Essentially the basic difference between economic and non economic activity is that economic activities are the activities in the economy that contribute to the  gross domestic product(GDP) of the you provide/produce a good or a service in exchange for money.For eg: you grow apples and sell them at the market.This is economic activity.
Whereas non-economic activity is just the opposite.activity in this economic does nt affect the GDP.and most of the times it is unpaid work.For eg:cleaning of the house .
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