# Does the investment component of GDP (demand side) identity include expenditures by the government and households?

In the identity GDP=C+I+G+(X-M) does "I" include expenditures by the government and households?

For example, if a construction firm builds new residential properties and a household buys this property. Is the value of the new residential property allocated as 'firm' expenditure or 'household' expenditure and where in the identity above would these expenditures fall?

Also if a government builds a school or bridge would this go under "I" or "G"?

• It is just a convention, but $I$ usually covers all gross domestic capital formation by consumers, companies and government; the alternative is to exclude it and have $I$ as gross private domestic capital formation – Henry May 4 '20 at 19:41
• What does 'it' mean in "alternative is to exclude it"? – StatsScared May 4 '20 at 20:23
• The alternative is to exclude Government gross capital formation from $I$ and instead include it in $G$. – Henry May 5 '20 at 0:31