Each year a weather shock scales the harvest up or down. Because food demand is price-inelastic (people can't cut consumption much when prices rise, or eat much more when prices fall), the market-clearing price has to move by far more than the supply shock itself to force quantity demanded back down to the smaller harvest — or up to absorb a bumper one.
Price ∝ Supply^(−1/e)
e = demand elasticity (small ⇒ inelastic ⇒ big price swings)
Turn on the price floor and, in a bumper-harvest year where the free market price would crash below the floor, the government buys up the surplus at the floor price instead — farmers still get the floor price for everything they grow, but the government's storage/purchase bill grows. In a bad-harvest year the floor never binds (the free price is already above it), so it costs nothing.
- Weather volatility — how wildly the harvest swings year to year before any price effect.
- Demand inelasticity — a smaller elasticity means consumers resist changing consumption more, amplifying price swings further.
- Floor level — the guaranteed minimum price; a higher floor protects farmers more often but costs the government more when it binds.