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Lost volume to

Posted by Sphinx on August 27, 2003

Private letter-carrying and express businesses developed. Although their activities were only semilegal, they thrived, and actually advertised that between Boston and Philadelphia they were a half-day speedier than the government mail. The government postal service lost volume to private competition and was not able to handle efficiently even the business it had.

How to explain volume in "lost volume to"?
BTW, I'm confused by the author saying, "even the business it had." Any help?