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What Do Taxes on Goods Actually Tax?
Taxes require measurement and measurement is often imperfect
Given that Brian and I started this newsletter to share our appreciation for price theory, it seems only appropriate that we mention Walter Williams, who died earlier this week. Walter Williams had a passion for price theory and for teaching it. He was trained at UCLA and spoke favorably of Armen Alchian’s influence not only on his thinking but on his ultimately on Walter’s successful completion of the program. Like Alchian before him, there are generations of students who have a better understanding of price theory today than they would have without Walter.
Both Thomas Sowell and Don Boudreaux shared their thoughts on Walter Williams yesterday. What is really inspiring for us is what his students wrote about him. He set a great example of how to teach price theory. We hope to keep building on his legacy.
Back when I was an undergrad, I had a part-time job working for a tobacco company. One summer, my boss and I were talking about a proposed tax on our product. My boss told me that our company had resigned itself to the fact that there was going to be some sort of tax. Given that the state was intent on implementing that tax, our company wanted the state to levy a per-unit tax rather than an ad valorem tax (a tax on the value). Some people might be puzzled by this. For example, suppose that the tax was $1 per unit, or 25% of the price.
Why would the company care about whether the tax was $1 per unit or 25% if these values were equivalent amounts?
The key price-theoretic insights are that 1) there are multiple goods and therefore multiple margins for customers to adjust to any price change and 2) those markets are connected via prices.
To understand why my company wanted a per unit tax, let’s think about a simple example. Suppose that there are two goods: a high-quality good and a low-quality good. The monetary price of the high-quality good is double that of the low-quality good. Suppose also, for the sake of simplicity, that the entire incidence of the tax falls on consumers and suppose that there are multiple goods in the market. An ad valorem tax of 25% raises both prices by 25%. The relative price of the high-quality good remains unchanged. As a result, the fraction of consumption devoted to the high-quality good remains unchanged even though total consumption of both goods declines.
However, suppose that there is a $1 tax per unit. For this to be a 25% tax on the high-quality good, the monetary price of that good must be $4. This means that before the tax, the monetary price of the low-quality good is $2. A $1 per unit tax on these goods changes the price of the high-quality good to $5 and the price of the low-quality good to $3. The relative price of the high-quality good has fallen and therefore people will want to devote a greater proportion of their consumption to the high-quality good since its relative price declined.
The reason that the company wanted the per unit tax was due to the fact that the company sold the premium brand of tobacco in the market. Its competitors sold the cheaper, lower-quality brand. So while demand would decline for both products, it would decline more for our competitor.
The tax did not merely shift up our marginal cost; it also shifted out the demand curve for our product by raising the price of a substitute.
People tend to find examples like this pretty intuitive. But what if I told you that the same basic concepts apply when we think about the taxation of a good with particular, distinct characteristics?
Take the example of a lightbulb. When you buy a light bulb, what are you buying? (This sort of question typically makes my students think I’ve lost my mind.) The purchase of a lightbulb is akin to purchasing a flow of services of light for the duration of the life of the bulb. Suppose that there are two types of lightbulbs. The first type of lightbulb lasts for one year. The other lightbulb lasts for two years. If the cost of the first bulb is half the price of the second bulb, then consumers should be indifferent between buying two of the one-year bulbs and one of the two-year bulbs. However, suppose that the marginal cost of producing bulbs that last for different periods of time is not proportional to the time they last.
The marginal cost of producing the one-year bulb is $1 per bulb. The marginal cost of producing a two-year bulb is $3 per bulb. In a competitive market, the market price will be equal to the marginal cost. Customers will therefore prefer the one-year bulb to the two-year bulb since the one-year bulbs provide two years of light for $1 less than the two-year bulb.
If the government levies a tax of 10% on all lightbulbs, the customers will still prefer the one-year bulbs since the new price of the one-year bulb is $1.10 and the new price of the two-year bulb is $3.30.
However, suppose that the government levies a tax of $1.10 on each lightbulb. In this case, the price of the one-year bulb is $2.10 whereas the price of the two-year bulb is now $4.10. Now two years of light costs $4.20 if the consumer buys one-year bulbs and $4.10 if the consumer buys two-year bulbs. The two-year bulbs are now cheaper than the one-year bulbs because of the tax.
There are a couple of interesting things to note here. First, even though the tax is $1.10, the observed increase in the price of lightbulbs is $3.10! Why? In the original equilibrium, only one-year bulbs are sold. In the post-tax equilibrium, only two-year bulbs are sold. Second, tax revenue might be less than would have been the case if the durability of the bulbs had remained constant. If only one-year bulbs were available, the government would collect $1.10 per bulb per year in tax revenue. With the two-year bulb, the government collects only $0.55 per bulb per year. However, the number of two-year bulbs purchased with the tax would be higher than the number of one-year bulbs purchased with the tax (remember, people will also choose more darkness). Third, it follows from the second point that the deadweight loss associated with the tax is smaller. And finally, the switch to the high-durability bulbs is inefficient. These bulbs are much costlier than the one-year bulbs, but customers now prefer the more durable bulbs because doing so helps them to avoid some taxes.
This lightbulb example, or some version of it, was first articulated by Yoram Barzel. In his paper, Barzel pointed out that the effects of per unit taxes and ad valorem taxation depended on what characteristics of the good that was being taxed. A per unit tax on lightbulbs taxes all of the characteristics of lightbulbs that are common, but does not tax the characteristic of durability. As a result, more durability will be provided in the market. In contrast, ad valorem taxes are a tax on the entire value of the good. But some goods are bundles of various characteristics. If these characteristics can be isolated and sold separately, then ad valorem taxes provide an incentive for unbundling.
In short, per unit taxes will tend to increase the quality of the good being taxed if there is a characteristic of the good that is untaxed. Ad valorem taxes will tend to reduce the quality of a good as characteristics that can be unbundled from the taxed good will be unbundled and sold separately. In each case, tax revenue declines relative to the constant quality case. However, the measured increase in the price will be greater than the tax for per unit taxes and less than the tax for ad valorem taxes.
Therein lies an important lesson for policy. Much like the discussion in my post on corporate income taxes, we must ask ourselves what (and who) we are trying to tax. We also have to think carefully about what this implies. For example, suppose that society deems the consumption of alcohol to be something that it wants to discourage. One policy solution is to tax alcohol. The effects of a per unit tax on alcoholic drinks depend on the unit of alcohol. For example, a tax on a liter of alcohol might cause customers to buy liters with a higher proof. It might also lead to a higher proof per liter for many brands. As a result, the extent to which alcohol consumption declines is less than the product of the previous proof and the decline in the number of liters sold.
Barzel’s insight not only provides a great example of how policies often have unintended consequences but also how price theory can help to predict those consequences.