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I understand a non-autonomous increase in AD as an increase in AD caused by an increase in income (please correct me if I am wrong). However, I do not understand why the multiplier effect must be triggered by an increase in autonomous AD.

I suppose that an increase in income will increase household's purchasing power thus consumption. This will in turn encourage the firms to increase output and hire more factors of production, thus increasing the national income, which will further increase expenditure? Is this not the multiplier effect's working?

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Because if the increase doesn't come from an autonomous component, it already amounts to the non-autonomous demand increase + multiplier.

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