Spotify is one of the most popular streaming music services in the world, and since its July debut in the U.S. and the recent launch of a deep Facebook integration , it has gained 250,000 U.S. subscribers, bringing the company’s worldwide paid subscriber total to “well north” of 2m.

But it’s not all good news for the Swedish-based company: while revenue grew from just over £11m in 2009 to just over £63m in 2010, during the same period Spotify’s after-tax loss jumped grew by nearly £10m to £26m.

For a company that was supposed to be Sweden’s most profitable music export, surpassing even Abba, the company’s losses, which are largely attributable to increased administrative costs and expensive music licensing deals, might be worrisome to observers of the streaming music market. Spotify’s situation isn’t unique in the market; United States-based streaming music provider Pandora has also seen its revenue grow while it continues to lose money.

Spotify and Pandora should remind us of a humorous business anecdote that goes something like this: a middle manager notices that his company is losing money on every widget it sells. He goes to his boss, worried about the company’s business model. The boss reassures him, “Don’t worry. We’ll make it up on volume!

Of course, while economies of scale can turn transactions that aren’t profitable at low volume into profitable transactions at high volume in certain markets, the reality is that you can’t necessarily make it up in volume. Selling more stuff doesn’t always lead to profit, and some times, selling more stuff makes profitability even more difficult to achieve.

Will this be the case for Spotify and Pandora? Time will tell. In the meantime, both companies provide useful case studies for entrepreneurs and business owners who are often led to believe that profitability necessarily follows scale. That isn’t always the case, and it’s important not to make assumptions about the relationship between the two, which sadly, is done quite a lot in digital businesses.