Is there errata for continuous magic item pricing?

Question

The price guidelines for magic items with use-activated or continuous spell effects are as follows:

Spell level × caster level × 2,000 gp ²

^{2 — If a continuous item has an effect based on a spell with a duration measured in rounds, multiply the cost by 4. If the duration of the spell is 1 minute/level, multiply the cost by 2, and if the duration is 10 minutes/level, multiply the cost by 1.5. If the spell has a 24-hour duration or greater, divide the cost in half.}

The example item given is the Lantern of Revealing. It's one of the simplest items - duplicating the 3rd level spell Invisibility Purge from a 5th level caster exactly when it's in use. Since Invisibility Purge's duration is 1 min./level, its cost should be calculated as such:

Spell level 3 × CL 5 × 2,000gp × 2 = 60,000gp

Seems easy enough.

Except it's not. It's listed as 30,000 gp.

Am I missing something obvious or some errata somewhere? Do other use-activated/continuous magic items follow the given formula? It seems odd that the extraordinarily textbook example item isn't by the book, as it were.

Answer 1

From the left of the box containing the formulae:

Not all items adhere to these formulas. First and foremost, these few formulas aren't enough to truly gauge the exact differences between items. The price of a magic item may be modified based on its actual worth. The formulas only provide a starting point. The pricing of scrolls assumes that, whenever possible, a wizard or cleric created it. Potions and wands follow the formulas exactly. Staves follow the formulas closely, and other items require at least some judgment calls.

So... basically, things don't necessarily follow the formulae. I suspect that this is a just a case of limited utility; for example, an item capable of performing same-duration, same-level Protection From Energy with use activation is significantly more useful for the same nominal price by the formulae as a Lantern of Revealing in the vast majority of cases (energy-using foes being generally more common than invisible foes. ProtEnergy would also let you avoid friendly fire incidents, and doesn't have the downside of revealing your own invisible rogue like the lantern does).

Answer 2

The lantern also has the limitation of needing to be lit, meaning that oil is a limitation, which could be considered as having the "Charged" disadvantage which halves the price.