Final answer:
For a function to satisfy all properties of an expenditure function, it needs to meet specific conditions related to investment, government spending, and export expenditures, as well as the slope of the aggregate expenditure function.
Step-by-step explanation:
In order for a function to satisfy all properties of an expenditure function, it needs to meet certain conditions. These conditions are determined by the levels of investment, government spending, and export expenditures, which do not vary with national income. The slope of the aggregate expenditure function is determined by the marginal propensity to save, the tax rate, and the marginal propensity to import. A higher marginal propensity to save, a higher tax rate, and a higher marginal propensity to import will make the slope of the aggregate expenditure function flatter.