Measures Of Business Concentration

Business Concentration Prof. Tarun Das, IILM, New Delhi

Business Concentration- Prof. T. Das

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Contents of this presentation 1. Market Power and Learner Index 2. Measures of Business Concentration 3. Examples 4. Relation Between Market power and Business Concentration 5. Review Questions

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1.1 Market power and Lerner Index 1. Market power is the ability of the pricesetting firm to raise their prices without loosing 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 elasticity of demand. 3. Market power varies inversely with price elasticity of demand, and equals zero under perfect competition.

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1.2 Determinants of Market power 1. Strong barriers to entry due to government licensing, investment and franchise policies. 2. Existence of very large firms with economies of scale. 3. Input barriers and immobility of inputs 4. Loyalties to brand names/ trade marks 5. Consumers lock-in due to large switching cost caused by installation and other costs. 6. Network externalities

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2.1 Business concentration Market power is closely related to business concentration. It means the share enjoyed by dominant firms in an industry. There are various indices to measure business concentration. An ideal concentration ratio has the following properties;  (a) It depends on sizes of all firms in an industry, and it is unaffected by any permutation of sizes i.e. We do not want to 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 the case of monopoly). Business Concentration- Prof. T. Das

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2.2 Properties of Ideal Concentration Ratios

 

(c) It is homogeneous of degree zero in sizes of all firms i.e. if all sizes rise or fall equiproportionately, then the concentration ratio remains unchanged. It also means that it is independent of units of measurement. (d) An equal absolute increase in sizes of all firms leads to reduction of business concentration, and an equal absolute reduction of sizes of all firms leads to an increase of business concentration. (e) A transfer of size from the smaller to the larger firm increases the degree of business concentration and vice versa.

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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 an industry with levels of turnover (T1, T2, T3, ……Tn) arranged in descending order i.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

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2.4 Concentration ratio (CR) (a) Concentration ratio (CR) = Share of top k (say one, two, or three) firms combined 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 large number of firms, each firm has negligible share and CR tends to zero. In all other cases, CR ranges in between zero and unity.   Business Concentration- Prof. T. Das

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2.4-A Example- Concentration Ratio SalesInd.A

SalesInd.B

SharesInd.A

SharesInd.B

40 30 15 10 5 Total=10 0

30 25 20 15 10 100

0.40 0.30 0.15 0.10 0.05 1

0.30 0.25 0.20 0.15 0.10 1

CR1 (%) CR2 (%) CR3 (%)

40 70 Business Concentration- Prof. T. Das 85

30 55 75

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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 in the case of CR, HH equals 1 in the case of monopoly, and zero in the case of perfect competition, and CR ranges in between zero and unity in all other situations. If all the firms have equal shares in output, then Qj=1/n, and HH = Σ (1/n) ² = 1/ n.   Business Concentration- Prof. T. Das

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2.5-A Example- HH Index Sales-A     40 30 15 10 5 Total=10 0 HH Index

Sales-B

Ind-A (Share)²

Ind-B (Share)²

30 25 20 15 10 100

0.16 0.09 0.0225 0.01 0.0025 0.285

0.09 0.0625 0.04 0.0225 0.01 0.225

0.285

0.225

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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, the largest 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.     Business Concentration- Prof. T. Das

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2.6-A An Example- HT Index Sales-A

Sales-B

  40 30

30 25

15

20

10

15

5

10

T=100

100

Ind-A Ind-B Rj x Qj Rj x Qj 1x0.4=0.4 1x0.3=0.3 2x0.3=0.6 2x0.25=0.5 3x0.15=0.45 3x0.2=0.6 4x0.1=0.4 4x0.15=0.6 5x0.05=0.25 5x0.1=0.5 Sum=2.1

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Sum=2.5

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2.7 CV and Var (Log) (d) Coefficient of variation = 100 x SD / AM where SD is the standard deviation and 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 the variance of the logarithms of outputs of individual firms = Σ (log Qj– AML)² / n where AML = Σ log Qj/ n. Business Concentration- Prof. T. Das

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2.7-A Example of CV and Var (Log) Tj

Pj

40 0 .2 30 0 .2 15 0 .2 10 0 .2 5 0 .2 1 00 1 .0 AM = SD= 20 13

Qj

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

0 .4 0 .16 0 4 00 3 .69 0 .3 0 .09 0 1 00 3 .40 0 .15 0 .02 3 25 2 .71 0 .1 0 .01 0 1 00 2 .30 0 .05 0 .00 3 2 25 1 .61 1 .00 0 .28 5 8 50 1 3.7 C V = A M (L o gV) a r (l o g ) 65 2 .74 0.5 6

0.9 0 0.4 3 0.0 0 0.1 9 1.2 8 2.8 1

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2.8 Lorenz Concentration Curve and 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 ascending order and CQj = Cumulative shares of output of these firms.

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2.9 Lorenz Concentration Curve and Gini-Lorenz ratio Both CPj and CQj range in between 0 and 1. A Lorenz curve is drawn within a unit-square box diagram. The 45 degree radius vector is called the egalitarian line as on it CPj equals CQi for each i=1, 2, 3 ….. n. The area between the Lorenz curve and the egalitarian line is called the area of concentration (A). Gini-Lorenz ratio equals the area of concentration (A) divided by the area of the triangle below the egalitarian line.

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2.10 Lorenz Concentration Curve and Gini-Lorenz ratio- Industry-A

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2.11 Lorenz Concentration Curve and Gini-Lorenz ratio-Industry-B

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2.12 LorenzConcentration Curves

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2.13 Do the various ratios satisfy characteristics of ideal index?

Index F(Tj)? 1≥R≥ 0 Hom°? R(T+a)< Transfer R(T)

criteria?

CR HHI HTI CV VarLog

No Yes Yes Yes Yes

Yes Yes Yes No No

Yes Yes Yes Yes Yes

Yes Yes Yes Yes Yes

Yes? Yes Yes Yes Yes

Gini

Yes

Yes

Yes

Yes

Yes

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3.1 Industry-1

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3.2 Industry-2

Rj 1

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3.3 Industry Comparisons

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A H

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4.1 Review Questions 1. Define Lerner’s index of monopoly power. Discuss factors which determine monopoly power in an industry. 2. What are the characteristics of an ideal measure of business concentration? Define concentration ratio, Herfindahl and Hirschmann Index, and Hall and Tideman Index of business concentration. Do they satisfy characteristics of an ideal measure? 3. Define Lorenz curve and Gini Lorenz ratio. Does it satisfy characteristics of an ideal measure of business concentration.

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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 concentration ratios for top-3 (CR3) and top-4 (CR4) firms. Suppose the smallest two firms propose to merge. What would be the impact of such merger on these concentration ratios? What would be the Gini-Lorenz ratio after merger? Is their any conflicts among the concentration ratios after merger?

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4.2-A Answer for Q.4.2 B e fo r e M e r g e r F i r mT u r n oPv reo r p So hr ta. rQe j x QR j x Q Cj P j Rj Tj Pj Qj 1 2 5 0 .2 0 .2 5 0 .0 6 3 0 .2 5 0 .2 0 2 2 5 0 .2 0 .2 5 0 .0 6 3 0 .5 0 0 .4 0 3 2 5 0 .2 0 .2 5 0 .0 6 3 0 .7 5 0 .6 0 4 1 5 0 .2 0 .1 5 0 .0 2 3 0 .6 0 0 .8 0 5 1 0 0 .2 0 .1 0 .0 1 0 0 .5 0 1 .0 0 T o ta l 1 0 0 1 .0 1 .0 0 0 .2 2 02 .6 0 0 C R 3 C R 4 H H H T G in i 0 .7 5 0 .9 0 0 .2 2 0 .2 4 0 .1 6 0

C Q j P j x (C Q j + C Q j-1 ) 0 .2 5 0 .0 5 0 0 .5 0 0 .1 5 0 0 .7 5 0 .2 5 0 0 .9 0 0 .3 3 0 1 .0 0 0 .3 8 0 1 .1 6 0

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4.2-B Answer for Q4.2 A fte r M e r g e r F i r mT u r n oP v r eo rpS ohr at . rQe j x RQ j x QCj P j Rj Tj Pj Q j 1 2 5 0 .2 5 0 .2 5 0 .0 6 3 0 .2 5 0 .2 5 2 2 5 0 .2 5 0 .2 5 0 .0 6 3 0 .5 0 0 .5 0 3 2 5 0 .2 5 0 .2 5 0 .0 6 3 0 .7 5 0 .7 5 4 2 5 0 .2 5 0 .2 5 0 .0 6 3 1 .0 0 1 .0 0 T o t a l 1 0 0 1 . 0 1 . 0 0 0 . 2 5 02 . 5 0 0 C R 3 C R 4 H H H T G in i 0 .7 5 1 .0 0 0 .2 5 0 .2 5 0 .0 0 0

C Q j P j x (C Q j + C Q j-1 ) 0 .2 5 0 .0 6 3 0 .5 0 0 .1 8 8 0 .7 5 0 .3 1 3 1 .0 0 0 .4 3 8 1 .0 0 0

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4.2-C There are conflicts among the various ratios. CR3 remains unchanged. CR4, HHI and HTI increase after merger. But Gini ratio declines to zero after merger and shows no concentration. Thus while Gini-Lorenz ratio indicates degree of dispersal, others indicate degree of market power by dominant firms. CR and Gini donot depend on number of firms while HHI and HTI depend on number of firms. C R 3 C R 4 H H H T G in i B e f o r e M0 e. 7r 5g 0e .r9 0 . 2 2 0 . 2 4 0 . 1 6 A f t e r M e 0r g. 7 e5 r 1 . 0 0 . 2 5 0 . 2 5 0

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Thank you Have a Good Day

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