Perfectly Inelastic Demand: When Price Doesn't Matter
What is Price Elasticity of Demand (PED)?
Before diving into the extreme case, let's understand the general rule. Price Elasticity of Demand (PED) measures how much the quantity demanded of a good changes when its price changes. It's a number that tells us how sensitive buyers are to price fluctuations. We calculate it using this formula:
$ PED = \frac{\%\ Change\ in\ Quantity\ Demanded}{\%\ Change\ in\ Price} $
The result of this calculation places demand into one of several categories:
| Elasticity Type | PED Value | Meaning | Example |
|---|---|---|---|
| Elastic Demand | PED > 1 | Quantity demanded changes by a larger percentage than the price change. | Brand-name soda; a small price increase makes people buy much less. |
| Unit Elastic Demand | PED = 1 | Quantity demanded changes by the exact same percentage as the price change. | Rare in practice, but a theoretical midpoint. |
| Inelastic Demand | 0 < PED < 1 | Quantity demanded changes by a smaller percentage than the price change. | Gasoline; a price increase doesn't drastically reduce how much people need to drive. |
| Perfectly Inelastic Demand | PED = 0 | Quantity demanded does not change at all when the price changes. | Life-saving insulin for a diabetic patient. |
The Mathematics and Graph of Perfect Inelasticity
Perfectly inelastic demand is the endpoint on the spectrum of elasticity. Mathematically, it's defined by a PED of exactly zero. Let's see why using the formula:
If the % Change in Quantity Demanded is 0 (because the quantity bought stays the same), then no matter what the % Change in Price is (unless it is also zero), the calculation becomes:
On a standard demand graph, with Price (P) on the vertical axis and Quantity (Q) on the horizontal axis, a perfectly inelastic demand curve is drawn as a vertical straight line. This vertical line shows that at every possible price level, consumers will purchase the exact same fixed quantity. For example, if a person needs exactly 1 vial of insulin per month to survive, the demand curve would be a vertical line at a quantity of 1. Whether the price is $50 or $500, the quantity demanded remains 1 vial.
Real-World Examples of Perfectly Inelastic Demand
While perfectly inelastic demand is a theoretical extreme—meaning absolutely zero change in quantity—some goods and services come very close in the short run or for specific individuals. Here are the most common categories:
1. Life-Saving Medicine: This is the classic example. For a diabetic patient, insulin is not a choice; it is a necessity for survival. If the price rises, the patient cannot simply decide to buy less. They will find a way to pay for it, even if it means cutting spending on other things. The demand, for that patient, is perfectly inelastic.
2. Essential Utilities in the Very Short Term: Think about the water coming into your home. If the price of water doubles for a month, you are unlikely to significantly reduce your usage for drinking, cooking, and basic hygiene. Your demand is highly inelastic and close to perfectly inelastic over a short period. Over a longer time, you might install water-saving devices, showing elasticity can change with time.
3. Goods with No Substitutes for a Specific User: A student who must have a specific, proprietary textbook for a class (and cannot use an older edition or share) faces a nearly perfectly inelastic demand for that book. The professor has mandated it, so the quantity demanded is 1, regardless of the price set by the publisher.
4. Addictive Substances: For someone with a severe addiction, the demand for the substance (like cigarettes for a heavy smoker or a drug for an addict) can be highly inelastic. Price changes may have little effect on the quantity they feel compelled to consume, though this is more a behavioral extreme than a pure economic one.
Implications and Consequences in the Market
Understanding perfectly inelastic demand is not just an academic exercise; it has powerful real-world consequences for consumers, producers, and governments.
For Consumers: When you are the buyer of a good with perfectly inelastic demand, you are in a vulnerable position. You have no bargaining power. Sellers know you must buy the product, which can lead to very high prices. Your entire budget can be affected because spending on this essential good cannot be reduced, forcing cuts elsewhere.
For Producers (Sellers): A seller facing a perfectly inelastic demand curve has significant power to increase revenue[1] simply by raising the price. Since the quantity sold does not fall, Total Revenue = Price x Quantity will always go up when the price goes up. This is why pharmaceutical companies can charge high prices for patented, essential drugs.
Government Policy and Perfect Inelasticity
Governments pay close attention to the elasticity of demand when designing taxes and subsidies. Goods with inelastic demand are often targets for "sin taxes" or are heavily regulated.
Tax Incidence: When a good has perfectly inelastic demand, the burden of a tax falls entirely on the consumer. Here's why: Sellers can pass on 100% of the tax to the buyer in the form of a higher price, and because demand is perfectly inelastic, buyers will continue to purchase the same quantity despite the higher price. The government collects the tax revenue, but it comes straight out of consumers' pockets.
Price Controls: Due to the vulnerability of consumers, governments may impose price ceilings[2] on goods with highly inelastic demand, such as essential medicines or rent in certain housing markets. These controls are designed to prevent sellers from exploiting consumers' lack of alternatives. However, if set too low, they can cause shortages because producers may not want to supply the good at the controlled price.
Important Questions
Q1: Is perfectly inelastic demand common in the real world?
A: True perfectly inelastic demand (where quantity does not budge at all) is very rare and usually exists only for specific individuals in specific situations (like one person's need for a specific drug). For large market populations, demand is almost never perfectly inelastic because as prices rise extremely high, some people will eventually be forced to go without, reducing the total quantity demanded. However, many goods have highly inelastic demand (close to zero), such as basic food staples, electricity, and gasoline in the short term.
Q2: How does time affect the elasticity of demand?
A: Time is a critical factor. Demand is usually more inelastic in the short run and more elastic in the long run. For example, if the price of home heating oil spikes in winter, you might not be able to reduce consumption immediately (inelastic). But over the next year, you could install better insulation, buy a more efficient furnace, or switch to a different heat source, making your demand for heating oil more elastic over the long term. Perfect inelasticity is most likely to be observed in immediate, short-run scenarios.
Q3: If demand is perfectly inelastic, what happens to total revenue if price increases?
A: Total revenue increases proportionally with the price increase. Since quantity sold (Q) is constant, revenue (P x Q) depends only on price (P). If price goes up 10%, revenue goes up 10%. If price goes up 50%, revenue goes up 50%. This direct relationship is unique to perfectly inelastic demand and gives sellers a strong incentive to raise prices.
Footnote
[1] Revenue: The total income a firm receives from selling its goods or services. Calculated as Price multiplied by Quantity Sold.
[2] Price Ceiling: A government-imposed maximum price that can be charged for a good or service. It is typically set below the equilibrium market price to make essential goods affordable.
PED: Price Elasticity of Demand. A measure of the responsiveness of the quantity demanded of a good to a change in its price.