Measures Of Business Concentration By Tarun Das

Tarun Das Business Concentration

Page 1

11/26/2009

Market Power and Business concentration Prof. Tarun Das, IILM, New Delhi-110003. 1.1 Market Power and Lerner Index 1. Market power is the ability of the price-setting 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)/P = -1/ Ep 3. Market power varies inversely with price elasticity of demand, and equals zero under perfect competition. 1.2 Determinants of market power 1. Barriers to entry due to government licensing, investment and franchise policies. 2. Existence of very large firms with economies of scale. 3. Input barriers 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 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. 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). (c) It is homogeneous of degree zero in sizes of all firms i.e. if all sizes rise or fall equi-proportionately, 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 concentration and vice versa. 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

1

Tarun Das Business Concentration

Page 2

11/26/2009

2.2 Various measures of business concentration (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. (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. (c) Hall and Tideman Index (HT) = 1 / ( 2 Σ Rj x Qi – 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. (d) Coefficient of variation (CV) = 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, VAR = Σ (Qj-AM) ² /n SD = √ (VAR) CV = 100 x SD / AM (e) Variance of logarithms- It is the variance of the logarithms of outputs of individual firms. Var (Log) = Σ (log Qj – AML) ² / n Where AML = Σ log Qj/ n. (f) Gini-Lorenz ratio = Σ CPj (CQj+ CQi) –1, where i=j-1. A Lorenz curve is the locus of all points (CPj, CQj), Where CPj = Cumulative proportion of units up to j-th firm arranged in ascending order and CQj = Cumulative shares of output of these firms. Both CPj and CQj range in between 0 and 1. A Lorenz curve is drawn within a unitsquare box diagram. The 45 degree radius vector is called the egalitarian line as on it CPj equals CQj 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.

2

Tarun Das Business Concentration

Firm Rj 1 2 3 4 5 Total Firm Rj 1 2 3 4 5 Total AM= AM (Log) SD= CV=

Turnover Proport. Tj Pj 40 0.2 30 0.2 15 0.2 10 0.2 5 0.2 100 1.0 Turnover Proport. Tj Pj 40 0.2 30 0.2 15 0.2 10 0.2 5 0.2 100 1.0 20 2.74 13 65

Firm Turnover Proport. Rj Tj Pj 1 30 0.2 2 25 0.2 3 20 0.2 4 15 0.2 5 10 0.2 Total 100 1.0 Firm Turnover Proport. Rj Tj Pj 1 30 0.2 2 25 0.2 3 20 0.2 4 15 0.2 5 10 0.2 Total 100 1.0 AM= 20 AM (Log) 2.93 SD= 7 CV= 35

Page 3

Example: Industry-A Share Qj x Qj (Tj-AM)^2 Qj 0.4 0.160 400 0.3 0.090 100 0.15 0.023 25 0.1 0.010 100 0.05 0.003 225 1.00 0.285 850 Share CPj CQj Qj 0.4 0.20 0.40 0.3 0.40 0.70 0.15 0.60 0.85 0.1 0.80 0.95 0.05 1.00 1.00 1.00 CR1= 0.40 CR2= 0.70 CR3= 0.85

11/26/2009

LogTj

(LogTj-AML)^2

3.69 3.40 2.71 2.30 1.61 13.7 Pj x (CQj +CQj-1) 0.080 0.220 0.310 0.360 0.390 1.360 HH = HT = Var (log) Gini =

0.90 0.43 0.00 0.19 1.28 2.81 Rj x Qj

Example: Industry-B Share Qj x Qj (Tj-AM)^2 logTj Qj 0.3 0.090 100 3.40 0.25 0.063 25 3.22 0.2 0.040 0 3.00 0.15 0.023 25 2.71 0.1 0.010 100 2.30 1.00 0.225 250 14.6 Share CPj CQj Pj x (CQj Qj +CQj-1) 0.3 0.20 0.30 0.060 0.25 0.40 0.55 0.170 0.2 0.60 0.75 0.260 0.15 0.80 0.90 0.330 0.1 1.00 1.00 0.380 1.00 1.200 CR1= 0.30 HH = CR2= 0.55 HT = CR3= 0.75 Var (log) Gini =

3

0.4 0.6 0.45 0.4 0.25 2.10 0.29 0.91 0.56 0.36 (LogTj-AML)^2 0.43 0.23 0.06 0.00 0.19 0.92 Rj x Qj 0.3 0.5 0.6 0.6 0.5 2.50 0.23 0.67 0.18 0.20

Tarun Das Business Concentration

Concentration Ratios and other indicators AM= AM (Log) SD= CR1= CR2= CR3= HH = HT = CV= Var (log) Gini =

Industry-A 20 2.74 13.0 0.40 0.70 0.85 0.29 0.91 65 0.56 0.36

Page 4

Industry-B 20 2.93 7.1 0.30 0.55 0.75 0.23 0.67 35 0.18 0.20

Lorenz Concentration Curves CQJ CQj CQJ Egalitarian Line Industry-A Industry-2 0.0 0.0 0.0 0.2 0.4 0.3 0.4 0.7 0.55 0.6 0.85 0.75 0.8 0.95 0.9 1.0 1.0 1.0

4

11/26/2009