Saving-Investment Equality and Income Adjustment

Planned saving and planned investment are brought into equality when national income adjusts until households wish to save exactly what firms wish to invest. In the simple Keynesian income-determination model, this adjustment occurs through changes in output and income following unintended inventory changes, rather than through an assumed change in the interest rate. This is an equilibrium between ex ante, or intended, saving and investment.

Planned expenditure and equilibrium income

Consider a two-sector closed economy with households and firms, but no government or foreign trade. The short-run model assumes fixed prices and scope for output to respond to demand.

• Households divide income between consumption and saving, so Y = C + S; planned aggregate expenditure is C + I.
• Goods-market equilibrium requires Y = C + I: planned expenditure equals the value of output produced.
• Combining these relationships gives S = I. Thus, equality of planned saving and planned investment is another way of expressing goods-market equilibrium.
• In the simplest model, consumption rises with income, while planned investment is taken as autonomous, or independent of current income.

How income restores equality

The adjustment begins when planned expenditure differs from output, creating unintended inventory changes that lead firms to revise production.

• If planned saving exceeds planned investment, planned expenditure is below output. Unsold goods accumulate, prompting firms to reduce production and employment.
• The resulting fall in income reduces consumption and saving. With planned investment unchanged, saving falls until it equals investment at a lower equilibrium income.
• If planned investment exceeds planned saving, planned expenditure exceeds output. Inventories decline unexpectedly, encouraging firms to expand production and employment.
• Rising income increases saving until it matches investment at a higher equilibrium income, provided output can expand.

Multiplier and the distinction from accounting equality

With consumption C = C₀ + cY, where C₀ is autonomous consumption and c is the marginal propensity to consume, equilibrium income is Y = (C₀ + I)/(1 - c).

• An increase in autonomous investment raises equilibrium income through successive rounds of consumption spending: ΔY = ΔI/(1 - c) = ΔI/s, where s is the marginal propensity to save.
• In this two-sector framework, ex post saving equals ex post investment as an accounting identity because actual investment includes unintended inventory changes.
• Accounting equality therefore does not establish equilibrium: equilibrium requires planned saving and planned investment to be equal, with no unintended inventory change.