Suppose we have an economy with domestic supply SS and domestic demand DD.

Under free trade, with a world price of P_W:

Domestic producers produce M₁,

domestic consumers consume M₂,

and the economy imports (M₂ - M₁).

The consumer surplus is AP_WC and the producer surplus is HP_WB. (1)

If a quota is imposed on the imports of M - say, as much as Q - the total supply SS' will be the domestic supply plus the amount Q imported by quota - in other words, SS' = SS + Q. Then:

The economy consumes at E,

domestic production is M₃,

domestic demand is M₄,

the amount Q imported is (M₄ - M₃),

and the domestic price increases to P_d. (2)

The consumer surplus, AP_dE, has decreased, and the producer surplus, HP_dD, has increased.

The surplus reduced with the quota imposed is the area DBCE. (3) As in the tariff case, DBF and EGC represent "efficiency loss". But now DFGE, which was previously government tariff revenue, is now the quota rent belonging to import license holders.

We can analyse the effect of quotas using an offer curve approach, in a similar way to tariffs.

Consider two countries with offer curves O_H and O_F. The home country imports M₁ and exports X₁. If it imposes a quota, say M', it restricts its imports, so that its new offer curve is OE'M'. (4)

Its offer curve intersects the foreign country's offer curve at E", which means that it will now export X₃ and import M'.

However, when importing M', the home country is willing to pay X₂. The difference (X₂ - X₃) is the quota license holder's revenue. (5)

You can compare this with imposing a tariff.