More on "epsilon" in the "Reciprocal Tariffs" equation

 

In the equation published by the Office of the U.S. Trade Representative* ($\Delta\tau_{i}=\frac{x_{i}-m_{i}}{\varepsilon*\varphi*m_{i}}$), we see the Greek letter $\varepsilon$, epsilon. This number is stated to be the elasticity of import demand with respect to import prices. An economist would call this the "price elasticity of demand (PED)", a number which represents the rising and falling of demand with the falling and rising of prices.

The actual definition is that the PED at a given point on the supply and demand curve  is the percentage change in quantity demanded divided by the percentage change in price ($\frac{\%\Delta\text{Q}_{d}}{\%\Delta\text{P}}$).

Let's toss in some numbers and see what this means. Suppose that, at an existing aggregate price for widgets of $100,000,000.00 there are 1,000,000 widgets demanded. Next, suppose the PED is -4. Then $\frac{\%\Delta\text{Q}_{d}}{\%\Delta\text{P}}=-4$. Then suppose, as a result of a price increase due to tariffs, the price of widgets increases by 10%. Arranging the equation above, $\%\Delta\text{Q}_{d}=-4\%\Delta\text{P}=-40\%$. That is, a 10% increase in price will result in a 40% decrease in demand.

In thinking about whether this is reasonable, we need to consider the actual items being evaluated. For example, a Type 1 diabetic relies on insulin to stay alive, and hence must pay whatever the cost is for insulin. This is referred to as "demand being inelastic." On the other hand, it's likely that a significant increase in the price of, for example, iPhones will reduce demand, since new iPhones are not a necessity. This is referred to as "demand being elastic."

There are many considerations that go into PED. These include individual choices, availability of substitutes, the length of time a price increase has been in place (more time gives a greater time to search for substitutes), and others.

Whether it's stated as such or not, the "Reciprocal Tariffs" equation is intended specifically to reduce trade deficits. A larger $\varepsilon$ in the equation will reduce the magnitude of the fraction and imply smaller tariffs, a smaller $\varepsilon$ will do the opposite.

However, a "one size fits all" policy doesn't make a lot of sense. Some of our imports could, in theory, be replaced with domestic products (e.g., automobiles, microchips, etc.) while others could not (e.g., coffee, cobalt, bananas). Going back to Malaysia from my previous post, top U.S. imports are electrical and electronic equipment and machinery, nuclear reactors, and boilers. These items total about 71% of our imports and are among the categories that could, in principle, be produced domestically, though at considerably higher cost.

As examples, the PED for coffee in the U.S. is estimated to be 0.25 (quite inelastic, gotta have that caffeine!), that of fresh tomatoes is estimated to be 4.6 (very elastic). Note that economists typically utilize the absolute value of PED, that is, only showing its magnitude.

With this information, it's quite clear that, on top of the analysis of non-tariff trade barriers shown on the Trump Reciprocal Tariff chart and the rationalization on the U.S. Trade Representative's web page*, the numbers have little, if any, relation to the actual trade situation or to any deep analysis of price elasticity.

Ps: I guess I do have to thank Trump for getting me reengaged with blogging!

*As noted in my previous post, the page with the equation and the explanation has disappeared, or at least been moved to where I can't find it. If someone can find it and post a link in the comments, that would be great. Also as I alluded to, given all the mockery and derision the chart and the equation have engendered, I'd be embarrassed and ashamed as well.