When a tariff is imposed, its full effect is not felt immediately. Instead, prices adjust gradually as inventories turn over, contracts are renegotiated, and consumers become aware of the new cost. One common way to model this gradual adjustment is to use an exponential lag model. For a good with an initial price P 0 P_0 and a tariff that ultimately raises the price by Δ P \Delta P (expressed in absolute terms or as a percentage), we can write the time‑dependent price as: P ( t ) = P 0 + Δ P ( 1 − e − λ t ) , P(t) = P_0 + \Delta P\,\Bigl(1 - e^{-\lambda t}\Bigr), where: P ( t ) P(t) is the price at time t t (with t t measured in months, for example), P 0 P_0 is the initial price before the tariff, Δ P \Delta P is the full price increase that the tariff would induce (e.g. if a 10% tariff on a $100 product, then Δ P = $ 10 \Delta P = \$10 ), λ \lambda is a positive parameter (per month) that describes the speed of the adjustment (the higher λ \lambda is, the faster the...
