An import quota is a limit on the quantity of a good that can be produced abroad and sold domestically. It is a type of protectionist trade restriction that sets a physical limit on the quantity of a good that can be imported into a country in a given period of time. If a quota is put on a good, less of it is imported.  Quotas, like other trade restrictions, are used to benefit the producers of a good in a domestic economy at the expense of all consumers of the good in that economy.
The primary goal of import quotas is to reduce imports and increase domestic production of a good, service, or activity, thus "protect" domestic production by restricting foreign competition. As the quantity of importing the good is restricted, the price of the imported good increases, thus encourages consumers to purchase more domestic products. In general, a quota is simply a legal quantity restriction placed on a good imported that is imposed by the domestic government.
Because the import quota prevents domestic consumers from buying an imported good, the supply of the good is no longer perfectly elastic at the world price. Instead, as long as the price of the good is above the world price, the license holders import as much as they are permitted, and the total supply of the good equals the domestic supply plus the quota amount. The price of the good adjusts to balance supply (domestic plus imported) and demand. The quota causes the price of the good to rise above the world price. The imported quantity demanded falls and the domestic quantity supplied rises. Thus, the import quota reduces the imports.
Because the quota raises the domestic price above the world price, domestic sellers are better off, and domestic buyers are worse off. In addition, the license holders are better off because they make a profit from buying at the world price and selling at the higher domestic price. Thus, import quotas decrease consumer surplus while increasing producer surplus and license-holder surplus.
While import quotas and other foreign trade policies can be beneficial to the aggregate domestic economy they tend to be most beneficial, and thus most commonly promoted by, domestic firms facing competition from foreign imports. Domestic firms benefit with higher sales, greater profits, and more income to resource owners. However, by increasing domestic prices and restricting accessing to imports, foreign trade policies also tend to be harmful to domestic consumers.
Domestic Employment: Decreasing imports and increasing domestic production also increases domestic employment.
Low Foreign Wages: Restricting imports produced by foreign workers who receive lower wages "levels the competitive playing field" compared to domestic goods produced by higher paid domestic workers.
Infant Industry: If foreign imports compete with a relatively young domestic industry that is neither mature enough nor large enough to benefit from economies of scale, then import quotas protect the "infant industry" while it matures and develops.
Unfair Trade: The foreign imports might be sold at lower prices in the domestic economy because foreign producers engage in unfair trade practices, such as "dumping" imports at prices below production cost. Import quotas seek to prevent foreign producers such activity.
National Security: Import quotas can also discourage imports and encourage domestic production of goods that are deemed critical to the security of the national economy.
Corruption: Import quotas can lead to administrative corruption in countries with import quotas as the importers chosen to meet the quota are the ones who can provide the most favors to the customs officers.
Smuggling: Import quotas are more likely to cause smuggling. It's likely that people will try to sneak the bats into the country illegally if the import quota is only a small fraction of the demand for the product. So governments have to set the import quota at a reasonable level.
United States import quotas may be divided into two types: absolute quota and tariff-rate quota. Once a specific quota has been reached in a particular category, goods may still be entered, but at a considerably higher rate of duty.
Absolute quotas 
Absolute quotas limit the quantity of certain goods that may enter the commerce during a specific period. Once the quantity permitted under an absolute quota is filled, no further entries or withdrawals from warehouse for consumption of merchandise subject to the quota are permitted for the remainder of the quota period.
Importers may hold shipments in excess of a specified absolute quota limit until the opening of the next quota period by entering the goods into a foreign trade zone or bonded warehouse. The goods may also be exported or destroyed under [ Customs and Border Protection] (CBP) supervision.
Tariff-rate quotas 
Tariff rate quotas permit a specified quantity of imported merchandise to be entered at a reduced rate of duty during the quota period. There is no limitation on the amount of merchandise that may be imported into the United States, however quantities entered in excess of the quota limit during that period are subject to a higher duty rate.
If the importer has not taken possession of the goods, and elects not to pay the higher rate of duty, they may enter the goods into a foreign trade zone or bonded warehouse until the opening of the next quota period, or export or destroy the goods under CBP supervision.
Once CBP determines the date and time a quota is filled, field officers are authorized to make the required duty rate adjustments on the portion of the merchandise not entitled to quota preference.
Under the North American Free Trade Agreement (NAFTA), there are trade-preference levels (TPL), which are administered like tariff-rate quotas. The U.S. Customs Service administers the majority of import quotas. The Commissioner of Customs controls the importation of quota merchandise, but has no authority to change or modify any quota. The Department of Commerce, in conjunction with the Office of the United States Trade Representative, determines and fixes quota limits. Quota merchandise is subject to the usual Customs procedures applicable to other imports. No import licenses are currently required for quotas administered by the Commissioner of Customs.
Both tariffs and import quotas reduce quantity of imports, raise domestic price of good, decrease welfare of domestic consumers, increase welfare of domestic producers, and cause deadweight loss. However, a quota can potentially cause an even larger deadweight loss, depending on the mechanism used to allocate the import licenses. The difference between these tariff and import quota is that tariff raises revenue for the government, whereas import quota generates surplus for firms that get the license to import.
For a firm that gets a license to import, profit per unit equals domestic price (at which imported good is sold) minus world price (at which good is bought) (minus any other costs). Total profit equals profit per unit times quantity sold.
Government may charge fees for import license. If the government sets the import license fee equal to difference between domestic price and world price, the import quota works exactly like a tariff. The entire profit of the firm with an import license is paid to the government. Thus government revenue is the same under such an import quota and a tariff. Also, consumer surplus and producer surplus are the same under such an import quota and a tariff.
So why do countries use import quotas instead of always using a tariff?
When an import quota is used, it allows a country to be sure of the amount of the good imported from the foreign country. When there is a tariff, if the supply curve of the foreign country is unknown, the quantity of the good imported may not be predictable.
If world supply in the home country is upward-sloping and less elastic than domestic demand (as may be the case when the home country is the United States) then the incidence of the tariff may fall on producers, and the price paid domestically may not rise by much. Then if the tariff is supposed to make price of the good rise to allow domestic producers to sell at a higher price, the tariff may not have much of the desired effect. A quota may do more to raise price. However in competitive markets there is always some tariff that raises the price as high as the quota does.
See also 
- Mankiw, N. Gregory (2004). Principles of Macroeconomics. South-Western College Pub; 3 edition (February 19, 2003). p. 189. ISBN 0-324-16862-4.
- Sullivan, Arthur; Steven M. Sheffrin (2003). Economics: Principles in action. Upper Saddle River, New Jersey 07458: Pearson Prentice Hall. p. 449. ISBN 0-13-063085-3.
- "IMPORT QUOTAS". Encyclonomic WEBpedia.
- "REPORT SMUGGLING TO U.S. CUSTOMS SERVICE 1-800-BE-ALERT". U.S. CUSTOMS SERVICE WASHINGTON, DC 20229. Retrieved Revised February 2002.
- Assaf, Michael; Bonincontro, Cynthia; Johnsen, Stephen (2006). Global sourcing purchasing post 9/11 : new logistics compliance requirements and best practice. Fort Lauderdale, Fla.: J. Ross Pub. p. 53. ISBN 1-932159-39-8.
- Jerison, Amalia. "Lecture 21,Eco 110 (6963) Introduction to Microeconomics". University at Albany. Retrieved fall 2008.