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A Layman's Guide to Shortages
If you want to understand why price caps cause shortages, there's fundamentally only one economic principle you need to study. It's straightforward. It's easy. Even a Congressman or television pundit should be capable of understanding this.
It's all about the Law of Demand. Notice the capitalization, this is a big-"L" Law, not some wishy-washy usually correct guideline with important exceptions. The Law of Demand is one of the foundational principles of economics; it's big-"T" True. The Law of Demand is: The quantity demanded of a good varies inversely with its price, other things being equal.
"Eeek!", you're thinking, "that doesn't sound like a layman's anything." Don't worry. It's simple. It means that people will buy more of something if the thing is cheaper, and less if it's more expensive. People respond to low prices by buying more, and to high prices by buying less.
What's the connection to shortages? Let's look at a concrete example. Let's say you live in the Southeast United States and the area's supply of gasoline has been interrupted because a major pipeline isn't running. (Let's pick a reason at random and say a hurricane temporarily shut it down.) Gasoline suddenly costs $4.00/gal, and politicians spot a way to curry favor with the electorate. "Price gouging!", they scream, "Let's put a cap on prices!"
What they're trying to do is enable everyone to buy gasoline at $3.00/gal instead of $4.00/gal. But this is impossible. You read that correctly: impossible. It cannot happen. It's impossible in a breaking-the-laws-of-physics kind of way.
Sure, politicians could cap the price of gasoline at $3.00/gal. Establishing the cap is possible — even easy. The hard part, the impossible part, comes from the other portion of the politicians' goal: the "enable everyone to buy" part. This is where the Law of Demand steps in and renders politics impotent.
Think about a gasoline station with 500 gallons of fuel priced at $4.00 each. How did the owner decide on the price of $4.00? He estimated what price would maximize his profits. And he understands the Law of Demand. If he sold gas for $1.00/gal, his 500 gallons would be gone very quickly and his revenues would be only $500.00. He would have to turn away many customers because he'd be out of gas. He doesn't want that to happen. He wants his gasoline to last until he gets resupplied. (Ideally, he wants the last gallon to be sold just as the fuel truck rolls in.)
If he sold gasoline for $10.00/gal, he wouldn't sell much. Even if we ignore his competitors whose lower prices would win over his customers, people will respond according to the Law of Demand by buying less. Maybe they'll drive less. Maybe they'll only fill their tank halfway, expecting lower prices in the future. But the station owner will only sell 100 gallons out of 500, for revenues of $1,000.
At $4.00/gal, he'll sell all 500 gallons, for revenues of $2,000. The Law of Demand says that at any price lower than $4.00/gal, he'll sell all 500 gallons. When the politicians enact the price cap at $3.00/gal, he'll sell all 500 gallons (for revenues of $1,500), but not to the same people. The Law of Demand says that the people who buy gas will buy more gallons each at $3.00/gal than at $4.00/gal. The station will run out of gas but will serve a fewer number of customers. The people who show up early will be able to buy, but latecomers will be turned away: there's a shortage.
(Hey you, the wise-guy in the back. I don't want to hear your counterargument about gasoline being a price-inelastic good so that the profit-maximizing price might occur at a quantity less than 500 gallons. If that were true, the station owner would simply hold less than 500 gallons as inventory to begin with. Why hold a sterile asset in the ground when the money to buy it could have been invested to earn a return? The quantity he has is the quantity he intends to sell.)
It's very important to understand that this has nothing whatsoever to do with profits. Not the profits of the gasoline station owner, not the profits of the refinery, not the profits of the oil company. The shortage occurs because the retail price is below $4.00/gal. There are physically only 500 gallons of gasoline. At $3.00/gal, people will want to buy more than 500 gallons. But they can't — it doesn't exist! That's why the price cap must cause a shortage.
(Unless politicians can will physical gasoline into existence with the power of their minds. But that really would be breaking the laws of physics.)