A convenient way to understand how national income equilibrium is determined is to use a version of the 'cross' diagram which looks at the factors which can increase and reduce the flow of income in an economy over time.
The cross diagram used here maps out injections and withdrawals (or leakages) against national income, and excludes consumption from the analysis.
Injections into the flow of income in an economy include investment by firms, government spending on public goods, merit goods and income transfers, and demand for an economy’s exports.
It is assumed that injections are not determined by current GDP and remain constant as GDP increases. In the current time period the decision to invest by firms is assumed to have taken place in the previous time period.
Similarly, government spending decisions are taken at the time of the national budget, which will precede the current time period.
Finally, export spending is assumed to depend on overseas income, hence it is not related to the current income of the economy under consideration.
Of course, these assumptions may not hold, but are employed to simplify the 'cross' model.
Withdrawals include household savings, taxation, and import spending, and are assumed to be dependent on current GDP.
Saving is clearly influenced by current income, and we can assume S=fY. Similarly, tax revenue and the level of imports are also determined (partially) by the level of current income.
Changes in current income will, therefore, induce changes in savings, tax revenues and import spending. Each withdrawal has its own 'marginal propensity' (likelihood) which indicates precisely how the specific withdrawal changes as income changes.
Hence withdrawals increase as GDP increases. In this example, equilibrium exists when injections equal leakages, at 'a', and Y (at $600 bn).
There is some debate about how 'stable' marginal propensities are over time. The more stable they are the more accurate are predictions made about changes in GDP on withdrawals.
Evidence tends to suggest that marginal propensity values are not stable as a result of 'shocks' to GDP. For example, research by Karger et al1 found that the impact of emergency COVID-19 relief in the US in 2020 had a significant effect on spending for the first two weeks of receipt, only to fall back to more 'normal' levels of spending. Other research (Gross et al)2 supports the view that the value of the marginal propensity to consume varies over the business cycle.
1. Karger, Ezra and Rajan, Aastha, Heterogeneity in the Marginal Propensity to Consume: Evidence from Covid-19 Stimulus Payments (May, 2020). FRB of Chicago Working Paper No. WP 2020-15, Available at SSRN: viewed 21st February, 2021.https://srn.com/abstract=3625104 or http://dx.doi.org/10.21033/wp-2020-15
2.Gross, T, Notowidigdo, M, Wang, J, The Marginal Propensity to Consume Over The Business Cycle; Working Paper 22518, viewed 21 February 2021,<http://www.nber.org/papers/w22518>