Measuring Performance of Long-Term Power Generating Portfolios - Green Energy and Efficiency: An Economic Perspective - page 410

1, the above general form reduces to the so-called Shannon-Wiener
diversity index:

For a ¼

X

I
i ¼1 p i ln ðp i Þ :

¼

SW

The higher the SW index, the more diverse the system. If SW < 1, the system is
highly concentrated and therefore subject to the risk of collusion or monopoly,
leading to interrupted supply and/or price hikes [ 23 ].
For a ¼ 2, the reciprocal of the resulting expression is the Her ndahl-Hirschman

concentration index:

X

I

p i : HH ¼

i ¼1

cation) to 10,000 (total concen-
tration). A value HH < 1,000 is taken by antitrust authorities as indicating no
concentration. A value of HH > 1,800 has been interpreted as problematic in terms
of exposure to supply risk.
Krey and Zweifel [ 23 ] apply these two indexes to U.S. and Swiss data to
determine the trade-off between economic ef

The HH index can range from 0 (full diversi

ciency and security of supply. As they

“

point out, both [SW and HH] indices permit evaluation of the security of supply of

different power generating technologies thanks to a greater number of suppliers.
They therefore complement the MVP approach for policy makers who fear pur-
chases of primary energy to be exposed to collusion or monopoly — a consideration
of relevance especially in the markets for natural gas and uranium ” . Both indices

help to determine whether a power generation portfolio is suf ciently diversi ed in

terms of technologies (this in turn implies diversi cation in terms of purchases of

primary energy sources).
We rst looked at the initial capacities and those at the end of the time horizon

under each scenario. Table 2 shows that the SW index is always higher than 1;
below this threshold the risk of collusion looms. Relative to 2012, the SP portfolio
points to a reduction of diversity; the opposite happens with the CB portfolio: it is
the most diversi

ed one. The HH index instead suggests that the SP portfolio is the
least concentrated while CB is the most so.
It may be of interest to apply the SW and HH indexes not only to installed
capacities but to generation levels as well. One or two scenarios suggest that some

Table 2 Diversity and concentration indexes of GB installed capacity from 2012 to 2032
Installed
capacity
(2012)

Gone
green
(2032)

Slow progres-
sion (2032)

Accelerated
growth (2032)

Contracted
background
(2032)

SW 1.455 1.440 1.281 1.441 1.500

HH 4,161 4,096 3,464 4,004 4,556