (k t ) p( y ) . 1 by buyers is The amount of the tax paid t p( yt ) p( y*). (k t ) k t p( y ) p( y*) 1 1 1 t •is the amount of the tax passed on to buyers. •E.g. if = -2, the amount of the tax passed on is 2t. •Because < -1（to make MR positive）, /1) > 1 and so the monopolist passes on to consumers more than the tax! Social welfare=consumer surplus+ producer surplus A market is Pareto efficient if it achieves the maximum possible total gains-to-trade. Otherwise a market is Pareto inefficient. $/output unit The efficient output level ye satisfies p(y) = MC(y). p(y) MC(y) p(ye) ye y $/output unit The efficient output level ye satisfies p(y) = MC(y). p(y) CS MC(y) p(ye) ye y $/output unit The efficient output level ye satisfies p(y) = MC(y). p(y) CS p(ye) MC(y) PS ye y $/output unit p(y) CS p(ye) The efficient output level ye satisfies p(y) = MC(y). Total gains-to-trade is maximized. MC(y) PS ye y $/output unit p(y) p(y*) MC(y) y y* MR(y) $/output unit p(y) p(y*) CS MC(y) y y* MR(y) $/output unit p(y) p(y*) CS MC(y) PS y y* MR(y) $/output unit p(y) p(y*) CS MC(y) PS y y* MR(y) $/output unit p(y) p(y*) CS MC(y) PS y y* MR(y) $/output unit p(y) p(y*) CS PS MC(y*+1) < p(y*+1) so both seller and buyer could gain if the (y*+1)th unit of output was produced. Hence the MC(y) market is Pareto inefficient. y y* MR(y) $/output unit Deadweight loss（额外净损失） measures the gains-to-trade p(y) Not achieved by the market. p(y*) MC(y) DWL y y* MR(y) The monopolist produces $/output unit less than the efficient quantity, making the p(y) market price exceed the efficient market p(y*) MC(y) price. e DWL p(y ) y* y ye MR(y) A natural monopoly arises when the firm’s technology has economies-of-scale （规模经济） large enough for it to supply the whole market at a lower average total production cost than is possible with more than one firm in the market. $/output unit ATC(y) p(y) MC(y) y $/output unit ATC(y) p(y) p(y*) MC(y) y* MR(y) y A natural monopoly deters entry by threatening predatory pricing （掠夺性定价）against an entrant. A predatory price is a low price set by the incumbent firm when an entrant appears, causing the entrant’s economic profits to be negative and inducing its exit. E.g. suppose an entrant initially captures onequarter of the market, leaving the incumbent firm the other three-quarters. $/output unit ATC(y) p(y), total demand = DI + DE DE DI MC(y) y $/output unit ATC(y) An entrant can undercut the incumbent’s price p(y*) but ... p(y), total demand = DI + DE DE p(y*) pE DI MC(y) y $/output unit An entrant can undercut the ATC(y) incumbent’s price p(y*) but p(y), total demand = DI + DE the incumbent can then DE lower its price as far p(y*) as pI, forcing DI pE the entrant to exit. pI MC(y) y Like any profit-maximizing monopolist, the natural monopolist causes a deadweight loss. $/output unit ATC(y) p(y) p(y*) MC(y) y* MR(y) y $/output unit ATC(y) p(y) Profit-max: MR(y) = MC(y) Efficiency: p = MC(y) p(y*) p(ye) MC(y) y* MR(y) ye y $/output unit ATC(y) p(y) Profit-max: MR(y) = MC(y) Efficiency: p = MC(y) p(y*) DWL p(ye) MC(y) y* MR(y) ye y Why not command that a natural monopoly produce the efficient amount of output? Then the deadweight loss will be zero, won’t it? $/output unit At the efficient output level ye, ATC(ye) > p(ye) ATC(y) p(y) ATC(ye) p(ye) MC(y) MR(y) ye y $/output unit ATC(y) p(y) ATC(ye) p(ye) At the efficient output level ye, ATC(ye) > p(ye) so the firm makes an economic loss. MC(y) Economic loss MR(y) ye y So a natural monopoly cannot be forced to use marginal cost pricing. Doing so makes the firm exit, destroying both the market and any gains-totrade. Regulatory schemes can induce the natural monopolist to produce the efficient output level without exiting. Average cost pricing 2nd best solution Difficulty: How to measure costs? Government-ownership $/output unit ATC(y) p(y) P(y)=AC(y) MC(y) PAC MR(y) yAC y Underlying technology Market size Minimum efficient scale----output level that minimizes average cost. Openness Collusion Cartel---- several different firms in an industry collude to reduce output and increase price. p AC Demand p* MES y AC Demand p* MES y What causes monopoly Profit-maximizing choices of monopoly Markup pricing Taxing a monopoly Inefficiency of monopoly Natural monopoly (自然垄断)