marginal vs average

Also called: marginal cost, marginal value, average cost, marginal

A marginal quantity is the change between two neighbouring points, Δy ÷ Δx, such as the cost of the next customer; an average is the total divided by the total. They are equal only on a line through zero.

A marginal quantity asks what the next step adds: Δy ÷ Δx between two neighbouring points. An average divides everything by everything: y ÷ x.

$\text{marginal} = \frac{\Delta y}{\Delta x} \qquad \text{average} = \frac{y}{x}$

On a straight line through zero the two are the same. On a curve that flattens, such as customers bought by ad spend, the marginal cost runs away from the average: the first money buys cheap customers and hides how expensive the last ones are. With fixed costs the opposite happens: the average cost per unit falls with volume while the marginal cost stays at the slope.

Decisions about one more (raise the budget, add a lesson, hire one more) need the marginal number; reports about how we did overall use the average.

Example

A channel brings 25 families for 50,000 UAH, 40 for 100,000, 50 for 150,000 and 55 for 200,000.

Average CAC at 200,000: 200,000 ÷ 55 ≈ 3,636.
Marginal CAC of the last step: 50,000 ÷ (55 − 50) = 10,000.
If a family is worth 6,000, stop at 150,000: the last step loses 20,000 a month.

Common mistakes

Deciding on the average. A healthy average can hide a loss-making last step.
Forgetting step costs. One more unit can bring a whole new salary at the margin.
Mixing the direction. Marginal CAC is Δspend ÷ Δcustomers, the inverse of the slope of the customer curve.

Learn it in the course

Slope as a marginal quantity · What one more unit adds: marginal vs average CAC and cost, operating leverage as 1 ÷ margin of safety, and price elasticity as a ratio of relative changes.
Inequalities, intervals and formulas with cases · <, ≤, ± and intervals, "if and only if", min and max, formulas with cases, fences, payback as the first month that clears a bar, and tiered rates with effective vs marginal.