Aggregate expenditure or aggregate spending is the sum of expenditure by the households, by business enterprises, the government and the rest of the world on an economy’s output of goods and services. Thus, as shown earlier,
AE = C + I + G + (X - M)
where C is the private consumption expenditure, I is the investment expenditure, G is the government expenditure and X – M or net exports (also denoted by NX) is the expenditure by the rest of the world on an economy's aggregate output.
Since, we are discussing here only a two-sector model comprising of the households sector and the business enterprises and assuming that there is no government (hence, no government expenditure G) and no external transactions (closed economy and so on exports and no imports and hence no expenditure by the rest of the world, viz., no NX or (X-M), the aggregate expenditure thus comprises of only private consumption expenditure (C) and investment expenditure (I) so,
AE = C + I