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.

#### Solution

GDP can be calculated by the following three methods :-

(a)** Income method :-**

GDP = Total payments made to the factors of production

`"GDP" equiv sum_(i=1)^MW_i+sum_(i=1)^MP_i+sum_(i=1)^M"In"_i+sum_(i=1)^MR_i...................(1)`

`sum_(i=1)^MW_i` represents total wages and salaries received by i-th households.

`sum_(i=1)^MP_i` represents total profit received by i-th households.

`sum_(i=1)^M"In"_i` represents total Income received by i-th households.

`sum_(i=1)^MR_i` represents total Rent received by i-th households.

Equation (1) can be simplified as

GDP ≡ W + R + In + P

(b)** Value added or product method**

GDP ≡ Sum of gross value added by all firms in an economy

or GDP ≡ GVA_{1} + GVA_{2} + …GVA_{n}

Where,

GVA_{1 }represents gross value added by the 1^{st} firm

GVA_{2 }represents gross value added by the 2^{nd} firm and so on

.

.

.

GVA_{n}_{ }represents gross value added by the n^{th }firm

Therefore,

`"GDP" equiv sum_(i=1)^N "GVA"_i`

(c)** Expenditure method or final consumption method**

GDP ≡ Sum total of revenues that firms earn

Or

GDP ≡ Total consumption + Investment + Government Consumption expenditure + Net exports

`equiv sum_(i=1)^N C_i+sum_(i=1)^NI_i+sum_(i=1)^NG_i+sum_(i=1)^N X_i`

As households spend some part of their income on imports, some portion of consumption expenditure also comprises of imports, which are denoted by C_{M}. Similarly, some part of the investment expenditure and government consumption expenditure is spent on the foreign investment goods and imports. These portions of investment and government consumption expenditure are denoted by I_{M}_{ }and G_{M }respectively. Thus, the final household's consumption expenditure, investment expenditure and final government expenditure that are spent on the domestic firms are denoted by C − C_{M}, I − I_{M} and G − G_{M} respectively.

Substituting these values in the above equation

`"GDP" equiv C-C_m+I-I_m+G-G_m+sum_(i=1)^N X_i`

`equiv C+I+G+sum_(i=1)^N-(C_m+I_m+G_m)`

`equiv C+I+G+X-M`

The three methods give the same result for measuring GDP because what is produced in the economy is either consumed or invested. The three methods depict the same picture of an economy from three different angles. While the product method presents the value added or total production, the income method depicts the income earned by all the factors, lastly, the expenditure method presents the expenditure incurred by all the factors. In the economy, the producer employs four factors of production to produce final goods and earns revenue by sale, which is equivalent to the total value addition by the firm. The firms pay remunerations to the factors, which act as the income of all the factors. These remunerations are equivalent to the factors’ contributions to the value addition. These factor incomes are then expended on the goods and services, which verifies the equality between the factor income and expenditure. Hence, the three methods will always give the same value of GDP.