Answer:
[AD = C + I + G] = [AS = Y]
S = I
Explanation:
Economy is at equilibrium when : Aggregate Demand = Aggregate Supply
Aggregate Demand [AD] is the total value of goods & services, all sectors of an economy are planning to buy, during a period of time.
Assuming 3 sector Economy having : Households, Firms, Government
AD = Consumption (C) + Investment ( I ) + Net Govt. Expenditure (NG = G-T)
Aggregate Supply [AS] is the total value of goods & services, all producers of economy are planning to sell, during a period of time. Total value of goods & services is distributed among all production factors as factor incomes. And, Income is either saved or consumed.
AS = National Income [ Y ] = Consumption (C) + Saving (S)
So, Equilibrium : [AD =C + I + NG] = [ AS = Y] → ∴ C + I + NG = Y
[AD = C + I + NG] = [ AS = C + S] → ∴ C + I + NG = C + S
Assuming : leakage (tax) = injection (govt expenditure) ; NG = G-T = 0
So, C + I = C + S → ∴ I = S