Part VI Market Power y Competition

Outline Barriers Profit Maximization & Output Choice Misallocation Comparative Statics Quality Price Discrimination

Part VI:Market Power14. Monopoly15. Imperfect Competition

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Chapter 14MonopolyPart I

Ming-Ching Luoh

2021.3.26.

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Barriers to Entry

ProûtMaximization and Output Choice

Misallocated Resources UnderMonopoly

Comparative Statics Analysis ofMonopoly

Monopoly Product Quality

Price Discrimination

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Monopoly

● AMonopoly is a single supplier to amarket. ais ûrmmaychoose to produce at any point on themarket demand curve.

● Monopolies choose the quantity of output thatmaximizesproûts and then settle for themarket price that the chosenoutput level yields.

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Barriers to EntryTechnical barriers● A primary technical barrier is that the production may

exhibit decreasing marginal (and average) costs over a widerange of output levels.

● In this situation, referred to as natural monopoly, one ûrmmay ûnd it proûtable to drive others out of the industry bycutting prices.

● Another technical basis ofmonopoly is special knowledge ofa low-cost productive technique. Itmay be diõcult to keepthis knowledge out of the hands of other ûrms unless it isprotected by a patent.

● Ownership of unique resourcesmay also be a lasting basisformaintaining amonopoly.

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Legal barriers

● Many puremonopolies are created as amatter of law ratherthan as amatter of economic conditions.

● Legal protection of a product by patent or copyright is oneexample of a government-grantedmonopoly position.

● Patent and copyright systemmakes innovation moreproûtable and acts as an incentive.

● Another example of a legally createdmonopoly is theawarding of an exclusive franchise to serve amarket such aspublic utility and communications industries.

● ae arguments in favors of franchisedmonopolies is that theindustry is a natural monopoly where average cost isdiminishing and theminimum average cost can be achievedonly by organizing the industry as amonopoly.

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Barriers erected by themonopolist

● Some barriers to entry result from actions taken by the ûrm.● For example, ûrmsmay develop unique product or

technologies and keep these from being copied bycompetitors.

● Firmsmay buy up unique resources to prevent potentialentry.

● A would-bemonopolistmay lobby for legislation thatrestrict new entrants to “maintain an ordelymarket" or forhealth and safety regulations that raise potential entrants’costs.

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ProûtMaximization and Output Choice● aemonopolist chooses quantity Q to maximize its proûts

π(Q) = R(Q) − C(Q) = p(Q)Q − C(Q).ae ûrst-order condition is

π(Q) = dRdQ− dCdQ= MR(Q) −MC(Q) = 0.

● To maximize proût, themonopolist produces the outputlevel at which MR(Q) = MC(Q).

● aemonopolist faces a negatively slopedmarket demandcurve, implying P′(Q) < 0. aus

MR(Q) = P(Q) + QP′(Q) < P(Q).To sell an additional unit, themonopolymust lower its priceon all units.

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Figure 14.1 ProûtMaximization and Price Determination for aMonopoly

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ae inverse elasticity rule

● ae gap between a ûrm’s price and itsmarginal cost inpercentage terms (the Lerner index) is inversely related tothe price elasticity of demand faced by the ûrm,

Pm −MCPm

= Pm − (Pm + QmP′(Qm))Pm

= − 1eD,P

.

● Amonopoly will operate in regions in which themarketdemand curve is elastic (eD,P < −1).

● ae ûrm’s “markup" overmarginal cost depends inversely onthe elasticity ofmarket demand.

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Monopoly proûts

● As shown by the retangle PmEACm in Figure 14.1,monopolyproûts will be positive as long as Pm > ACm

● aemonopolist’s positive can continue into the long runbecause entry is not possible. ae proûts sometimes arereferred to asmonopoly rents. aese proûts can be regardedas a return to the factor that forms the basis of themonopoly.

● ae size ofmonopoly proûts in the long run depend on therelationship between average costs andmarket demand forthe product.

● Figure 14.2 shows that large proûts from amonopoly are notinevitable, and the actual extent of economic proûtsmay notalways be a good guide to the signiûcance ofmonopolisticin�uences in amarket.

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Figure 14.2Monopoly Proûts Depend on the Relationshipbetween the Demand and Average Cost Curves

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aere is no monopoly supply curve

● With a ûxedmarket demand curve, the supply “curve" for amonopolist will only be one point—namely, the price-outputcombination where MR = MC.

● If demand shi�s, themarginal revenue curve shi�s, and anew proût-maximizing output will be chosen.

● aemonopoly ûrm has no well-deûned “supply curve."

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Example 14.1 Calculating Monopoly Output

● Suppose themarket for Frisbees has a linear demand curve

Q = 2, 000 − 20P or P = 100 − Q20

and the cost function is

C(Q) = 0.05Q2 + 10, 000

● Total revenue is

R(Q) = P ⋅ Q = 100Q − Q2

20.

Consequently,

MR = 100 − Q10= MC = 0.1Q

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● aerefore,

Qm = 500, Pm = 75.

At themonopolist’s preferred output level,

C(Q) = 0.05(500)2 + 10, 000 = 22, 500,ACm = 22, 500

500= 45.

And we can calculate proûts as

πm = (Pm − ACm) ⋅ Qm = (75 − 45) ⋅ 500 = 15, 000.

● MC(500) = 0.1Q = 50, themarkup is (75 − 50)/75 = 33.3%.

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Example 14.2Monopoly with Simple Demand Curves

● Linear demand. Suppose that the inverse demand functionis linear

P = a − bQPQ = aQ − bQ2,

and the cost function is C(Q) = cQ. Hence proûtmaximization requires that

MR = a − 2bQ = MC = c, or Qm =a − c2Q

and

Pm = a − bQm = a −a − c2= a + c

2Notice that ∂P/∂c = 1/2, only half of the amount of increasein marginal cost will show up in themarket price.

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● Constant elasticity demand. Suppose that the cost functionis still C(Q) = cQ, but if the demand curve is now Q = aPe ,implying e is the price elasticity of demand because

PQ⋅ dQdP= PaPe ⋅ aeP

e−1 = e

thenMR = P + Q ∂P

∂Q= P (1 + 1

e) = c

Pm = c ( e1 + e)

Note that we need e < −1 for proûtmaximization, and

∂Pm∂c

= e1 + e > 1

epm ,c =∂Pm∂c⋅ cPm= 1

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Misallocated Resources UnderMonopoly

● Because themonopoly produces a level of out for whichMR = MC < P, themarket price no longer conveys accurateinformation about production costs.

● Consumers’ decision will no longer re�ect true opportunitycost of production, and resources will bemisallocated.

Basis of comparison

● Perfectly competitive, constant-cost industry where theindustry’s long-run supply curve is inûnitely elastic andprice is equal to both marginal and average cost.

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Figure 14.3 Allocational and Distributional Eòects ofMonopoly

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Example 14.3Welfare Losses and Elasticity

● Assume that the constantmarginal (and average) costs for amonopolist are given by c and that the demand curve has aconstant elasticity form of

Q = Pe

where e is the price elasticity of demand (e < −1).● We know the competitive price will be Pc = c and the

monopoly price is Pm = c1+1/e > c.

● ae consumer surplus associated with any price P0 can becomputed as

∫∞

P0Q(P)dP = ∫

∞

P0PedP = Pe+1

e + 1

RRRRRRRRRRR

∞

P0

= −Pe+10

e + 1

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● Hence under perfect competition we have

CSc = −ce+1e + 1

and undermonopoly,

CSm = −( c1+1/e)

e+1

e + 1Taking the ratio of these two surplusmeasures yields

CSmCSc

= ( 11 + 1/e)

e+1

If e = −2, this ration is 0.5. If e = −3, this ratio is o.42. Ife = −1.1, this ratio is 0.79.

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● ProûtsMonopoly proûts are

πm = PmQm − cQm = (c

1 + 1/e − c)Qm

= ( −c/e1 + 1/e) ⋅ (

c1 + 1/e)

e

= −( c1 + 1/e)

e+1

⋅ 1e.

aerefore,

πmCSc= ( e + 1

e)( 1

1 + 1/e)e+1

= ( e1 + e)

e

● For e = −2, this ratio is 1/4. Since CSm/CSc = 1/2 whene = −2, the deadweight loss from monopoly in this case ifalso 1/4 (=1-1/2-1/4) of the consumer surplus under perfectcompetition (CSc).

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Comparative Statics Analysis ofMonopoly

● We want to use the techniques of comparative statics toprove that amonopolist reduces its output in response to anupward shi� in marginal cost curve.

● Letmarginal cost be given by MC(Q , γ), where γ is somefactor shi�ing the curve up, that is, ∂MC/∂γ > 0.

● ae ûrst-order condition for proût-maximization is

MR(Q) −MC(Q , γ) = 0.

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● Total diòerentiating with respect to γ,

MR′(Q) ⋅ dQmdγ− ∂MC

∂Q⋅ dQmdγ− ∂MC

∂γ= 0.

● Solving dQmdγ yields

dQmdγ= ∂MC/∂γMR′(Q) − ∂MC/∂Q< 0

because ∂MC/∂γ > 0 and MR′(Q) − ∂MC/∂Q < 0 from thesecond-order condition.

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● Suppose α is a shi�er in demand P(Q , α), where ∂P/∂α > 0,what is the eòect of α on Qm, ∂Qm/∂α?

● ae ûrst order condition is

MR(Q , α) = P(Q , α) + Q ⋅ ∂P∂Q= MC(Q)

● If the increase in α makes the inverse demand curve steeper(i.e. makes ∂P/∂Q more negative) at the same time it shi�sthe curve P(Q , α) out, α will have an ambiguous eòect onMR(Q , α), and thus an ambiguous eòect on Qm.

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Monopoly Product Quality● aemarket power enjoyed by amonopolymay be exercised

along dimensions other than themarket price, such as type,quality, or diversity of goods it produces.

● Whether amonopoly will produce higher-quality orlower-quality goods than competitive ûrms depends on theûrm’s cost and the nature of consumer demand.

● Suppose consumers’ willingness to pay for a good of qualityX is given by the inverse demand function P(Q , X), where∂P/∂Q = PQ < 0 and ∂P/∂X = PX > 0.

● Let C(Q , X) be the cost producing Q unit of quality X,With∂C/∂Q = CQ > 0 and ∂C/∂X = CX > 0

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● aemonopolist chooses Q and X maximize

π = P(Q , X)Q − C(Q , X)● For simplicity, suppose we have already know the optimal

value of Qm, and just need to solve for Xm. ae ûrst-ordercondition for X is

∂π∂X= PX(Qm , X)Qm − CX(Qm , X) = 0.

● For the eõcient choice of quality by social planner, socialwelfare which is the sum of proût and consumer surplus, ismaximized.

SW = π + CS = PmQm − C(Qm , X) + ∫Qm

0[P(Q , X) − Pm]dQ

= ∫Qm

0P(Q , X)dQ − C(Qm , X)

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● Diòerentiating the equation of SW with respect to X yieldsthe ûrst-order condition

∂SW∂X

= ∫Qm

0PX(Q , X)dQ − CX(Qm , X) = 0

● aemonopolist’s choice of quality targets themarginalconsumer. Increasing the attractiveness of the product to themarginal consumer increases sales.

● ae eõcient quality chosen by the social plannermaximizesconsumer surplus across all buyers, given output is keptconstant at Qm, is equivalent to maximizing the averageconsumer surplus across buyers.

● If themarginal consumer ismore (less) responsive to qualitythan the average consumer, themonopolist will choose anineõciently high (low) quality. (see Problem 14.9.)

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Product durability● Durable goods are goods that provide services to their

owners over several period.● Do monopolists “under-produce" durability just as they

choose an output below the competitive level?● Australian economist Peter Swan in the early 1970s view the

demand for durable goods as the demand for a �ow ofservices over several periods.

● He argued that both amonopoly and a competitivemarketwould seek to minimize the cost of providing this �ow toconsumers. aere is no reason that durability per se wouldbe aòected bymarket structure.

● ais result is referred to as Swan’s independent assumption.Output decisions can be treated independently fromdecisions about product durability.

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Price Discrimination● Price discrimination. Amonopoly engages in price

discrimination if it is able to sell otherwise identical units ofoutput at diòerent prices.

● Whether a price discrimination strategy is feasible dependscrucially on the inability of buyers to practice arbitrage.

Perfect price discrimination

● ae strategy of perfect price discrimination (sometimescalled ûrst degree price disrimination) charge each buyer themaximum price he would be willing to pay for the good.

● It extracts all consumer surplus and there is no deadweightloss so that the allocation of resources is eõcient.

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Figure 14.4 Perfect Price Discrimination

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Example 14.4 Perfect Price Discrimination● Consider again the Frisbeemonopolist in Example 14.1. If

possible, it will want to produce the quantity at which priceis exactly equal to marginal cost

P = 100 − Q20= MC = 0.1Q so Q∗ = 666.

● Total revenue and total costs will be

R = ∫Q∗

0P(Q)dQ = 100Q − q2

40

RRRRRRRRRRR

Q=666

Q=0

= 55, 511

C(Q) = 0.05Q2 + 10, 000 = 32, 178.and proûts are π = R − C = 23, 333which is a substantial increase over the single-price policy inExample 14.1 ($15,000).

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Price discrimination across segmentedmarkets

● Perfect price discrimination poses a considerableinformation burden because it requires themonopolist toknow the demand function for each potential buyer.

● A less stringent requirement would be to assumemonopolycan segment its buyers into a few identiûablemarkets andpursue a diòerent pricing policy in each market. ais pricingstrategy is sometimes called third-degree price discrimination.

● Knowing the price elasticities of demand in thesemarkets isenough to pursue such a policy. aemonopoly then sets aprice in each market according to the inverse elasticity rule.

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● Assuming thatmarginal cost is the same in all markets, theresult is a pricing policy in which

Pi (1 +1ei) = Pj (1 +

1e j) ,

or,

PiPj=

1 + 1/e j1 + 1/ei

,

where Pi and Pj are prices charged in markets i and j, whichhave price elasticities of demand given by ei and e j.

● ae proût-maximizing price will be higher in markets wheredemand is less elastic. For example, if ei = −2 and e j = −3,then pi/p j = (1 − 1/3)/(1 − 1/2) = 4/3, prices will be 1/3higher in market i, the less elasticmarket.

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Figure 14.5 Price Discrimination across SegmentedMarkets

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● ae welfare consequences of price discrimination acrosssegmentedmarkets are, in principle, ambiguous.

● If the total amount sold in the two markets is the same underprice discrimination as under a single price, then the singleprice will generally lead to higher welfare.

● ais is because there will always be some consumers who aredenied the good in the high-pricemarket who value itmorethan some consumers who end up purchasing in thelow-pricemarket.

● A possible oòsetting eòect is that price discrimination can insome cases increase total output sold across themarkets.(See Example 14.5) It is possible to have higher welfare underprice discrimination.

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Example 14.5 Price Discrimination across SegmentedMarkets

● Suppose that amonopoly producer of widgets has a constantmarginal cost of c = 6 and sells its products in two separatedmarkets whose inverse demand functions are

P1 = 24 − Q1, P2 = 12 − 0.5Q2

● ae conditions for proût-maximization give

MR1 = 24 − 2Q1 = MR2 = 12 − Q2 = MC = 6

ae optimal choices of output and prices are

Q∗1 = 9,Q∗2 = 6, P∗1 = 15, p∗2 = 9,

and proûts are

π = (P1 − 6)Q1 + (P2 − 6)Q2 = 81 + 18 = 99.

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Figure 14.6 Scale Drawing of the TwoWidgetMarkets inNumerical Example

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● ae deadweight-loss under the third-degree pricediscrimination is

DW = DW1 + DW2

= 12(15 − 6)(18 − 9) + 1

2(9 − 6)(12 − 6)

= 40.5 + 9 = 49.5● A single-price policy. If thismonopoly were constrained to

charge a single price, then themonopoly would set the priceof 15 and cease serving market 2 because themaximumwillingness to pay in market 2 is only 12.

● ae deadweight loss increases

DW = DW1 + DW2 = 40.5 +12(12 − 6)(12 − 0) = 76.5.

● ais illustrates a situation where price discrimination iswelfare improving over a single-price policy.

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Part VI Market Power y Competition

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