Deadweight loss

Based on Wikipedia: Deadweight loss

The Hidden Tax Nobody Collects

Imagine you're about to hire someone to clean your house for a hundred dollars. You value the clean house at a hundred and twenty, and the cleaner values their time at eighty. Everyone walks away happy—you're twenty dollars better off (clean house worth more than you paid), and the cleaner pockets twenty in profit above what their time was worth. Forty dollars of value, created from thin air through voluntary exchange.

Now the government slaps a fifty-dollar tax on cleaning services.

Suddenly the math doesn't work. The cleaner needs at least eighty dollars to make it worth their while, but with a fifty-dollar tax, you'd have to pay a hundred and thirty—more than the clean house is worth to you. The deal falls apart. You live in a dirtier house. The cleaner doesn't get paid. And here's the kicker: the government doesn't collect a dime either, because there's no transaction to tax.

That forty dollars of value just vanished. It didn't go to the government. It didn't go to anyone. It simply ceased to exist. Economists call this deadweight loss—the economic equivalent of money being thrown into a furnace.

What Makes Deadweight Loss Different

Most economic losses involve a transfer. When you pay more for something, someone else receives that money. When a company raises prices, consumers lose but shareholders gain. It's a zero-sum game, or close to it.

Deadweight loss is different. It's pure destruction.

Think of it this way: if a pickpocket steals your wallet, society hasn't lost any wealth—it's just changed hands (illegally, but still). But if fear of pickpockets keeps you from visiting a city altogether, and you miss out on a business deal that would have benefited both you and your counterpart, that value never gets created in the first place. Nobody ends up with it. It simply doesn't exist.

This is what happens whenever something prevents mutually beneficial trades from occurring. The benefit that would have flowed to both buyer and seller evaporates. It's attributed to nobody because nobody gets it.

The Nail That Changed Economics

Economists love their simplified examples, and the market for nails has become a teaching staple. Here's how it works.

Suppose nails cost ten cents each to produce—that's the marginal cost, the expense of making one more nail. In a competitive market with many producers, that's roughly what they'll sell for. Anyone who values a nail at more than ten cents will buy one. Perfect efficiency.

But what if one company controlled all nail production? A monopolist doesn't think like a competitor. They ask a different question: "What price maximizes my profit?" The answer might be sixty cents.

At sixty cents, the monopolist makes fat margins on every sale. Sure, they sell fewer nails, but each nail is far more profitable. The problem is that everyone who values nails between ten and sixty cents gets priced out of the market. These people would happily pay more than the actual cost of production. Value would be created if these trades happened. But they don't.

The monopolist's gain doesn't offset the customers' loss. The customers who can't buy nails don't transfer their money to the monopolist—they simply don't spend it on nails at all. The trades that would have created value for both parties never occur. This gap, this missing economic activity, is the deadweight loss of monopoly.

When the Cure Becomes the Disease

Here's where it gets counterintuitive: deadweight loss can come from trying to help people too.

Return to those nails. The government decides nail-users need a break and offers producers a three-cent subsidy for every nail made. Now nails sell for seven cents even though they still cost ten cents to produce.

Sounds great, right? Cheaper nails for everyone!

Not quite. Now people who only value nails at eight or nine cents will buy them. These consumers receive less benefit from the nail than it actually costs society to produce. Every one of these sales represents a net loss—resources being consumed to create something worth less than its inputs.

The subsidy doesn't transfer wealth; it destroys it. Society pays ten cents to make something that delivers only eight cents of value to anyone. That two-cent gap is deadweight loss, repeated across millions of transactions.

Harberger's Triangle

In 1964, economist Arnold Harberger gave us a visual tool for understanding these losses. If you've ever seen a supply-and-demand graph—two lines crossing to show where buyers and sellers meet—Harberger's contribution was showing what happens when something drives a wedge between them.

Picture the intersection point of supply and demand as the ideal outcome, where everyone who should trade does trade. Now imagine a tax pushing those lines apart. The gap between them forms a triangle, and the area of that triangle represents the deadweight loss.

Why a triangle? Because the loss isn't uniform. The trades closest to the equilibrium point were barely profitable anyway—they're the first to disappear when costs rise. The further you get from equilibrium, the more valuable the trades that get killed. This creates a shape that tapers to a point.

The triangle has become so associated with this concept that economists simply call it "Harberger's triangle" when discussing market distortions. It's the scar left behind whenever policy or market power prevents the natural meeting of supply and demand.

The Sin Tax Paradox

Governments often levy "sin taxes" on alcohol, tobacco, and gambling. The explicit goal is to reduce consumption of these goods by making them more expensive. From a pure efficiency standpoint, these taxes create deadweight loss—they prevent trades that would have benefited both buyer and seller.

But here's the wrinkle: sin taxes are meant to create deadweight loss. That's the point.

The economic argument goes like this: these products create costs that don't show up in their price tags. Smoking causes healthcare expenses borne by everyone. Alcohol contributes to accidents that harm third parties. When economists call these "externalities," they mean the costs that spill over onto people who weren't part of the transaction.

A well-designed sin tax can actually reduce overall deadweight loss by bringing the price closer to the true social cost. If cigarettes cost five dollars to produce but create eight dollars in healthcare costs, then without a tax, society is subsidizing smoking. A three-dollar tax would, in theory, make the price reflect reality.

Of course, setting the "right" tax rate requires knowing the true cost of externalities—a number that economists argue about endlessly. Too low and you haven't solved the problem. Too high and you've created new inefficiency.

Why Doubling a Tax Quadruples the Damage

Here's a mathematical fact that should terrify tax policymakers: deadweight loss grows faster than the tax that causes it.

Specifically, it grows with the square of the tax rate.

Remember that triangle representing lost value? When you double a tax, you double both the base and the height of the triangle. Since area equals half of base times height, doubling both dimensions quadruples the area.

This means a ten percent tax might create one unit of deadweight loss, but a twenty percent tax creates four units. A thirty percent tax creates nine. A fifty percent tax creates twenty-five times the damage of the original ten percent tax, not five times.

This relationship explains why economists often prefer broad taxes at low rates over narrow taxes at high rates. Taxing everything at ten percent creates far less deadweight loss than taxing one thing at fifty percent, even if total revenue is similar.

It also explains the strange phenomenon of taxes that reduce government revenue. Push the rate high enough and you shrink the market so severely that your bigger slice comes from a much smaller pie. At some point—the peak of what economists call the Laffer curve—further tax increases actually bring in less money while destroying more economic activity.

The Elasticity Factor

Not all markets suffer equally from intervention. The key variable is elasticity—how much buyers and sellers change their behavior when prices move.

Consider insulin for diabetics. If the price doubles, diabetics will still buy roughly the same amount because they need it to survive. Demand is "inelastic," meaning it doesn't stretch much in response to price changes. A tax on insulin would generate revenue without preventing many transactions, creating relatively little deadweight loss.

Now consider luxury vacations. Double the price and people simply stay home or find substitutes. Demand is "elastic"—it responds dramatically to price changes. A tax on vacations would cause people to change their plans entirely, wiping out transactions that would have happened.

The same logic applies to supply. If producers can easily enter or exit a market, supply is elastic, and taxes cause large changes in quantity. If production requires specialized equipment and skills, supply is inelastic, and taxes mostly just transfer money rather than preventing activity.

This is why economists often advocate taxing things with inelastic supply, like land. The amount of land doesn't change based on how much you tax it—nobody can make more Manhattan real estate no matter how high property values climb. A land value tax creates almost no deadweight loss because it doesn't discourage any economic activity.

The Monopolist as Tax Collector

There's a deep structural similarity between monopoly pricing and taxation. Both drive a wedge between what consumers pay and what producers receive. Both reduce the quantity of goods sold below the efficient level. Both create the distinctive triangular pattern of deadweight loss.

The crucial difference is who gets the wedge.

With a tax, the government collects the difference between buyer price and seller price. This money can, at least theoretically, be returned to citizens through services or transfers. The deadweight loss is the cost of redistribution, a side effect of a process that moves money around.

With a monopoly, a private company collects the wedge. The same distortion occurs, the same transactions are prevented, the same value is destroyed. But instead of funding public goods, the proceeds enrich shareholders.

This parallel explains why economists view monopolies with such suspicion. A monopolist effectively levies a private tax on everyone who wants their product, creating all the efficiency losses of taxation with none of the public benefit.

Two Ways to Measure Loss

Economists have developed competing frameworks for calculating deadweight loss, and the choice between them isn't just academic—it can change the answer substantially.

The Marshallian approach, named after nineteenth-century British economist Alfred Marshall, uses ordinary demand curves based on observed purchasing behavior. Under this framework, if demand is perfectly inelastic—if people will buy the same quantity no matter the price—there's no deadweight loss from taxation. The tax just transfers money without changing behavior.

The Hicksian approach, developed by John Hicks in the twentieth century, takes a different view. It focuses on "equivalent variation"—how much money you'd have to give someone to make them as happy as they would have been without the tax. Even with perfectly inelastic demand, Hicks recognized that the tax distorts relative prices between goods, causing people to substitute in inefficient ways.

Here's a concrete example: suppose both bread and rice are essential foods, and a tax is placed only on bread. Even if people don't reduce their total food consumption, they'll shift toward rice and away from bread. If bread was actually the better choice for them before the tax, this substitution destroys value. Hicks's framework captures this loss; Marshall's doesn't.

Modern economists generally prefer the Hicksian approach because it accounts for subtler distortions. But Marshall's simpler framework remains common in textbooks and quick analyses.

The Great Debate: Trivial or Transformative?

Economists have fought for decades over whether deadweight loss matters much in practice.

Martin Feldstein, who served as chief economic advisor to President Ronald Reagan, argued that small triangles compound over time. Each year's distortion slightly reduces investment, innovation, and growth. These effects magnify over decades until tiny inefficiencies become major drags on prosperity. In Feldstein's view, reducing deadweight loss should be a top policy priority.

James Tobin, a Nobel laureate known for proposing a tax on financial transactions, took the opposite position. He argued that the triangles are simply too small to worry about much. The real action in economics happens elsewhere—in managing unemployment, stabilizing prices, distributing resources fairly. Obsessing over efficiency losses from taxation is rearranging deck chairs on the Titanic.

The truth likely lies somewhere between. In markets where supply and demand are highly elastic, deadweight losses can be substantial. In markets with inelastic factors, losses are minimal. The magnitude depends entirely on the specific characteristics of each market and each intervention.

Why This Matters for Land Taxes

This brings us back to why economists almost universally favor taxing land value over other forms of taxation.

Land supply is perfectly inelastic. No matter how high the tax, the same amount of land exists. You can't manufacture more San Francisco, and you can't make existing land disappear because of taxes. The triangle that would represent deadweight loss collapses to essentially nothing.

Compare this to taxing income, where higher rates discourage work; or taxing capital, where higher rates discourage investment; or taxing sales, where higher rates discourage consumption. All of these create real triangles, real lost trades, real value that evaporates into nothing.

A land value tax is as close to a free lunch as economics offers. It can fund government without the side effect of preventing beneficial economic activity. The money comes from land values that would exist anyway, capturing gains that landowners did nothing to create.

And yet, as the original Substack article notes, almost nobody likes land taxes. The economic efficiency argument, compelling as it is, runs headlong into political reality. The people who would pay more—current landowners—vote. The diffuse beneficiaries of a more efficient tax system don't organize around this issue.

Deadweight loss may be invisible, but property tax bills are not.