An ad valorem tax is a percentage of the value of the item, say 10 cents on the dollar, while a specific tariff is so-much per weight, say $5 per ton.
A "revenue tariff" is a set of rates designed primarily to raise money for the government. A tariff on coffee imports, for example (by a country that does not grow coffee) raises a steady flow of revenue.
A "protective tariff" is intended to artificially inflate prices of imports and "protect" domestic industries from foreign competition. For example, a 50% tax on a machine that importers formerly sold for $100 and now sell for $150. Without a tariff the local manufacturers could only charge $100 for the same machine; now they can charge $149 and make the sale.
A prohibitive tariff is one so high that no one imports any of that item.
The distinction between protective and revenue tariffs is subtle: protective tariffs in addition to protecting local producers also raise revenue; revenue tariffs produce revenue but they also offer some protection to local producers. (A pure revenue tariff is a tax on goods not produced in the country, like coffee perhaps.)

Tax, tariff and trade rules in modern times are usually set together because of their common impact on industrial policy, investment policy, and agricultural policy. A trade bloc is a group of allied countries agreeing to minimize or eliminate tariffs against trade with each other, and possibly to impose protective tariffs on imports from outside the bloc. A customs union has a common external tariff, and, according to an agreed formula, the participating countries share the revenues from tariffs on goods entering the customs union.

If a country's major industries lose to foreign competition, the loss of jobs and tax revenue can severely impair parts of that country's economy. Protective tariffs have been used as a measure against this possibility. However, protective tariffs have disadvantages as well. The most notable is that they increase the price of the good subject to the tariff, disadvantaging consumers of that good or manufacturers who use that good to produce something else: for example a tariff on food can increase poverty, while a tariff on steel can make automobile manufacture less competitive. They can also backfire if countries whose trade is disadvantaged by the tariff impose tariffs of their own, resulting in a trade war and disadvantaging both sides.

There are two main ways of implementing a tariff:

An ad valorem tariff is a fixed percentage of the value of the good that is being imported. Sometimes these are problematic as when the international price of a good falls, so does the tariff, and domestic industries become more vulnerable to competition. Conversely when the price of a good rises on the international market so does the tariff, but a country is often less interested in protection when the price is higher. They also face the problem of transfer pricing where a company declares a value for goods being traded which differs from the market price, aimed at reducing overall taxes due.
A specific tariff is a tariff of a specific amount of money that does not vary with the price of the good. These tariffs may be harder to decide the amount at which to set them, and they may need to be updated due to changes in the market or inflation.
Adherents of supply-side economics sometimes refer to domestic taxes, such as income taxes, as being a "tariff" affecting inter-household trade.

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