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Deadweight Loss: Definition and How to Calculate It

By Matthew Zeitlin · June 28, 2021 · 5 minute read

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Deadweight Loss: Definition and How to Calculate It

What Is Deadweight Loss?

One of the most important concepts in economics is known as “deadweight loss.” The deadweight losses are those transactions that do not happen because of inefficiencies in an economy, often due to government interventions such as price floors or ceilings, or taxation.

To understand, we need to think about how government interventions can impact the equilibrium between supply and demand.

First: How to Calculate Surplus

In order to know how to calculate deadweight loss, we must first be able to calculate surplus.

Typically a business will only sell something if they can do so at a price that’s greater than what they paid for it themselves, and a consumer will only buy something if it’s at or less than the price they want to pay for it.

Scenario A – The Equilibrium: Let’s imagine a store selling comic books for $10 each. The store buys the comic books from the wholesaler for $5 and sells them for $10, pocketing $5 of “producer surplus.” Before the store opened, comic book readers would go over to the other town to buy comic books for $15, the price they were willing to pay, but now can buy them for $10. This $5 difference between the price they’re willing to pay is the “consumer surplus”.

In this case, let’s say the store is able to sell 1,000 comic books, that means the combined producer and consumer surplus is $10,000.

Breakdown:

•  P1 = Producer’s Cost of a Comic Book = $5

•  P2 = Producer’s Price to Sell a Comic Book = $10

•  P3 = Price A Consumer Pays = $10

•  P4 = Price A Consumer Is Willing to Pay = $15

•  Units Sold = 1000

•  Producer Surplus = (P2 – P1) * Units Sold = ($10 – $5) * 1000 = $5,000

•  Consumer Surplus = (P4 – P3) * Units Sold = ($15 – $10) * 1000 = $5,000

•  Total Surplus1 = Producer Surplus + Consumer Surplus = $5,000 + $5,000 = $10,000

How to Calculate Deadweight Loss

To properly calculate deadweight loss, you need to be able to represent the supply and demand of the goods being sold graphically in order to determine prices. According to supply and demand, the higher a price goes, the fewer of that item will get sold; and vice versa.

Example of Deadweight Loss

Scenario B – Imposed Tax: Let’s go back to our comic book example and imagine that the town’s government imposes a $2 tax on comic books.

What happens to the price of comic books and the surplus generated by the sales of comic books? If consumers had to buy comic books to live (and for some, it may feel that way) and there were no other way to buy them, then the comic book seller could simply bump up prices $2 and sell 1,000 comic books for $12 each, maintaining his $5 of producer surplus on each comic book sold with $2 going to the government and consumer surplus of $3.

In this case the combined consumer and producer surplus is lower — $5×1,000 +$3×1,000 = $8,000. So there’s a missing $2,000 of what economics call “gains from trade.” But, the government is collecting $2,000, so the money does not disappear from the economy.

The government can buy things, hire people, and literally send money to people, via economic stimulus, meaning the tax revenue does not disappear from the economy.

But, despite how fervently people want them, comic books are not a necessity in the same way food is and remember that comic book store in the neighboring town? If the demand for comic books can not literally be unchanged by its price, that means the comic book seller may think twice about passing on the tax fully on to his customers and that any price increase will result in some comic books going unsold.

If he were to increase the price to $12, thus passing on the tax to his customers, he may not be able to sell enough comic books to maintain the revenue he needs to keep his store open, so he lowers the price to $11, thus splitting the tax between himself and his buyers but still reducing the number of total comic books sold. In this case, let’s say he sells 600 comic books instead of 1,000.

The combined consumer and producer surplus is $4,800 ($4×600 + 600x$4) with $1,200 of tax collected (600 x $2) meaning there’s a total of $6,000 of consumer surplus, producer surplus, and government revenue. In this case the deadweight loss is $4,000.

Breakdown:

•  P1 = Producer’s Cost of a Comic Book = $5

•  P2 = Producer’s Price to Sell a Comic Book = $9

•  P3 = Price A Consumer Pays = $11

•  P4 = Price A Consumer Is Willing to Pay = $15

•  Units Sold = 600

•  Tax = $2/Comic Book

•  Producer Surplus = (P2 – P1) * Units Sold = ($9 – $5) * 600 = $2,400

•  Consumer Surplus = (P4 – P3) * Units Sold = ($15 – $11) * 600 = $2,400

•  Gains From Trade (Tax) = $2 * 600 = $1,200

•  Total Surplus2 = Producer Surplus + Consumer Surplus + Gains From Trade = $6,000

•  Deadweight Loss = Total Surplus1 – Total Surplus2 = $10,000 – $6,000 = $4,000

The higher price, created through taxation, has impacted the equilibrium between supply and demand and created a deadweight loss – the surplus that evaporates due to fewer transactions happening between the comic book seller and the readers.

While this is a rather extreme example of what happens when taxes force up prices, it’s a good way of thinking about how deadweight losses are more than just items getting more expensive. Rather, the deadweight loss formula can illustrate the evaporation of mutually beneficial economic transactions due to different types of taxes.

Deadweight loss of taxation refers specifically to deadweight loss that occurs due to taxes, but a similar impact can occur when a government puts price floors or ceilings on items.

Why Investors Should Care About Deadweight Loss

Deadweight loss can affect investors in a number of ways, and it’s important to consider it when looking at different types of investments. One of the most debated issues in economics is the effects that the tax system has on income, investment, and economic growth in the short and long run.

Some argue that income taxes, payroll taxes (the flat taxes on wages that fund Social Security and Medicare) and capital gains taxes work like the comic book tax described above, preventing otherwise beneficial transactions from happening and reducing the economic gains available to all sides. There’s evidence on all sides of this debate, and the effects of tax rates on overall economic growth are, at best, unclear.

As an investor, deadweight loss might matter when it comes to companies or sectors impacted by specific taxes, such as sales taxes or excise taxes on alcohol or cigarettes. Deadweight loss shows how taxes on specific items can not only reduce profitability by increasing a company’s tax bill, but also affect revenue by reducing overall sales or driving down prices that businesses can charge or receive from buyers. As an investor, this knowledge and insight can be useful when allocating capital between companies, sectors, or types of assets.

The Takeaway

But taxes and the economy only matter to your investments if you have them in the first place. You can start with investing with the SoFi Invest brokerage platform. SoFi can help you construct portfolios with professional advice suited to your financial needs and situation. Stocks, bonds, exchange traded funds and even crypto are available through SoFi, with low fees and customized advice.

Photo credit: iStock/akinbostanci


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