Question

In the simple two-sector economy (households and business), investment equals saving. With three sectors (households, business, and government), this relationship no longer has to hold. Why?

Answer 1

In two sector model, the income/output equals consumption and investment, ie , where C is consumption expenditure and I is investment expenditure. Also, the household either saves or consumes, as or . But as can be written as , we have the equality , ie .

But, in three sector model, government is included and the income/output equals , where G is government expenditures. Also, the government finances these expenditures by taxes on the househols, as , where T is tax taken to finance the government expenditure, and is a part of income. In this case, we have the expenditure side as or and the income side as or , and we have the equality as , ie .

Hence the relationship doesn't have to hold in three sector economy as it will only hold if or , and the is the government budget deficit.

The equality can be further stated as , referring that if government have a budget surplus or , then household saving must have increased due to less taxes (T) and overcomes the I, and if government have a budget deficit or , then household saving can no longer finance the investment I, as taxes have increased so much that it has cut the household saving. Unless government have a balanced budget, ie , the household saving can not exactly finance the investment in the economy as .