Why a percentage charge can become cheaper as a share of price

An effective charge rate is the total charge divided by its specified price base. A marginal rate is the additional charge on the next increment of that base. A declining effective rate does not require the total charge to fall.

Caps and declining marginal bands create two distinct mechanisms. A cap stops the charge growing after a limit. A declining band continues adding charges, but at a lower rate on later portions of the base.

A cap changes the arithmetic above its threshold

Let P be the chargeable price, r a proportional rate, and C the maximum charge, all using consistent currency units. For a simple capped charge:

charge = min(r * P, C)
effective_rate = charge / P

With positive r and P, the cap begins binding at P = C / r. Below that threshold, the effective rate is r. Above it, the charge remains C while the effective rate becomes C / P.

Take a rate of 10% and a cap of 100. At a price base of 1,000, the charge is 100 and its effective rate is 10%. At a base of 5,000, the charge is still 100 and the effective rate is 2%. The more expensive transaction has a smaller percentage burden without paying fewer currency units of that charge.

This constructed model assumes one proportional base and one cap. Additional taxes, exemptions, minimum charges, and other schedules are excluded.

Marginal bands do not reprice earlier portions

Take a separate schedule charging 20% on the first 100 and 10% above it. At a base of 200, the charge is 20 plus 10, or 30. The effective rate is 15%. Applying 10% to the whole amount would incorrectly reduce the charge already attributable to the first band.

Auction buyer’s premiums provide a contractual example of marginal bands. The applicable house, location, category, and sale terms determine the schedule and its base.

Similar formulas can describe different obligations

The Florida boat provisions cap specified sale, use, and repair taxes. The US federal large-cigar excise structure caps a charge per cigar based on the relevant manufacturer or importer price, rather than the retail shelf price. The UK Artist’s Resale Right Regulations 2006, as made, combine bands and a total royalty cap for transactions qualifying under that instrument.

Those are different obligations. Their bases, covered transactions, and payment responsibilities cannot be inferred from their shared shape. A percentage of retail price is not directly comparable with a percentage of an upstream taxable price.

The arithmetic conclusion applies only to the specified charge. A falling effective rate on one component does not establish that the buyer’s entire tax or transaction burden falls. Other charges can use different bases and continue increasing after that component is capped.