Turn delayed price adjustment into a bounded, controllable bifurcation

For a cobweb with downward-sloping demand and delayed supply response, work in log-price deviations and normalize the supply/demand elasticity ratio into one feedback gain. Linearizing the delayed recurrence gives a characteristic polynomial; its first unit-circle crossing is the stability boundary, and longer production/build lags lower that boundary. A bounded physical response such as a saturating capacity curve makes the post-boundary orbit analytically bounded, so crossing the threshold yields endogenous boom/bust instead of divergence. Normalize the gain by the lag-specific critical value: below one the market converges, above one cycle amplitude grows monotonically and comparable lag cases collapse without per-lag tuning. The implementation lesson is to derive the control from real elasticities and observed construction/extraction lag, use physically bounded capacity response, and never add a separate scripted boom scheduler.