Perfectly Elastic vs Perfectly Inelastic
Perfectly Elastic and Perfectly Inelastic are two Elasticity concepts in AP Economics that students often mix up. Perfectly elastic demand is when any change in price leads to an infinite change in quantity demanded. Perfectly inelastic demand is when any change in price leads to no change in quantity demanded. Here is how they compare side by side.
In perfectly elastic demand, consumers are infinitely sensitive to price changes. This means that even the slightest increase in price will cause the quantity demanded to drop to zero. Perfectly elastic demand is a theoretical concept that is not often observed in real markets.
In perfectly inelastic demand, consumers are completely insensitive to price changes. This means that changes in price have no effect on the quantity demanded. Perfectly inelastic demand is a theoretical concept that is not often observed in real markets.
Perfectly Elastic vs Perfectly Inelastic: The Two Ends of the Scale
| Perfectly Elastic | Perfectly Inelastic | |
|---|---|---|
| Elasticity value and shape | Infinite, and the curve is drawn horizontal at one price | Zero, and the curve is drawn vertical at one quantity |
| What buyers are assumed to have | A perfect substitute at the same price, so one cent more sends every buyer to another seller | No substitute worth taking over that price range, so the same quantity is bought at any price in it |
| Total revenue when the seller raises price | Falls to zero, since nothing sells above the going price | Rises in exact proportion to the price, since quantity never moves |
| Share of a per unit tax borne by this side | None, the whole tax lands on the other side of the market | All of it, and the price paid rises by the full amount of the tax |
| Deadweight loss from that tax | Large, since quantity falls by more than any downward-sloping demand curve would give up | Zero, since the quantity traded does not change |
| Closest real example | Demand facing one seller among many identical sellers, or supply from an industry with constant unit cost | Demand for an essential medicine over a narrow price range, or the supply of land on a fixed site |
The letter I in inelastic is a vertical stroke, and that settles the graph
These two curves are the easiest marks on an elasticity question and the easiest to reverse under time pressure. Perfectly inelastic is vertical, and the memory hook is that a capital I is itself a vertical stroke. Perfectly elastic is horizontal, and a capital E is built from horizontal bars. Everything else follows from the picture. A vertical demand curve sits at one quantity, so no price on the axis changes what buyers take. A horizontal demand curve sits at one price, so buyers take everything offered at that price and nothing at all one cent above it. Slope is a poor guide to elasticity everywhere else on the scale, since a single straight demand line runs from elastic to inelastic along its own length, but at these two extremes the shape is the definition rather than a hint. Both labels also describe a curve over a price range, not a good for all time. Gasoline can face near-vertical demand across a small price change and something far flatter across a large one.
At one extreme a one cent price rise wipes out revenue, at the other revenue tracks price exactly
Take a seller currently moving 50 units at $10, so revenue is $500. If demand is perfectly inelastic, raising the price to $12 leaves quantity at 50 and revenue becomes $600. Raise it to $14 and revenue is $700. Revenue moves one for one with price because quantity never budges, and no price exists at which a seller facing this demand should stop raising. That conclusion is exactly why perfectly inelastic demand works as a theoretical benchmark rather than as a description of a real market. If demand is perfectly elastic instead, raising the price to $10.01 sends quantity to zero and revenue to zero. Cutting the price below $10 is equally pointless, since the seller could already move every unit at $10 and would simply collect less on each of them. One price is available and no other. That is the position of a single firm in perfect competition, which is why such a firm is called a price taker and why its marginal revenue equals the market price at every quantity.
A tax on the perfectly inelastic side raises revenue with no deadweight loss
Impose a $2 per unit tax on a market where 50 units trade at $10. If demand is perfectly inelastic, the price buyers pay rises to $12, all 50 units still trade, the government collects $100, and consumers bear the entire $100. No trade is lost, so deadweight loss is zero. Now run the same tax where demand is perfectly elastic at $10 and supply slopes upward. Buyers still pay $10, because any higher price sends them elsewhere, so producers absorb the full $2 and net $8. Quantity falls, say from 50 to 30. The government collects $2 on 30 units, which is $60, all of it out of producer surplus, and the 20 units no longer traded generate a deadweight loss of one half times $2 times 20, or $20. Same tax, opposite outcomes. The side that cannot respond pays, and the side that responds hardest destroys the most trade. That pairing, full burden with no lost trade against no burden with heavy lost trade, is the cleanest demonstration that elasticity governs both incidence and efficiency.
Frequently asked questions
Is any real demand curve perfectly elastic?
Perfectly elastic demand comes closest in perfect competition, where one small seller faces a market price it cannot influence. A single wheat farmer among many can sell as much as the harvest allows at the going price and nothing at all above it, since buyers have identical wheat available elsewhere. The market demand curve for wheat itself still slopes downward in the normal way. The horizontal line describes what one seller sees, not what all buyers do, and confusing those two curves is a standard exam error.
Who pays a tax when demand is perfectly inelastic?
Consumers pay every cent of it. With a vertical demand curve quantity does not fall when the price rises, so the seller passes the whole tax forward and loses no sales. A $2 tax on 50 units lifts the price from $10 to $12, all 50 units still trade, and buyers hand over $100 more than before while producers keep the same net price they had. Because no trade disappears, the tax creates no deadweight loss, which is the efficiency argument for taxing goods with very inelastic demand.
Can supply be perfectly elastic or perfectly inelastic too?
Supply reaches both extremes as well, and the graphs look the same. Perfectly inelastic supply is vertical, which fits a fixed quantity such as land, a finished stadium, or a painter's completed works, where a higher price brings out no extra units. Perfectly elastic supply is horizontal, which fits an industry able to produce any quantity at a constant cost per unit. The incidence rule carries over unchanged: whichever side is perfectly inelastic bears the whole tax, and whichever side is perfectly elastic bears none of it.
Live Elasticity graph. Drag the curves, or open the full version.
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