In: Economics
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?
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
.