Write down the three identities of calculating the GDP of a country by the three methods. Also briefly explain why each of these should give us the same value of GDP.
The three identities for calculating GDP are:
1. Value Added Method (Production Method): GDP = ∑(i=1 to N) GVA_i Where GVA = Sales – Intermediate Goods. This method sums the value added by each producing unit in the economy.
2. Expenditure Method: GDP = C + I + G + X – M Where C is consumption, I is investment (both planned and unplanned), G is government expenditure, X is exports, and M is imports. This method looks at the demand side of products.
3. Income Method: GDP = W + P + In + R Where W is wages and salaries, P is profits, In is interest payments, and R is rents received by households.
Why all three methods give the same value:
All three identities are different expressions of the same variable, namely GDP. The sum of final expenditures in the economy must be equal to the incomes received by all the factors of production taken together. This follows from the simple idea that the revenues earned by all the firms put together must be distributed among the factors of production as salaries, wages, profits, interest earnings, and rents. No matter how complicated an economic system may be, the annual production of goods and services estimated through each of the three methods is the same.
Explanation
The textbook establishes the fundamental identity (equation 2.6) that equates all three methods: GDP = ∑GVA = C + I + G + X - M = W + P + In + R. The equivalence arises because whatever is produced (value added) is either consumed or invested (expenditure), and the revenue generated is distributed as factor incomes (wages, profits, interest, rent). The numerical example with firms A and B demonstrates this clearly: GDP calculated as value added (50+150=200) equals the final expenditure on cloth (200).
Solution Steps
Step 1: Write the Value Added Method identity: GDP = ∑GVA_i
Step 2: Write the Expenditure Method identity: GDP = C + I + G + X - M
Step 3: Write the Income Method identity: GDP = W + P + In + R
Step 4: Explain that all three are expressions of the same variable GDP
Step 5: Explain that revenues earned by firms are distributed as factor incomes, establishing equivalence