Consider the data from Problem $27-11$. Suppose that antitrust authorities have determined that the relevant market includes both e-books and physical books. These authorities perceive that a monopoly situation exists that can be challenged on legal grounds if the value of the Herfindahl-Hirschman Index exceeds $5000$. On the basis of this criterion, do the antitrust authorities conclude that there are grounds for a legal challenge? Explain.

Physical books are known to as printed books. A printed book is composed of a number of pages bound together by the front and rear covers. The term "e-book" refers to a digital book. All pages of an e-book are in digital format, which indicates the book has been converted to an electronic format.

Calculating the Herfindahl-Hirschman index value for mixed marketplaces (e-books and physical books):

$HHI=42.5^2+20.5^2+{20}^2+7.5^2+5^2+4.5^2$

$HHI=1806.25+420.25+400+56.25+25+20.25$

$HHI=2728$

The combined market value of the Herfindahl-Hirschman index (e-books and physical books) is$2728$.

If the value of $HHI$exceeds $5000$, authorities believe a monopoly situation exists in the market, which can be contested on legal grounds.

Since $HHI$'s combined [e-books and physical books] market value is less than $5000$, antitrust authorities can decide that there is no basis for a legal challenge in the combined market.