Step 1: Value Added (Production) Method:
$GDP = \sum GVA_i = \sum (Value\ of\ Output_i - Intermediate\ Consumption_i)$ summed across all producing sectors/firms $i$ in the economy — this avoids double counting by only adding the value each stage of production contributes.
Step 2: Income Method:
$GDP = Compensation\ of\ Employees + Operating\ Surplus + Mixed\ Income\ of\ Self\text{-}employed + Net\ Indirect\ Taxes + Depreciation$, i.e. the sum of all factor incomes (wages, rent, interest, profit) paid out in production, plus depreciation and net indirect taxes to move from factor cost/NDP to market-price GDP.
Step 3: Expenditure Method:
$GDP = C + I + G + (X - M)$, where C = private final consumption expenditure, I = gross investment, G = government final consumption expenditure, and (X−M) = net exports (exports minus imports).
Final Answer:
The three identities are the Production/Value-Added method, the Income method, and the Expenditure method — all three must yield the same GDP figure since they measure the same economic activity from three different angles (what is produced, what is earned, and what is spent).