Incremental annual profit from agent access
Use the slider or click the chart to inspect a share. At zero profit the retailer is indifferent; “allow” includes equality.
Why this decision?
Show sensitivity analysis
Compare alternative values of one input while keeping every other input at the current settings.
| Scenario | Profit at 0% | Profit at 100% | Participation |
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Equations and assumptions
ΔΠ(s) = aN[(1 − s)A + sD] − F
ΔΠ′(s) = aN(D − A)
s* = [A − F/(aN)] / (A − D)
The threshold formula applies when a > 0 and A ≠ D. If A > D, profit falls with share; if D > A, it rises. The endpoint profits determine whether the threshold is feasible or access is preferred everywhere or nowhere. With zero adoption, incremental profit is −F.
Case 2 requires δ > c/m + r(1 − c/m), for a > 0. This condition concerns the slope, not whether profit covers F. For an interior Case 1 threshold, the paper’s comparative statics apply; outside that regime, inspect the full curve.
Adoption a is the fraction using agents; δ is the probability of retailer defection conditional on agent use and blocked access. The baseline assumes no defection under access, a common agent cost, and constant probabilities across initial market shares. Market size N is held fixed along each curve.