Perfectly Inelastic Supply: PES = 0
What Is Price Elasticity of Supply (PES)?
Before diving into perfect inelasticity, we must understand the broader concept of elasticity. In economics, "elasticity" measures how much one variable changes when another variable changes. Price Elasticity of Supply (PES) specifically measures the responsiveness or sensitivity of the quantity supplied of a good or service to a change in its price. It is calculated using the following formula:
The result of this formula places supply into one of several categories, from highly responsive (elastic) to completely unresponsive (inelastic). The table below illustrates these categories.
| Elasticity Type | PES Value | Meaning | Example |
|---|---|---|---|
| Perfectly Elastic | $PES = \infty$ | Suppliers will provide any quantity at a specific price, but none at a lower price. | Digital goods with zero marginal cost. |
| Relatively Elastic | $PES > 1$ | Quantity supplied changes by a larger percentage than the price change. | Manufactured items like t-shirts. |
| Unit Elastic | $PES = 1$ | Quantity supplied changes by the exact same percentage as the price change. | A theoretical benchmark; rare in practice. |
| Relatively Inelastic | $0 < PES < 1$ | Quantity supplied changes by a smaller percentage than the price change. | Agricultural products in the short term. |
| Perfectly Inelastic | $PES = 0$ | Quantity supplied does not change at all when the price changes. | Land, original artwork, or seats at a sold-out concert. |
The Zero Response: Understanding PES = 0
When PES equals zero, the numerator in the formula (the percentage change in quantity supplied) is zero. This is true whether the price goes up or down. Plugging this into the formula gives:
$PES = \frac{0\%}{\%\ Change\ in\ Price} = 0$
This means producers or suppliers are physically unable or completely unwilling to change the amount they offer for sale, no matter how high or low the price gets. The quantity is absolutely fixed. Imagine a vertical line on a graph. On the vertical (y) axis, we have price. On the horizontal (x) axis, we have quantity supplied. For perfectly inelastic supply, this line is completely vertical. It shows that at every possible price level, the quantity supplied remains exactly the same.
Real-World Markets with Perfectly Inelastic Supply
Perfectly inelastic supply is more common than you might think. It often applies to goods or resources that are fundamentally limited by nature, time, or legal constraints. Here are some key examples:
1. Land: In a specific location, the amount of land is fixed. You cannot create more land in the heart of a city. If the price for plots in downtown Manhattan skyrockets, the quantity of land there does not increase. It remains the same. This makes the supply of land in a particular area perfectly inelastic in the long run.
2. Original Artwork and Historical Artifacts: There is only one original Mona Lisa painting by Leonardo da Vinci. No matter how much someone is willing to pay, the Louvre museum cannot produce another original. The supply is fixed at one. This applies to all unique, non-reproducible items.
3. Tickets for an Immediate Event: Consider a championship game that is sold out. The stadium has a fixed number of seats. Once all tickets are sold, the supply is perfectly inelastic. Scalpers may resell tickets at much higher prices, but the total number of seats (the quantity supplied to the market) does not change.
4. Perishable Goods at a Specific Moment: A farmer at a market has 100 ripe strawberries that must be sold by the end of the day. As closing time approaches, the farmer might lower the price to sell them all, but the maximum quantity that can be supplied is still fixed at 100. He cannot magically produce more ripe berries in that instant.
Tax Incidence: Who Bears the Burden?
One of the most important applications of perfectly inelastic supply is in understanding tax incidence—who actually pays the cost of a tax. When supply is perfectly inelastic, suppliers cannot adjust their behavior by producing less. They must continue to supply the same fixed quantity to the market.
Imagine the government places a new tax on the sale of a rare mineral that exists in a fixed, limited amount. The sellers (suppliers) of this mineral have a perfectly inelastic supply. They cannot reduce the quantity they mine and sell because it is already fixed. Therefore, they have no choice but to absorb the tax themselves or try to pass the entire burden onto buyers. In practice, because demand is usually not perfectly inelastic, suppliers often end up bearing most of the tax burden. The consumer price may not rise by the full amount of the tax. This is a key lesson: the side of the market that is less elastic (less responsive to price changes) bears the greater share of the tax burden.
The Inelastic Supply of Human Organs for Transplant
A powerful and ethical example of perfectly inelastic supply is the market for human organs for transplantation. In most countries, it is illegal to buy or sell human organs. The legal supply comes almost entirely from altruistic donors (living or deceased). This creates a fixed, extremely limited quantity available at a monetary price of zero (in legal markets). The supply curve is effectively vertical at that fixed quantity.
The demand, however, from patients needing life-saving transplants is very high. This massive imbalance between the fixed, inelastic supply and high demand creates a severe shortage. Economists use this example to discuss the consequences of non-market allocation (waiting lists) versus potential market-based solutions, highlighting the profound real-world impact of a PES of $0$.
Important Questions
Q1: Can you have a perfectly inelastic supply in the long run?
True perfectly inelastic supply is rare in the long run for most goods because, given enough time, producers can often find ways to increase quantity (discover new resources, develop new technology). However, for truly non-reproducible goods like original artwork, historical artifacts, or land in a specific location, the supply remains perfectly inelastic forever.
Q2: What happens to market price if demand increases for a good with perfectly inelastic supply?
When supply is perfectly inelastic (a vertical line), an increase in demand (demand curve shifts right) leads to a very large increase in price, but no change in the quantity traded. The entire adjustment happens through price. This is why tickets for sold-out concerts or original paintings by famous deceased artists can reach astronomically high prices when many wealthy buyers want them.
Q3: Is perfectly inelastic supply good or bad for producers?
It depends on the direction of price change. If price rises, it is excellent for producers because they sell the same amount for much more revenue. If price falls, it is terrible because they are forced to sell the same amount for much less revenue. Producers with inelastic supply have no ability to respond to market signals by adjusting output, making them vulnerable to price drops but big winners from price increases.
Footnote
1 PES: Price Elasticity of Supply. A measure of the responsiveness of the quantity supplied of a good to a change in its price. Calculated as the percentage change in quantity supplied divided by the percentage change in price.
2 Taxation: The process by which a government levies a financial charge on individuals, entities, or goods. The study of who ultimately pays the economic burden of a tax is called tax incidence.
3 Vertical Supply Curve: A graphical representation of perfectly inelastic supply. It is a straight line parallel to the price axis (vertical), indicating that quantity supplied is constant at all price levels.
4 Fixed Resource: A resource, good, or factor of production whose available quantity cannot be increased in the relevant time period.