Advertising Campaign: Brand Awareness Response Curve

Campaign Controls

Weekly ad spend $30K

Creative effectiveness r 0.12

Diminishing returns γ 0.60

Forgetting rate 0.08

Market Response

Brand awareness

0.0%

Ad-stock (memory)

0.0

Week

Cumulative spend

$0K

Cost / awareness pt

—

Weekly Δ awareness

0.0%

How it works

This models the classic advertising response curve used in marketing science (a simplified Vidale–Wolfe / ad-stock model): awareness rises toward a ceiling of 100% as long as the campaign reinforces it, and decays back down whenever spend stops — exactly the "build, plateau, decay" shape real tracking studies show.

stimulus = (spend / 10)^γ
S(t)     = stimulus + 0.5 · S(t-1)        (ad-stock / media memory)
A(t+1)   = A(t) + r · stimulus · (1 - A(t)) − f · A(t)

Weekly ad spend — the budget fed into the campaign each simulated week.
Effectiveness r — how efficiently spend converts into awareness gain among the still-unaware audience (1 − A).
Diminishing returns γ — exponent < 1 means each extra dollar of spend buys progressively less stimulus (the classic S-shaped/concave response curve seen in real media-mix models).
Forgetting rate — the fraction of current awareness lost each week without reinforcement; this is what makes awareness plateau instead of climbing to 100% forever, and what drives the decay when spend is cut.

The 3D field is a modeled audience: each block is a population segment, its height and color driven by that segment's individual awareness (spread around the campaign-wide average). The back wall traces cumulative awareness over the last 60 simulated weeks.

High awareness segment Unreached segment

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