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Justin Bieber with one of his followers.

An interesting rumor came into the Business Insider office the other day: Justin Bieber has so many followers on Twitter — more than 37 million — that a single tweet by the singer can change the price of promoted tweets for advertisers.

The logic of the rumor is that if Bieber tweets a word like "cologne," as he did the other day in reference to the European city he was visiting, then the sheer volume of retweets from his fans could move the price of the word "cologne" for advertisers trying to target "cologne" as a keyword for either fragrance shoppers or tourists interested in visiting the city.

An increase in the number of retweets is an increase in the supply of keyword inventory (in this case for "cologne"). Generally, an increase in supply should move the bid price for the word down, because the demand from advertisers wanting to buy "cologne" should stay the same. It's supply v. demand: Greater supply = cheaper prices.

Twitter has 500 million users, but 40 percent of those never tweet. So the active population is ~300 million. Bieber's audience — his inventory, if you will — is more than 1 percent of the entire active market.

His cologne tweet was retweeted 47,000 times. And that's a low count for Bieber.

To test the rumor, we turned to TBG Digital, one of Twitter's partners for its Ads API (the interface that delivers ads en masse into the twittersphere). We allowed TBG to run a small campaign on our behalf targeting followers of Bieber and Rihanna, who has 29 million followers. We wanted to see if there was a difference between the price of targeting Bieber's fans vs. Rihanna's fans vs. non-celebrity material.

Here are the results:

Cost per engagement for targeting celebrity followers with a promoted tweet:

• Bieber: $0.51

• Rihanna: $0.51

Cost per engagement (retweets, etc.) when targeting celebrity hashtags v. trending hashtags v. non-trending hashtags:

• Celebrity: $1.23

• Trending: $1.27

• Non-Trending: $1.26

Cost per acquisition of new followers who also follow Bieber or Rihanna:

• Bieber followers: $3.22

• Rhianna followers: $3.35

Our results:

• Impressions: 568,950

• Engagements: 6,316

• Increased follows: 274

The folks at TBG tell us that overall, there was no significant price difference between Bieber, Rihanna, or non-trending hashtags. While Rihanna fans are a little more expensive to acquire as followers than Bieber fans, it's a wash in the grand scheme of things. (We are, however, enormously grateful for our 274 new readers of @TBITheWire.)

The BIG caveat here is that our test was small, as was our sample size, so our evidence is merely anecdotal. (The campaign did not target "cologne," by the way.)