Economics & Market Microstructure
Rosenbluth / Hall-Tideman Index (HTI) Formula: Rank-Weighted Market Concentration
Measure antitrust market concentration with full sensitivity to small-fringe competitors using Gideon Rosenbluth (1955) and Marshall Hall & Nicolaus Tideman’s (1967) rank-weighted index HTI = 1 / (2 * SUM(i * s_i) - 1).
Why HHI ignores the number of small fringe competitors while Hall-Tideman penalizes entry barriers directly!
While the Herfindahl-Hirschman Index HHI = SUM(s_i^2) squares market shares—rendering tiny fringe competitors (s_i = 0.5%) practically invisible (0.005^2 = 0.000025)—industrial-organization economists Gideon Rosenbluth (1955) and Marshall Hall & Nicolaus Tideman (1967, JASA) formulated an axiomatic concentration index that explicitly rewards competitive fringe entry!
Ordering all N firms from largest (rank i = 1) to smallest (rank i = N) with market shares s_1 >= s_2 >= ... >= s_N summing to 1, the Rosenbluth / Hall-Tideman Index is HTI = 1 / (2 * SUM_{i=1..N} (i * s_i) - 1)! Like HHI (on 0..1 scale), HTI equals 1 / N for N equal-sized firms and 1.0000 under pure monopoly—and its reciprocal N_eq = 1 / HTI = 2 * SUM(i * s_i) - 1 gives the "Numbers-Equivalent" count of equal-sized competitors!
| Industry Structure (Descending Shares s_1 >= ... >= s_5) | Weighted Rank Sum SUM(i * s_i) | Hall-Tideman HTI & Equivalent Firms 1/HTI |
|---|---|---|
| Dominant Leader + Fringe [0.50, 0.25, 0.15, 0.06, 0.04] | 1.8900 | HTI = 0.3597 (Equivalent to 2.78 Equal Firms) |
| 5 Equal Competitors [0.20, 0.20, 0.20, 0.20, 0.20] | 3.0000 | HTI = 0.2000 (1 / 5 = 5.00 Equal Firms) |
| Near-Monopoly [0.92, 0.04, 0.02, 0.01, 0.01] | 1.1500 | HTI = 0.7692 (Equivalent to 1.30 Firms) |
Hall-Tideman / Rosenbluth Concentration Index HTI = 1 / (2 * SUMPRODUCT(Ranks, Shares) - 1)
Normalizes descending firm revenues B2:B6 into market shares and weights them by descending rank 1..5 in A2:A6.
=IF(OR(SUM(B2:B6) <= 0, MIN(B2:B6) < 0, B2 < B3, B3 < B4, B4 < B5, B5 < B6), "Sort Revenues Descending (Rank 1 = Largest) & Positive Total", ROUND(1 / (2 * (SUMPRODUCT(A2:A6, B2:B6) / SUM(B2:B6)) - 1), 4))Numbers-Equivalent Equal-Sized Firms N_eq = 1 / HTI = 2 * SUM(i * s_i) - 1
Expresses concentration as the intuitive count of equal-sized competitors generating the same Hall-Tideman index.
=IF(OR(SUM(B2:B6) <= 0, MIN(B2:B6) < 0, B2 < B3, B3 < B4, B4 < B5, B5 < B6), "Sort Revenues Descending (Rank 1 = Largest) & Positive Total", ROUND(2 * (SUMPRODUCT(A2:A6, B2:B6) / SUM(B2:B6)) - 1, 2))Try the example
Use the original values or change them to test your understanding.