Answer: 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
Step-by-step 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