Question

(15) 1. The following table gives new car registrations for Japan in September 1991: Toyota Nissan Honda Mazda Mitsubishi Daihatsu Suzuki Subaru-Fuji Isuzu Others 1,300,963 769,368 384,830 272,173 254,633 214,027 208,199 116,875 22,758 148,076 Source: Associazione Nationale Fra Industrie Automobilistiche, Notiziaro Statistico, Vol. 33, No. 12, December 1991. Compute the four-firm concentration ratio for autos for Japan in September 1991 (to four decimal places). Compute the Herfindahl-Hirschman index for the same month. (At each stage perform your calculations to four decimal places; and treat others' as a single manufacturer.) (10) 2. How many equal-sized firms would an industry need to produce a Herfindahl- Hirschman index of 0.018181818? (Show all work.) (Note: A method of solution based on trial and error is not acceptable.)

Answer 1

1.

Firm	Number of Car Registrations	Market Share	Square of Market Share
Toyota	1,300,963	0.3524	0.1242
Nissan	769,368	0.2084	0.0434
Honda	384,830	0.1042	0.0109
Mazda	272,173	0.0737	0.0054
Mitsubishi	254,633	0.0690	0.0048
Daihatsu	214,027	0.0580	0.0034
Suzuki	208,199	0.0564	0.0032
Subaru-Fuji	116,875	0.0317	0.0010
Isuzu	22,758	0.0062	0.0000
Others	148,076	0.0401	0.0016
Total	3,691,902	1	0.1979

Formulae used:

Market Share of a firm = Number of car registrations belonging to the firm/Total number of car registrations

Square of Market Share of a firm = (Market Share of the firm)²

a. Four-firm concentration ratio = Sum of the market shares of the 4 largest firms in the industry

In the given numerical, the four largest firms are Toyota, Nissan, Honda and Mazda

Four-firm concentration ratio for autos for Japan in september 1991= 0.3524 + 0.2084 + 0.1042 + 0.0737 = 0.7387

b. Herfindahl-Hirschman Index = Sum of the squares of market shares of all the firms in the industry

= 0.1242 + 0.0434 + 0.0109 + 0.0054 + 0.0048 + 0.0034 + 0.0032 + 0.0010 + 0 + 0.0016 = 0.1979

HHI = 0.1979