measures of business concentration

8/14/2019 Measures of Business Concentration

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Business Concentration- Prof. T. Das 1

Business ConcentrationProf. Tarun Das,

IILM, New Delhi




Contents of this presentation1. Market Power and Learner Index2. Measures of Business Concentration3. Examples4. Relation Between Market power and

Business Concentration5. Review Questions




1.1 Market power and Lerner Index

1. Market power is the ability of the price-

setting firm to raise their prices withoutloosing their market share.

2. Lerner Index =(P-MC)/P = (P-MR)/P

= [P-P(1+1/Ep)]/P = 1- (1+1/Ep)

= -1/ Ep where Ep is the price elasticityof demand.

3. Market power varies inversely with priceelasticity of demand, and equals zerounder perfect competition.




1.2 Determinants of Market power

1. Strong barriers to entry due to

government licensing, investment andfranchise policies.

2. Existence of very large firms witheconomies of scale.

3. Input barriers and immobility of inputs4. Loyalties to brand names/ trade marks5. Consumers lock-in due to large

switching cost caused by installation

and other costs.6. Network externalities




2.1 Business concentration

Market power is closely related to businessconcentration. It means the share enjoyedby dominant firms in an industry. Thereare various indices to measure businessconcentration. An ideal concentrationratio has the following properties;

(a) It depends on sizes of all firms in anindustry, and it is unaffected by anypermutation of sizes i.e. We do not wantto know who are the owners of the firms.It is called the property of anonymity or

impartiality.(b) It ranges in between zero (in the case of

perfect competition) and unity (in thecase of monopoly).




2.2 Properties of IdealConcentration Ratios

(c) It is homogeneous of degree zero in sizesof all firms i.e. if all sizes rise or fall equi-proportionately, then the concentration ratioremains unchanged. It also means that it isindependent of units of measurement.(d) An equal absolute increase in sizes of allfirms leads to reduction of businessconcentration, and an equal absolutereduction of sizes of all firms leads to anincrease of business concentration.(e) A transfer of size from the smaller to the

larger firm increases the degree of businessconcentration and vice versa.




2.3 Concentration Ratios

Concentration ratio depends of size of firms. Sizes can be measured by output,turnover, sales, capital stocks, profits etc.

Let us assume that there are n firms in anindustry with levels of turnover (T1, T2,

T3, ……Tn) arranged in descending orderi.e. T1 ≥T2≥ T3≥ ….≥Tn.Qj = Share of the j-th firm in total turnover(TT) of the industry = Tj/ TT = Tj / Σ Tj

Where TT = Σ Tj = T1 + T2+ T3+….+Tn




2.4 Concentration ratio (CR)

(a) Concentration ratio (CR) = Share of topk (say one, two, or three) firmscombined together. If there is monopoly(i.e. only one firm), then CR equals unity;

otherwise it is less than 1. In the case of perfect competition having very largenumber of firms, each firm hasnegligible share and CR tends to zero. In

all other cases, CR ranges in betweenzero and unity.




2.4-A Example- Concentration Ratio

Sales-

Ind.A

Sales-

Ind.B

Shares-

Ind.A

Shares-

Ind.B40 30 0.40 0.30

30 25 0.30 0.25

15 20 0.15 0.2010 15 0.10 0.15

5 10 0.05 0.10

Total=100

100 1 1

CR1 (%) 40 30

CR2 (%) 70 55

CR3 (%) 85 75




2.5 Herfindahl and Hirschmann (HH)

(b) Herfindahl and Hirschmann (HH) index= It equals the sum of the squares of shares of individual firms = Σ Qj². As inthe case of CR, HH equals 1 in the case

of monopoly, and zero in the case of perfect competition, and CR ranges inbetween zero and unity in all othersituations. If all the firms have equal

shares in output, then Qj=1/n, and HH =Σ (1/n) ² = 1/ n.




2.5-A Example- HH Index Sales-A Sales-B Ind-A

(Share)²Ind-B

(Share)²

40 30 0.16 0.09

30 25 0.09 0.0625

15 20 0.0225 0.04

10 15 0.01 0.0225

5 10 0.0025 0.01

Total=100

100 0.285 0.225

HH Index 0.285 0.225




2.6 Hall and Tideman Index (HT)

(c) Hall and Tideman Index (HT)= 1 / ( 2 Σ Rj x Qj– 1)

where Rj is the rank of the firm, thelargest firm has rank 1, next largest has

rank 2 and the smallest firm has rank n.If all the firms have equal shares,

HT = 1 / [2n x (n+1)/ 2n –1]

= 1/n.




2.6-A An Example- HT Index

Sales-A Sales-B Ind-A

Rj x Qj

Ind-B

Rj x Qj40 30 1x0.4=0.4 1x0.3=0.3

30 25 2x0.3=0.6 2x0.25=0.5

15 20 3x0.15=0.45 3x0.2=0.6

10 15 4x0.1=0.4 4x0.15=0.6

5 10 5x0.05=0.25 5x0.1=0.5

T=100 100 Sum=2.1 Sum=2.5




2.7 CV and Var (Log)

(d) Coefficient of variation = 100 x SD /AM where SD is the standard deviationand AM is the arithmetic mean of output of individual firms.

AM = Σ Qj/n, SD = √ (VAR),VAR = Σ (Qj-AM)² /n

(e) Variance of logarithms- It is thevariance of the logarithms of outputsof individual firms = Σ (log Qj– AML)² /n

where AML = Σ log Qj/ n.




2.7-A Example of CV and Var(Log)

T j P j Q j Q j x Q j ( T j - A M ) ^ 2lo g T j (L n T j -A M

4 0 0 . 2 0 . 4 0 . 1 6 0 4 0 0 3 . 6 9 0 . 9 0

3 0 0 . 2 0 . 3 0 . 0 9 0 1 0 0 3 . 4 0 0 . 4 3

1 5 0 . 2 0 . 1 5 0 . 0 2 3 2 5 2 . 7 1 0 . 0 0

1 0 0 . 2 0 . 1 0 . 0 1 0 1 0 0 2 . 3 0 0 . 1 9

5 0 . 2 0 . 0 5 0 . 0 0 3 2 2 5 1 . 6 1 1 . 2 8

1 0 0 1 . 0 1 . 0 0 0 . 2 8 5 8 5 0 1 3 . 7 2 . 8 1

A M = S D = C V = A M (L o g )V a r ( l o g )

2 0 1 3 6 5 2 . 7 4 0 . 5 6




2.8 Lorenz Concentration Curveand Gini-Lorenz ratio

(f) Gini-Lorenz ratio = 1 - Σ CPj(CQj+ CQi)where i=j-1.

A Lorenz curve is the locus of all points

(CPj, CQj)where CPj = Cumulative proportion of units upto j-th firm arranged in ascendingorder and CQj = Cumulative shares of

output of these firms.




2.9 Lorenz Concentration Curveand Gini-Lorenz ratio

Both CPj and CQj range in between 0

and 1. A Lorenz curve is drawn within aunit-square box diagram. The 45 degreeradius vector is called the egalitarian lineas on it CPj equals CQi for each i=1, 2, 3….. n. The area between the Lorenzcurve and the egalitarian line is calledthe area of concentration (A).Gini-Lorenz ratio equals the area of concentration (A) divided by the area of thetriangle below the egalitarian line.




2.10 Lorenz Concentration Curve

and Gini-Lorenz ratio- Industry-A

F i r m




2.11 Lorenz Concentration Curve

and Gini-Lorenz ratio-Industry-B

F i r m




2.12 LorenzConcentrationCurves




2.13 Do the various ratiossatisfy characteristics of ideal

index?

Index F(Tj)? 1≥R≥ 0Hom°?R(T+a)<R(T)

Transfercriteria?

CR No Yes Yes Yes Yes?

HHI Yes Yes Yes Yes YesHTI Yes Yes Yes Yes Yes

CV Yes No Yes Yes Yes

VarLog Yes No Yes Yes Yes

Gini Yes Yes Yes Yes Yes




3.1 Industry-1

F i rm




3.2 Industry-2

R j

1




3.3 Industry Comparisons




4.1 Review Questions

1. Define Lerner’s index of monopoly power.Discuss factors which determine monopolypower in an industry.

2. What are the characteristics of an idealmeasure of business concentration? Define

concentration ratio, Herfindahl andHirschmann Index, and Hall and TidemanIndex of business concentration. Do theysatisfy characteristics of an ideal measure?

3. Define Lorenz curve and Gini Lorenz ratio.

Does it satisfy characteristics of an idealmeasure of business concentration.




4.2 Review Questions

4. Five firms in a market have market shares of 25, 25, 25, 15 and 10 per cent respectively.Calculate the Herfindahl-Hirschmann index,Hall and Tideman index and concentrationratios for top-3 (CR3) and top-4 (CR4) firms.Suppose the smallest two firms propose to

merge. What would be the impact of suchmerger on these concentration ratios? Whatwould be the Gini-Lorenz ratio after merger?Is their any conflicts among theconcentration ratios after merger?




4.2-A Answer for Q.4.2

B e f o r e M e r g e r

F i r m u r n P r o S h a r eQ j x Q jR j x Q jC P j C Q j P j x ( CR j T j P j Q j + C Q j

1 2 5 0 . 2 0 . 2 5 0 . 0 6 3 0 . 2 5 0 . 2 0 0 . 2 5 0 . 0 5 0

2 2 5 0 . 2 0 . 2 5 0 . 0 6 3 0 . 5 0 0 . 4 0 0 . 5 0 0 . 1 5 0

3 2 5 0 . 2 0 . 2 5 0 . 0 6 3 0 . 7 5 0 . 6 0 0 . 7 5 0 . 2 5 0

4 1 5 0 . 2 0 . 1 5 0 . 0 2 3 0 . 6 0 0 . 8 0 0 . 9 0 0 . 3 3 0

5 1 0 0 . 2 0 . 1 0 . 0 1 0 0 . 5 0 1 . 0 0 1 . 0 0 0 . 3 8 0

T o t a l 1 0 0 1 . 0 1 . 0 0 0 . 2 2 0 2 . 6 0 0 1 . 1 6 0

C R 3 C R 4 H H H T G i n i

0 . 7 5 0 . 9 0 0 . 2 2 0 . 2 4 0 . 1 6 0




4.2-B Answer for Q4.2

A f t e r M e r g e r

F i r m u r n P r o S h a r eQ j x Q jR j x Q jC P j C Q j P j x (R j T j P j Q j + C Q j

1 2 5 0 . 2 5 0 . 2 5 0 . 0 6 3 0 . 2 5 0 . 2 5 0 . 2 5 0 . 0 6 3

2 2 5 0 . 2 5 0 . 2 5 0 . 0 6 3 0 . 5 0 0 . 5 0 0 . 5 0 0 . 1 8 8

3 2 5 0 . 2 5 0 . 2 5 0 . 0 6 3 0 . 7 5 0 . 7 5 0 . 7 5 0 . 3 1 3

4 2 5 0 . 2 5 0 . 2 5 0 . 0 6 3 1 . 0 0 1 . 0 0 1 . 0 0 0 . 4 3 8

T o t a l 1 0 0 1 . 0 1 . 0 0 0 . 2 5 02 . 5 0 0 1 . 0 0 0

C R 3 C R 4 H H H T G i n i

0 . 7 5 1 . 0 0 0 . 2 5 0 . 2 5 0 . 0 0 0




4.2-C There are conflicts among thevarious ratios. CR3 remains unchanged.CR4, HHI and HTI increase after merger.

But Gini ratio declines to zero aftermerger and shows no concentration. Thuswhile Gini-Lorenz ratio indicates degree of dispersal, others indicate degree of market power by dominant firms. CR and

Gini donot depend on number of firmswhile HHI and HTI depend on number of firms.

C R 3 C R 4 H H H T G i n

B e f o r e M e r g e r 0 . 7 5 0 . 9 0 . 2 2 0 . 2 4 0 . 1

A f t e r M e r g e r 0 . 7 5 1 . 0 0 . 2 5 0 . 2 5 0

Th k




Thank youHave a Good Day

measures of business concentration

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