Badr Alghamdi
العربية
Lessons

All units price break: the extra unit that lowers the invoice

At an all-units price break, buying one more unit can make the whole invoice smaller. Find the exact quantity where more costs less.

Your prediction before the experiment

Buying one more unit always makes the invoice larger. The inspected quantity is one unit below the price break. Move it once to reveal the step.
Buying one more unit always makes the invoice larger. The inspected quantity is one unit below the price break. Move it once to reveal the step.

The hypothetical schedule

Price break
10 units
Below the break
SAR 10 per unit
At or above the break
SAR 8.50 per unit
How it applies
The active price applies to every unit in the invoice
Excluded
No tax, fixed charge, minimum spend, rounding rule, or extra tier

The one quantity

units

The declared price break sits between 9 and 10 units.

Invoice by quantity under the declared scheduleEach bar is the whole invoice at that quantity. Below ten units the bars rise by SAR 10 each to SAR 90 at nine units. At ten units the bar falls to SAR 85, below the nine unit bar, then the bars rise by SAR 8.50 each to SAR 170 at twenty units. The inspected quantity is 9 units at SAR 90.Move the quantity to draw this

Open the threshold calculation

The piecewise invoice

Below 10 units, quantity is multiplied by SAR 10. At 10 units and above, quantity is multiplied by SAR 8.50 because that price applies retroactively to every unit.

ΔI=qb pb−(qb−1) p−\Delta I=q_b\,p_b-(q_b-1)\,p_-

where ΔI\Delta I is the threshold jump, qbq_b the threshold quantity, pbp_b the price at threshold, and p−p_- the price below threshold.

Worked example

Nine units cost SAR 90. Ten units cost SAR 85. The signed jump is −5, so one more unit reduces the invoice by SAR 5 under this schedule.

9×10=90,10×8.50=85,85−90=−59 \times 10 = 90,\qquad 10 \times 8.50 = 85,\qquad 85 - 90 = -59×10=90,10×8.50=85,85−90=−5\begin{gathered}9 \times 10 = 90, \\ 10 \times 8.50 = 85, \\ 85 - 90 = -5\end{gathered}

Eleven units cost SAR 93.50, which is above the SAR 90 that nine units cost, so ten units is the only quantity on this schedule whose invoice sits below the invoice for nine.

This hypothetical all-units schedule does not interpret a supplier term, recommend quantity, assess legality, or decide which purchase is better.

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