Perfectly inelastic describes a situation where one variable refuses to budge no matter how much another variable changes. The term shows up in two fields: economics and physics. In economics, it means the quantity of a good bought or sold stays exactly the same regardless of price changes, giving it an elasticity coefficient of zero. In physics, it describes a collision where two objects stick together and lose the maximum possible amount of kinetic energy.
Perfect Inelasticity in Economics
Price elasticity measures how sensitive buyers (or sellers) are to a change in price. When demand is perfectly inelastic, a price increase or decrease produces zero change in the quantity people buy. The elasticity coefficient is 0, and the demand curve on a graph is a straight vertical line. No matter where you move up or down on the price axis, the quantity stays locked in place.
This is the extreme end of the elasticity spectrum. Most goods fall somewhere in the middle: raise the price and people buy a bit less, lower it and they buy a bit more. With perfectly inelastic demand, consumers are completely unresponsive to price. They need a fixed amount, and they’ll pay whatever it takes to get it.
How It Differs From Relatively Inelastic
Perfectly inelastic and relatively inelastic sound similar but describe meaningfully different consumer behavior. A relatively inelastic good has an elasticity coefficient between 0 and 1 (in absolute value). Gasoline is a classic example: when gas prices rise, people cut back a little, maybe combining errands or carpooling, but they don’t stop driving. The quantity demanded does drop, just not by much compared to the size of the price increase.
With perfectly inelastic demand, the quantity doesn’t drop at all. There’s no “a little less.” You buy the same amount at $5 as you do at $50. The distinction matters because it determines who bears the cost when prices shift, whether from market forces or government policy.
Real-World Examples
True perfect inelasticity is rare, but several goods come very close. Insulin is the textbook example. A person with Type 1 diabetes needs a specific prescribed dose to survive. If the price doubles, they don’t cut their dose in half. If the price falls, they can’t stockpile extra and use it later. Research consistently treats insulin demand as inelastic because the quantity patients purchase stays essentially constant regardless of price.
On the supply side, perfectly inelastic goods are things that physically cannot be produced in greater quantities. Land is the classic case: no matter how high property prices climb, you can’t manufacture more of it. A one-of-a-kind item like the Mona Lisa has perfectly inelastic supply for the same reason. A stadium with 5,000 seats can’t add more seats just because ticket prices spike. In the short run, hotel rooms during a fully booked holiday weekend and airline seats on a specific flight are effectively fixed in supply too, though in the long run a hotel chain could build new properties.
Agricultural products at harvest time also behave this way. Once the crop is picked, the quantity available that day is what it is. Higher prices won’t make more potatoes appear in the field until next season.
Why It Matters for Taxes and Policy
Perfect inelasticity has a striking consequence when governments impose taxes. The burden of any tax falls most heavily on whichever side of the market, buyers or sellers, is less able to adjust to a price change. When demand is perfectly inelastic, that burden falls entirely on consumers.
Khan Academy illustrates this with a $10-per-vial tax on insulin. Because diabetic patients will buy the same quantity no matter what, the market price rises by the full $10. Producers keep their original revenue untouched. The entire tax comes straight out of what consumers pay, transferred directly from their pockets to the government. There’s no reduction in quantity sold, so there’s no “deadweight loss,” the economic waste that usually accompanies a tax. But the full financial hit lands on the people who have no choice but to keep buying.
This is why policymakers pay close attention to elasticity when designing taxes or price caps. Taxing a perfectly inelastic good is efficient in the economic sense (no lost transactions) but raises serious fairness concerns, since it effectively taxes people for a need they can’t walk away from.
Perfect Inelasticity in Physics
In physics, “perfectly inelastic” describes a specific type of collision. When two objects collide and stick together afterward, moving as a single combined mass, that’s a perfectly inelastic collision. Think of a hockey puck slamming into a goalie and stopping in the goalie’s glove, or two cars crashing and crumpling into each other.
The key physics principle: momentum is still conserved. The total momentum of the system before the collision equals the total momentum after. What isn’t conserved is kinetic energy, the energy of motion. A perfectly inelastic collision reduces internal kinetic energy to the minimum possible while still obeying conservation of momentum. In the puck-and-goalie example, nearly all of the puck’s kinetic energy is lost, converted into heat, sound, and deformation of materials.
This sits at the opposite end of the spectrum from an elastic collision, where kinetic energy is fully conserved (like two billiard balls bouncing off each other with minimal energy loss). Most real collisions fall somewhere between the two extremes, but the perfectly inelastic case represents the maximum possible energy loss for a given collision.
Connecting the Two Definitions
Despite appearing in different fields, both uses of “perfectly inelastic” share the same core idea: zero responsiveness. In economics, quantity doesn’t respond to price. In physics, the objects don’t bounce apart; they absorb the impact completely and move as one. In both cases, the “perfectly” signals that you’re at the absolute extreme of a spectrum, not just close to it but all the way at the endpoint where the measured value hits zero.