Indexing the archive…
Your Universe of Digital Possibilities
Farmers plant this year by last year’s price. A glut follows a shortage follows a glut, and the price spirals in or out depending only on which slope is steeper. Run the market twice from one seed, and publish a forecast everyone can trust in one of them: the spiral collapses to a point.
Demand a − bdp clears against supply c + bspe planted for the price farmers expect. With naive expectations — last season’s price — each deviation from the equilibrium p* comes back multiplied by −bs/bd: a glut, a shortage, a glut.
The spiral tightens when demand answers price more strongly than supply does, widens when supply is the steeper, and repeats a fixed square when they match. Nothing outside the market is needed for it to cycle for ever.
The expected price moves a fraction w of the way to the last price. The cobweb then converges whenever |1 − w(1 + bs/bd)| < 1 — enough caution tames a market that naive expectations (w = 1) would throw apart.
The share using predictor h follows its recent profit U — the rational predictor pays a cost C, the naive one is free. When the cobweb is unstable under naive expectations, raising β past β₁ = (2/C)·artanh(bd/bs) turns the steady price into a two-cycle, then a cascade of doublings into chaos: the crowd keeps leaving the expensive predictor while prices are calm, and coming back when they are not.
The Cascade’s period doublings, met again in a market: past β₁ the steady price splits into two, then four, then an aperiodic attractor — the same universal route, driven here not by a growth rate but by how hard the farmers chase last season’s profit.
The second prophecy is the oldest forecast in economics: last year’s price. Read by every farmer it makes its own cycle — Hanau’s hogs, Ezekiel’s potatoes. Muth’s answer was a forecast that accounts for its own effect, and on the response curve it is simply the crossing. The Bar had no crossing; this market has exactly one, and whether repeated publication finds it is the cobweb theorem again — the slope at the crossing, as The Prophecy will say of every world in this edition. Between them sits The Cascade’s route to chaos, which a market of free choosers walks just as a population does, and The Tide’s lesson that a forecast of a world that does not listen is a different instrument from one of a world that does.