Marketing Science
Response Curve Explorer
Visualize how marketing efficiency changes across spending levels — from threshold to saturation. Understand where each dollar stops working.
Response Function
R(x) = L / (1 + e−k(x−m))
Sigmoid model — L = max response, k = steepness, m = midpoint
Peak efficiency. Returns are still strong but beginning to flatten. This is the target range for most channels.
Efficiency Zones
Response Curve
$45K
Spend
40.1%
Response
1.924
Marginal ROI
Optimal
Zone
Interpretation
The response curve maps marketing execution to incremental impact. The shape is driven by two dynamics: frequency thresholds at the low end (minimum exposure before a consumer responds) and audience exhaustion at the high end (the addressable market is finite).
The optimal zone is not where total response is highest — it is where marginal efficiency is still strong enough to justify the spend. Beyond that point, the same budget produces more impact when reallocated to a channel still in its growth phase.
Scope
This explorer uses a fixed sigmoid function to illustrate zone dynamics. In a production MMM, the response curve shape is estimated per channel using Hill functions or similar transformations, with parameters inferred through Bayesian estimation. The zone boundaries shown here are illustrative — actual thresholds depend on channel, market, and creative quality.
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