Reciprocal Tariffs?

I'm wrapping my head around the equation stated by the Office of the President of the United States Trade Representative for calculating the so-called "Reciprocal Tariffs." * From that site, we see the following:$\Delta\tau_{i}=\frac{x_{i}-m_{i}}{\varepsilon*\varphi*m_{i}}$. We're told that $\Delta\tau_{i}$ is the "change in the tariff rate"; $x_{i}$ is "total exports to country i" (that is, U.S. exports); $m_{i}$ is "total imports from country i" (that is, U.S. imports); $\varepsilon$ is the "elasticity of imports with respect to import prices" (an economics concept measuring how much demand goes up or down when prices go down or up, but it can be ignored here because the next term cancels it out); and $\varphi$ is the pass through from tariffs to import prices (this is the term that cancels out the elasticity term since the latter is stated to be 4 and the former is stated to be 0.25, thus totaling 1). Finally, since "we are a kind people," the derived number is divided by two to determine the final "reciprocal tariff."

Multiple sites characterize this as "trade deficit divided by total imports." It took me a moment to understand this, because trade deficit is imports minus exports, whereas the numerator of the fraction is exports minus imports, the negative of the deficit. But the site states that "$\varepsilon\lt0$," so the denominator is negative and, lo and behold, it all works out as described.

The chart above has three columns: Country (more on that later); "Tariffs Charged to the U.S.A. Including Currency Manipulation and Trade Barriers"; and "U.S.A. Discounted Reciprocal Tariffs" (calculated as above). One might reasonably infer from these column labels that, for each country, an analysis was done of the tariffs on U.S. exports in place along with currency manipulation and trade barriers to determine the number, but no. The site linked above states that:

While individually computing the trade deficit effects of tens of thousands of tariff, regulatory, tax and other policies in each country is complex, if not impossible, their combined effects can be proxied by computing the tariff level consistent with driving bilateral trade deficits to zero. If trade deficits are persistent because of tariff and non-tariff policies and fundamentals, then the tariff rate consistent with offsetting these policies and fundamentals is reciprocal and fair.

That is, in lieu of the above analysis, the fraction calculated in accordance with the equation above is used as a proxy. Note the "If." If my mother had wheels, she'd be a bus.

Now, with the background out of the way, let's stipulate that the general concept of there being a strong relationship between trade barriers imposed by countries receiving U.S. exports and the trade deficit with such countries as a fraction of U.S. imports from those countries is not completely irrational. In essence, this is a theory that trade is only fair with any given country if the balance of trade with that county is $0.00 and that "reciprocal tariffs" are the fair way to force this equilibration. I do not agree with this stipulation, but let's proceed nevertheless. Does the fraction calculated per the above reasonably capture this?

Let's start with an easy one. We'll take Malaysia as an example. In 2024, the U.S. imported $52.5B in goods from Malaysia and exported $27.7B in goods to Malaysia. Using the equation, the imputed "tariffs" would then be 47.2% and we "kindly" will only reciprocate with a 24% tariff. But Malaysia's population is 35.13 million, that of the U.S. is 340.1 million, almost 10 times as large. So, to "balance trade," each Malaysian would have to purchase $\frac{340.1}{35.13}=\$9.68$ for every dollar of Malaysian goods purchased by Americans. Clearly, this makes zero sense.

Instead then, let's see how things change if we use per capita numbers. Then we have $\frac{\$52.5\text{ Billion}}{340.1\text{ million}}=\$154$ dollars of U.S. imports per capita and $\frac{\$27.7\text{ Billion}}{35.13\text{ million}}=\$788$ in Malaysian imports per capita (that is, U.S. exports). That is, each Malaysian (on average) imports $788 of U.S. goods per year, while each member of the U.S. population imports a measly $154 of Malaysian goods per year. What happens if we use the per capita numbers in the equation? Then we have $\frac{154-788}{154}=-431\%$. Trump constantly rails about the U.S. being "ripped off" by our trading partners. But, using the silly logic described in the block quoted section, I have to ask "who's ripping off whom?"

Another aspect of the naive calculation as presented is the fact that, for example, the median annual household income in the U.S. (2023 figure) is $78,538. That of a Malaysian is $1,419. Is it reasonable to expect a Malaysian to purchase as much in U.S. goods as a U.S. resident purchases Malaysian goods? I don't think anyone could justify a "yes" answer (with the possible exception of Peter Navarro). But can we consider an adjustment to the equation to capture this as we did with the per capita trade quantities as above?

We could consider dividing the U.S. import number by the U.S. household income, that would yield imports per dollar of income. Similarly, we could divide Malaysia's import of U.S. goods by Malaysian household income. This would have even a more dramatic effect on the fraction. Taking both population and household income together would show that we're absolutely pillaging Malaysia!

There are other categories of countries and entities as well. Let's think about some countries with more in common with the U.S. If we consider the so-called "developed" countries, e.g., European Union, United Kingdom, Japan, South Korea, Norway, Australia, New Zealand, etc. and normalize them all similarly, what do we see?

I ran the per capita numbers for these countries and the results were:

Note that, on a per capita basis, every country (or entity in the case of the EU) shows a negative number, with the exception of the EU. That is, each nominal resident of the foreign country purchases, on average, more U.S. goods than a nominal U.S. resident does of theirs. The EU's positive number is a bit higher than calculated by Trump, et al, on a per capita basis. The EU's population significantly exceeds ours. But again, who is ripping off whom?

Were I to go through and utilize household income, the results would be even more stark, but this post is already excessively long. But I do want to say a bit more about Peter Navarro. Navarro, who is now the Senior White House Counselor for Trade and Manufacturing in the Trump Administration is, at best, a fringe economist. Among other hilarities, in books and articles, he quotes "Harvard economist Ron Vara" in support of his policies. You'll note that Ron Vara is an anagram of Navarro, and Navarro has conceded that Vara is purely fictional.

I want to cite a couple of sites. Matt Parker, of Stand Up Maths, explains the calculations and some of their faults and, finally, Coyote Blog expresses a viewpoint very much aligned with my own with respect to what I'll call the "philosophy of tariffs."

* Apparently, The Office of the U.S. Trade Representative has decided that it's best not to try to explain the so-called "Reciprocal Tariffs." The equation and its purported explanation are no longer there, at least that I can find. I'd have been embarrassed too.