What are the exact elasticity assumptions behind the terms of trade argument [for tariffs]?

“The terms of trade argument for protectionism relies on specific assumptions about the elasticities of demand and supply for a country’s exports and imports. The key elasticity assumptions are:

Inelastic foreign demand for the country’s exports: This means that when the price of the country’s exports increases, the quantity demanded by foreign countries does not decrease much. In other words, the percentage change in quantity demanded is smaller than the percentage change in price.
Elastic domestic demand for imports: This means that when the price of imports increases (due to a tariff), the quantity of imports demanded by the domestic country decreases significantly. In other words, the percentage change in quantity demanded is larger than the percentage change in price.

Under these elasticity assumptions, a country can improve its terms of trade by imposing a tariff on its imports. Here’s how it works:

The tariff raises the domestic price of imports, leading to a decrease in the quantity of imports demanded due to the elastic domestic demand for imports.
The decrease in import demand leads to a decrease in the world price of the imported goods (assuming the country has a significant share of world import demand).
The country’s exports are not affected much by the tariff because foreign demand for the country’s exports is inelastic.
As a result, the country experiences an improvement in its terms of trade: the price of its exports relative to the price of its imports increases.

However, it’s important to note that these elasticity assumptions are not always met in the real world. The elasticities of demand and supply can vary depending on the specific goods being traded, the time horizon, and other market conditions. Moreover, even if a country can improve its terms of trade through tariffs, this does not necessarily imply that the tariffs are beneficial for the country’s overall economic welfare, as they can lead to distortions in production and consumption, as well as potential retaliation from trading partners.”

That is from Claude 3 Opus.