The Market in the Exponent: Endogenous Exposure, an Interior Turn in Responsiveness, and a Baseline No Locus Returns

An administration that publishes its findings chooses how loudly to publish, and the deterrence publicity produces is usually modelled as a fixed technology: a given rate of exposure per unit of loudness. The exposure is not supplied by the administration. It is supplied by a market — attention, intermediaries, the trade press — and that market responds to how loud the administration is. This paper asks what changes when the rate is itself a function of the control, and finds that the market enters inside the deterrence technology’s shape rather than beside it. Dividing the administration’s equal-value condition by its first-order condition removes both the composite weight and the floor and leaves a locus in the effective exposure alone; every result here is a property of that locus. A responsive market lowers the tightness at which an administration jumps when the response’s elasticity exceeds the exposure rate divided by the fraction already deterred, and where it lowers the tightness at all it lowers it by a bounded amount over a bounded range. The locus is the deterred fraction’s own logarithmic derivative, so it fixes that fraction only up to a scale — bounded above, because a fraction cannot exceed one — and the baseline rate is precisely what a silent administration’s locus cannot return.