Inelastic Demand vs Perfectly Inelastic
Inelastic Demand and Perfectly Inelastic are two Elasticity concepts in AP Economics that students often mix up. Inelastic demand is when the quantity demanded changes less than the price changes. 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 inelastic demand, the percentage change in quantity demanded is less than the percentage change in price. This means that consumers are not very sensitive to price changes. Goods with few substitutes, such as necessities, often have inelastic demand.
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.
Inelastic vs Perfectly Inelastic Demand: A Small Response and No Response At All
| Inelastic Demand | Perfectly Inelastic Demand | |
|---|---|---|
| Elasticity coefficient, absolute value | Between 0 and 1 | Exactly 0 |
| How quantity answers a price change | It moves, but proportionally less than the price | It does not move at all |
| Shape of the curve | Steep, and still downward sloping | A vertical line |
| Effect of a price rise on total revenue | Revenue rises, but by less than the price did in percentage terms | Revenue rises by exactly the same proportion as the price |
| Who carries a per unit tax | Buyers carry most of it when supply is more elastic | Buyers carry all of it whenever supply slopes upward |
| How time changes it | Demand grows more elastic as buyers find substitutes | Stays vertical by assumption, which is why it is only a benchmark |
| Status of the case | Common in real markets for necessities and habit goods | A limiting case used for comparison, rarely a full description |
Put both through the midpoint method and one numerator collapses to zero
Take an illustrative prescription whose price rises from $20 to $24 while quantity sold falls from 40 to 38 units a week. The price change is 4 over the average of 22, which is 18.18 percent. The quantity change is 2 over the average of 39, which is 5.13 percent. Elasticity is 5.13 divided by 18.18, giving about 0.28 in absolute value, comfortably inside the inelastic band. Revenue moves the way that band predicts: 20 times 40 is $800 before, and 24 times 38 is $912 after, a gain of $112. Now assume the same buyers are perfectly inelastic, so all 40 units still sell at $24. The percentage change in quantity is zero, so the whole elasticity is zero no matter how large the price change underneath it. Revenue rises from $800 to $960, exactly 20 percent higher, matching the 20 percent price rise unit for unit. That is the practical difference. Inelastic demand leaks a little quantity when the price rises, so revenue grows more slowly than the price. Perfectly inelastic demand leaks none, so the seller keeps every point of the increase. Try other figures at /calculate/midpoint-method.
A vertical demand curve is a teaching benchmark, not a real market
Four forces make demand less elastic: few substitutes, the good being a necessity, a small share of the budget, and a short time horizon. Push all four to their extreme and you approach the vertical case, but nothing reaches it. Even a patient who needs a medicine daily faces a price at which they borrow, ration, switch to an older drug, or go without. The benchmark still earns its place because it makes tax questions easy to reason about. When both curves are straight lines, buyers bear a share of a per unit tax equal to the elasticity of supply divided by the sum of the two elasticities. With demand at 0.28 and supply at 1.2, that share is 1.2 divided by 1.48, about 81 percent, so a $2 tax raises the price buyers pay by roughly $1.62 and cuts what sellers keep by about $0.38. Set demand elasticity to zero and the same expression gives 100 percent: the price buyers pay rises by the full $2, quantity does not change, and no trades are lost. This is also why governments tax goods with few substitutes when revenue is the aim. See /glossary/price-elasticity-of-demand for the general measure.
Frequently asked questions
What is the difference between inelastic and perfectly inelastic demand?
Inelastic demand has an elasticity between 0 and 1, so quantity does respond to a price change but by a smaller percentage, while perfectly inelastic demand has an elasticity of exactly 0 and quantity does not respond at all. Inelastic demand curves are steep; perfectly inelastic curves are vertical. The first is common in real markets and the second is a limiting case.
What is the elasticity of a perfectly inelastic demand curve?
It is zero, because the percentage change in quantity demanded on top of the fraction is zero no matter how large the price change beneath it. Zero divided by any non-zero number is zero, so the coefficient stays at zero for every size of price change. This is the lowest value price elasticity of demand can take.
Who pays a tax on a perfectly inelastic good?
Buyers pay the whole tax, as long as the supply curve slopes upward, because quantity cannot fall in response to the higher price and sellers therefore give up nothing. The price buyers pay rises by the full amount of the tax. No trades are lost either, so this is the one case where a per unit tax creates no deadweight loss.
Live Elasticity graph. Drag the curves, or open the full version.
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