Resource Allocation Tutorial - Technical Notes

Technical notes

The three options for response models are: (1) ADBUDG, (2) Logistic, and (3) Exponential.  All three have been used extensively in marketing to capture aggregate market response to effort.

The functional form for the ADBUDG response model is given by:

where Min, Max, c and d are parameters to be obtained via managerial calibration and/or statistical estimation.  X is the effort level, which is the decision variable.  For c > 1, we get an S-shaped curve; for c < 1, we get a concave curve. An example of the S-shaped response curve is shown below.

The functional form for the S-shaped Logistic response model is given by:

Finally, the function form for the concave Exponential response model is given by:

Unlike the ADBUDG and Logistic response model which only exhibits diminishing returns to effort at higher levels of effort, the Exponential response model exhibits diminishing returns from the start.