How is the savings function represented mathematically?

The savings function mathematically represents the relationship between total savings (S), disposable income (Y), autonomous savings (Co), and the marginal propensity to save (s). The correct formulation is S = -Co + sY, where:

• Co represents autonomous savings, which is the level of savings when income is zero. It underscores that there are still savings occurring, possibly financed by borrowing or using previous savings.

• s is the marginal propensity to save, indicating the fraction of additional income that is saved. As income (Y) increases, savings increase in proportion to this marginal propensity.

This formulation captures the idea that when income is zero, savings may not necessarily be positive due to the negative value of Co. The term sY indicates that as income rises, savings also rise, reflecting the behavior of individuals or households to save more when they have higher disposable incomes. This structure aligns with the fundamental principles of consumption and savings in economics, showing how savings change in response to changes in income.

Other representations do not accurately reflect the relationship outlined in the savings function. For instance, options involving positive or negative coefficients for terms in a way that contradicts the established relationship between income and savings do not correctly describe the dynamics of the savings function.