Question

In Market B, there are 7 hospitals. We know

B1’s share = 26%

B2’s revenue = $1 million

B3’s share = 27%

B4’s revenue = $2 million

B5’s share = 5%

B6’s revenue = $4 million

Total hospital revenue = $20 million

Find: Revenues of B1, B3, B5 and B7

Find: the Shares of B2, B4, B6 and B7

Solve for HHI in Market B.

Answer 1

Formula :

Revenue of Bi Hospital = (Hospital Bi share in percent / 100)*Total Hospital Revenue.

Thus using above formula we get :

(i)

Revenues of B1 = (Hospital B1 share in percent / 100)*Total Hospital Revenue

= (26/100)*$20 million

= 5.2 million

Revenues of B3 = (Hospital B3 share in percent / 100)*Total Hospital Revenue

= (27/100)*$20 million

= 5.4 million

Revenues of B5 = (Hospital B5 share in percent / 100)*Total Hospital Revenue

= (5/100)*$20 million

= 1 million

Revenues of B7 = Total Hospital revenue - Revenues of B1 - Revenues of B2 - Revenues of B3 - Revenues of B4 - Revenues of B5- Revenues of B6

=> Revenues of B7 = 20 million - 5.2 million - 1 million - 5.4 million - 2 million - 1 million - 4 million

=> Revenues of B7 = 1.4 million

(ii)

Using above formula we get : Revenue of Bi Hospital = (Hospital Bi share in percent / 100)*Total Hospital Revenue.

=> Hospital Bi share in percent = (Revenue of Bi Hospital / Total Hospital Revenue)*100

Thus using above formula we get :

Hospital B2 share in percent = (Revenue of B2 Hospital / Total Hospital Revenue)*100

= (1 million / 20 million)*100

= 5%

Hospital B4 share = (Revenue of B2 Hospital / Total Hospital Revenue)*100

= (2 million / 20 million)*100

= 10%

Hospital B6 share = (Revenue of B2 Hospital / Total Hospital Revenue)*100

= (4 million / 20 million)*100

= 20%

Hospital B7 share = 100 - (Sum of hospital shares of B1 , B2 , B3 , B4 , B5 , B6)

=> Hospital B7 share = 100 - (26 + 5 + 27 + 10 + 5 + 20) = 7%

Hence, Hospital B7 share = 7%

(iii)

Formula :

HHI(Herfindahl Index) = Sum of square of all market shares.

Hence, HHI = 26² + 5² + 27² + 10² + 5² + 20² 7²

=> HHI in Market B = 2004