### Diminishing Returns, The Square Root Rule, and Page Counts

One of the least understood issues in cataloging is knowing how many pages to have in each catalog. Let's apply the square root rule to this concept.

Assume that last year you mailed a 100 page catalog to 1,000,000 customers, generating \$5,000,000 demand via phone, mail and website. Demand was converted to profit at a rate of 35%, and the catalog cost \$800,000 to mail. Profit = \$5,000,000 * 0.35 - \$800,000 = \$950,000. Mmmmm .... profit!

The table below simulates what might have happened at different page counts.

 Circulation = 1,000,000 Customers Square Pages Root Demand Profit 60 0.775 \$3,872,983 \$875,544 80 0.894 \$4,472,136 \$925,248 100 1.000 \$5,000,000 \$950,000 120 1.095 \$5,477,226 \$957,029 140 1.183 \$5,916,080 \$950,628

If you're wondering, the square root function is calculated as (simulated pages / actual pages) ^ 0.5. At 60 pages, the value is 0.775.

Notice that peak profit occurs at a simulated page count of 120. If enough merchandise is available, at an appropriate presentation density, your page count could increase.

Folks, this stuff is about to become really important. In a few years, the ecological pressures (i.e. cutting down too many trees) on catalogers will be significant enough that intimate knowledge of appropriate page counts will have to be standard knowledge.

As you can see, this isn't rocket science. Combining page counts with circ depth (which can also be simulated in a similar manner), one can develop a circ plan for a catalog in about ninety seconds. An entire year's worth of catalogs can be "simulated" in a half our or an hour. Historically, our industry chose not to take the "simulation" route in figuring out how to configure a catalog.

Of course, you'll want to do the real work required to manage a circulation plan, including file forecasting, housefile vs. acquisition, and RFM profitability. But this is where your work starts.

Next up: A worksheet for combining circ depth and page count.