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Imports Quota

For a small domestic market that can buy completely price elastic imports from the world, the price of the good will be at (P world).

However, when there is an import quota of quantity (Q3 - Q2), why is the new price at (P quota), even for the imported goods? (At least that is what my notes said, and google did not give much answers) For me, I feel that the price should instead be (P quota) for quantity Q2, and then at (P world) for quantity (Q3 - Q2), is that correct?

Can anyone explain this in words other than simply saying it's because thats where the demand curve intersects the supply curve?

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