LONG TAIL ECONOMICSIMPLICATIONS OF POWER LAW DISTRIBUTIONS

THE LONG TAIL

Sales by sales rank: Blue line for Brick and Mortar Retailers; Red Line, Internet Retailers

LONG TAILS AND POWER LAWS

S = aRk

• S is quantity sold• R is sales rank of individual titles• A log-linear equation: Log S = log(a) + klog(R)

Brick and Mortar Retailers

• Market is limited to local area• Inventory is limited by high probability that low ranking items

will not sell

Internet Retailer

• Market is national or international in scope• Inventory relatively unlimited; even low ranking items likely to

sell

TRADITIONAL RETAILER’S PRODUCTS ACCOUNT FOR ONLY 10% OF ONLINE RETAILER’S INVENTORY, 75% OF REVENUES, 66% OF PROFIT

TRADITIONAL VS. ONLINE RETAILING

For Traditional Music Retail

• New album releases account for 63% of sales in 2005• The top 1000 albums make up almost 80% of sales• At big-box retailers, top 200 account for 90% of sales

For Online Music Retail

• New music accounts for one-third of sales with two-thirds from older “catalog” items

• The top 1000 albums account for less than 33% of sales• Albums beyond the top 5000 account for 50% of sales

POWER LAW OR LONG TAIL MARKETSRequire (Anderson):

• Variety (differentiated products)• Inequality (variations in “quality”)• Network effects that amplify differences

Notice similarity to superstars

• Imperfect substitutability among “goods”• Some sellers (“performers”) are preferred to others• Differentiated products

• Economies of scale in production (realized online)• Costs of production do not rise in proportion to a seller’s market

• Access to a market of large or increasing scope (due to Internet)• Often due to technological change

Online Retailing is a Superstar Phenomenon

ONLINE SUPERSTARS

As online music markets grow

• Total number of retailers declines• Traditional retail has become limited to

• Big-box retailers carrying 4,500 albums or less• Small local “specialty” retailers often selling “used” music as

well as new

Online Retailers expand

• Amazon carries about 500,000 albums (CDs)• iTunes, Amazon, Pandora, Spotify can carry almost unlimited

digital inventory at near zero marginal cost

INFINITE VARIETY?

About 30,000 items 500,000 itemsWalMart ≈ 5,000

POWER LAW SALES DISTRIBUTIONS DISPLAY “SELF-SIMILARITY AT MULTIPLE SCALES”

If S = f(R) = aRk , then f(cR) = a(cR)k = ck(aRk) = ckf(R), where c is a constant.

WHAT MAKES THE LONG TAIL CHANGE?

Anderson

• Increasing market scope (technology)• Network effects and filters or search functions• Niche titles’ sales increase relative to hits

Bentley, et al.

• Random copying behavior with “u” fraction of “innovators”• Produces power law sales distributions • Increasing numbers of “innovators” increases top list turnover

producing a longer tail

REFERENCES

Anderson, Chris. 2006. The Long Tail. Hyperion: New York.

Bentley, R. Alexander, Carl P. Lipo, Harold A. Herzog, and Matthew W. Hahn. 2007. “Regular Rates of Popular Culture Change Reflect Random Copying.” Evolution and Human Behavior, 28, 5-158.