All private consumption in a nation's economy is part of this expenditures approach for calculating the gdp.

Yes , private consumption in an economy is a part of expenditure mthod approach to calculate GDP .

But this is a necessary but not sufficicent condition to calculate GDP by this method

Explanation:

GDPmp (by expenditure method) = Private Final Consumption Expenditure + Government Final Consumption Expenditure + Gross Domestic Capital Formation + Net Exports (Exports - Imports)

The method is based on circular flow of income notion 'one person's expenditure is other person's income' . Hence summing expenditure of all the sectors of economy (households , firms , govt , financial sector , rest of world) - we get the income of the entire economy .

Considering 'private final consumption expenditure' :

This is = Households expenditure + expenditure of non public institutions serving households .

In tricky questions household expenditure might not be directly given , then it can be calculated by : Household Income - Household Saving

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