Pure Monopoly. Higher output y causes a lower market price, p(y). $/output unit p(y) Output Level, y
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1 24 Monopoly
2 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.
3 $/output unit p(y) Pure Monopoly Higher output y causes a lower market price, p(y). Output Level, y
4 Why Monopolies? What causes monopolies? a legal fiat; e.g. US Postal Service
5 Why Monopolies? What causes monopolies? a legal fiat; e.g. US Postal Service a patent; e.g. a new drug
6 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
7 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
8 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.
9 Pure Monopoly Suppose that the monopolist seeks to maximize its economic profit, ( y) p( y) y c( y). What output level y* maximizes profit?
10 Profit-Maximization ( y) p( y) y c( y). At the profit-maximizing output level y* d( y) dy so, for y = y*, d dy p y y dc( y) ( ) 0 dy d dy p ( y ) y dc( y). dy
11 $ Profit-Maximization R(y) = p(y)y y
12 $ Profit-Maximization R(y) = p(y)y c(y) y
13 $ Profit-Maximization R(y) = p(y)y c(y) y (y)
14 $ Profit-Maximization R(y) = p(y)y c(y) y* y (y)
15 $ Profit-Maximization R(y) = p(y)y c(y) y* y (y)
16 $ Profit-Maximization R(y) = p(y)y c(y) y* y (y)
17 $ Profit-Maximization R(y) = p(y)y c(y) y* y (y) At the profit-maximizing output level the slopes of the revenue and total cost curves are equal; MR(y*) = MC(y*).
18 Marginal Revenue Marginal revenue is the rate-of-change of revenue as the output level y increases; d MR y dy p y y p y ydp ( ( ) ( ) ( ) y ). dy
19 Marginal Revenue Marginal revenue is the rate-of-change of revenue as the output level y increases; d MR y dy p y y p y ydp ( ( ) ( ) ( ) 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 for y > 0. p( y)
20 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.
21 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. a p(y) = a - by a/2b a/b y MR(y) = a - 2by
22 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 + ay + by 2 then MC( y) a 2by.
23 $ Marginal Cost c(y) = F + ay + by 2 F $/output unit y a MC(y) = a + 2by y
24 Profit-Maximization; An Example At the profit-maximizing output level y*, MR(y*) = MC(y*). So if p(y) = a - by and c(y) = F + ay + by 2 then MR( y*) a 2by* a 2by* MC( y*)
25 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 + ay + by 2 then MR( y*) a 2by* a 2by* MC( y*) and the profit-maximizing output level is a a y* 2( b b)
26 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 + ay + by 2 then MR( y*) a 2by* a 2by* MC( y*) and the profit-maximizing output level is a a y* 2( b b) causing the market price to be p( y*) a by* a b a a 2( b b).
27 Profit-Maximization; An Example $/output unit a p(y) = a - by MC(y) = a + 2by a y MR(y) = a - 2by
28 Profit-Maximization; An Example $/output unit a p(y) = a - by MC(y) = a + 2by a y* a a 2( b b) y MR(y) = a - 2by
29 Profit-Maximization; An Example $/output unit p( y*) a p(y) = a - by a b a a 2( b b) MC(y) = a + 2by a y* a a 2( b b) y MR(y) = a - 2by
30 Monopolistic Pricing & Own-Price Elasticity of Demand Suppose that market demand becomes less sensitive to changes in price (i.e. the ownprice elasticity of demand becomes less negative). Does the monopolist exploit this by causing the market price to rise?
31 Monopolistic Pricing & Own-Price Elasticity of Demand d dy p y y p y ydp y dy MR( y) ( ) ( ) y dp( y) p( y). 1 p( y) dy ( )
32 Monopolistic Pricing & Own-Price Elasticity of Demand d dy p y y p y ydp y dy MR( y) ( ) ( ) y dp( y) p( y). 1 p( y) dy Own-price elasticity of demand is p ( y ) y dy dp( y) ( )
33 Monopolistic Pricing & Own-Price Elasticity of Demand d dy p y y p y ydp y dy MR( y) ( ) ( ) y dp( y) p( y). 1 p( y) dy Own-price elasticity of demand is p ( y ) y dy dp( y) ( ) so MR( y) p( y) 1 1.
34 Monopolistic Pricing & Own-Price Elasticity of Demand MR( y) p( y) 1 1. Suppose the monopolist s marginal cost of production is constant, at $k/output unit. For a profit-maximum MR( y*) p( y*) k 1 1 which is k p( y*). 1 1
35 Monopolistic Pricing & Own-Price Elasticity of Demand k p( y*). 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.
36 Monopolistic Pricing & Own-Price Elasticity of Demand 1 Notice that, since MR( y*) p( y*) 1 k, p( y*) 1 1 0
37 Monopolistic Pricing & Own-Price Elasticity of Demand 1 Notice that, since MR( y*) p( y*) 1 k, p( y*)
38 Monopolistic Pricing & Own-Price Elasticity of Demand 1 Notice that, since MR( y*) p( y*) 1 k, p( y*) That is,
39 Monopolistic Pricing & Own-Price Elasticity of Demand 1 Notice that, since MR( y*) p( y*) 1 k, p( y*) That is, 1 1.
40 Monopolistic Pricing & Own-Price Elasticity of Demand 1 Notice that, since MR( y*) p( y*) 1 k, p( y*) That is, 1 1. So a profit-maximizing monopolist always selects an output level for which market demand is own-price elastic.
41 Markup Pricing 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?
42 Markup Pricing k k p( y*) 1 1 k p( y*) is the monopolist s price.
43 Markup Pricing k k p( y*) 1 1 k p( y*) is the monopolist s price. The markup is k k p( y*) k k. 1 1
44 Markup Pricing k k p( y*) 1 1 k p( y*) 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.
45 A Profits Tax Levied on a Monopoly 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?
46 A Profits Tax Levied on a Monopoly 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*).
47 A Profits Tax Levied on a Monopoly 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.
48 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 profit-maximizing output level, causes the market price to rise, and input demands to fall. The quantity tax is distortionary.
49 Quantity Tax Levied on a Monopolist $/output unit p(y) p(y*) MC(y) y* y MR(y)
50 Quantity Tax Levied on a Monopolist $/output unit p(y*) p(y) t MC(y) + t MC(y) y* MR(y) y
51 Quantity Tax Levied on a Monopolist $/output unit p(y t ) p(y*) p(y) t MC(y) + t MC(y) y t y* y MR(y)
52 Quantity Tax Levied on a Monopolist $/output unit p(y t ) p(y*) 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. t MC(y) + t MC(y) y t y* y MR(y)
53 Quantity Tax Levied on a Monopolist 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
54 Quantity Tax Levied on a Monopolist The tax increases marginal cost to $(k+t)/output unit, changing the profitmaximizing price to t p( y ) ( k t). 1 The amount of the tax paid by buyers is t p( y ) p( y*).
55 Quantity Tax Levied on a Monopolist t p( y ) p( y*) ( k t) k 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, /1) > 1 and so the monopolist passes on to consumers more than the tax!
56 The Inefficiency of Monopoly A market is Pareto efficient if it achieves the maximum possible total gains-to-trade. Otherwise a market is Pareto inefficient.
57 The Inefficiency of Monopoly $/output unit p(y) The efficient output level y e satisfies p(y) = MC(y). p(y e ) MC(y) y e y
58 The Inefficiency of Monopoly $/output unit p(y) The efficient output level y e satisfies p(y) = MC(y). p(y e ) CS MC(y) y e y
59 The Inefficiency of Monopoly $/output unit p(y) The efficient output level y e satisfies p(y) = MC(y). p(y e ) CS PS MC(y) y e y
60 The Inefficiency of Monopoly $/output unit p(y) CS p(y e ) PS The efficient output level y e satisfies p(y) = MC(y). Total gains-to-trade is maximized. MC(y) y e y
61 The Inefficiency of Monopoly $/output unit p(y) p(y*) MC(y) y* y MR(y)
62 The Inefficiency of Monopoly $/output unit p(y*) CS p(y) MC(y) y* y MR(y)
63 The Inefficiency of Monopoly $/output unit p(y*) CS PS p(y) MC(y) y* y MR(y)
64 The Inefficiency of Monopoly $/output unit p(y*) CS PS p(y) MC(y) y* y MR(y)
65 The Inefficiency of Monopoly $/output unit p(y*) CS PS p(y) MC(y) y* y MR(y)
66 The Inefficiency of Monopoly $/output unit p(y) CS p(y*) PS y* 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 MR(y)
67 The Inefficiency of Monopoly $/output unit p(y) Deadweight loss measures the gains-to-trade not achieved by the market. p(y*) DWL MC(y) y* y MR(y)
68 The Inefficiency of Monopoly $/output unit p(y*) p(y e ) p(y) DWL The monopolist produces less than the efficient quantity, making the market price exceed the efficient market MC(y) price. y* y e y MR(y)
69 Natural Monopoly A natural monopoly arises when the firm s technology has economies-of-scale 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.
70 $/output unit Natural Monopoly ATC(y) p(y) MC(y) y
71 $/output unit Natural Monopoly ATC(y) p(y) p(y*) MC(y) y* MR(y) y
72 Entry Deterrence by a Natural Monopoly A natural monopoly deters entry by threatening predatory pricing 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.
73 Entry Deterrence by a Natural Monopoly E.g. suppose an entrant initially captures onequarter of the market, leaving the incumbent firm the other three-quarters.
74 Entry Deterrence by a Natural $/output unit ATC(y) Monopoly p(y), total demand = D I + D E D E D I MC(y) y
75 $/output unit Entry Deterrence by a Natural ATC(y) Monopoly An entrant can undercut the incumbent s price p(y*) but... p(y), total demand = D I + D E p(y*) D E p E D I MC(y) y
76 $/output unit Entry Deterrence by a Natural ATC(y) Monopoly An entrant can undercut the incumbent s price p(y*) but p(y*) p E p I D E MC(y) p(y), total demand = D I + D E the incumbent can then lower its price as far as p D I, forcing I the entrant to exit. y
77 Inefficiency of a Natural Monopolist Like any profit-maximizing monopolist, the natural monopolist causes a deadweight loss.
78 Inefficiency of a Natural Monopoly $/output unit ATC(y) p(y) p(y*) MC(y) y* MR(y) y
79 Inefficiency of a Natural Monopoly $/output unit ATC(y) p(y) Profit-max: MR(y) = MC(y) Efficiency: p = MC(y) p(y*) p(y e ) MC(y) y* MR(y) y e y
80 Inefficiency of a Natural Monopoly $/output unit ATC(y) p(y) Profit-max: MR(y) = MC(y) Efficiency: p = MC(y) p(y*) p(y e ) MC(y) DWL y* MR(y) y e y
81 Regulating a Natural Monopoly Why not command that a natural monopoly produce the efficient amount of output? Then the deadweight loss will be zero, won t it?
82 Regulating a Natural Monopoly $/output unit ATC(y) p(y) At the efficient output level y e, ATC(y e ) > p(y e ) ATC(y e ) p(y e ) MC(y) MR(y) y e y
83 Regulating a Natural Monopoly $/output unit ATC(y) p(y) At the efficient output level y e, ATC(y e ) > p(y e ) so the firm makes an economic loss. ATC(y e ) p(y e ) MC(y) Economic loss MR(y) y e y
84 Regulating a Natural Monopoly 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-to-trade. Regulatory schemes can induce the natural monopolist to produce the efficient output level without exiting.
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