The saving function is an economic concept that describes the relationship between household savings and disposable income. It shows how much of the income households save rather than consume. Essentially, saving is the part of income that is not spent on consumption. Mathematically, the saving function is often expressed as:
S=−a+(1−b)YS=-a+(1-b)YS=−a+(1−b)Y
where:
- SSS is saving,
- YYY is disposable income,
- aaa is autonomous consumption (consumption when income is zero),
- bbb is the marginal propensity to consume (MPC),
- 1−b1-b1−b is the marginal propensity to save (MPS).
This means saving equals income minus consumption, and since consumption depends on income, saving is also a function of income. The intercept −a-a−a represents autonomous saving (which can be negative if consumption occurs even at zero income), and the slope (1−b)(1-b)(1−b) represents the marginal propensity to save, indicating how much saving changes with a change in income
. Key points about the saving function:
- There is a direct relationship between income and saving: as income increases, saving generally increases
- The sum of the marginal propensity to consume and the marginal propensity to save is always 1 (MPC + MPS = 1)
- The saving function can be linear or curvilinear, but the linear form is most common and useful for Keynesian economic analysis
- The saving function helps economists understand saving behavior and is fundamental in Keynesian models that analyze income, consumption, and saving dynamics
In summary, the saving function mathematically links household savings to their disposable income, showing how saving changes as income changes, with key parameters being autonomous saving and the marginal propensity to save.
