Gillespie: Foundations of Economics 
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Figures from the textbookGillespie: Foundations of Economics
The Keynesian Savings Function
Income that consumers earn but do not spend on consumption will be saved in some form.
Y = C + S
If the consumption function is C = a + bYd
Then the savings function is given by:
S = -a + (1-b) Yd
With zero income consumers still spend the amount "a"; this means they dissave "a".
Out of each £1 consumers spend "b"; this means they save (1-b). e.g. if the marginal propensity to consume is 0.8 then the marginal propensity to save is 0.2
With saving we sometimes differentiate between contractual and discretionary savings. Contractual savings occur when an individual pays a given amount out at regular agreed intervals e.g. payments into a pension or savings scheme; discretionary savings occur when individuals save on a more ad hoc basis e.g. in their banks or building societies.
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