Chapter 4 — Determination of Income and Employment

Ex ante values are planned or intended values — what consumers or producers intend to consume, save, or invest. Ex post values are actual or realised values recorded after the fact. For example, a producer who plans to add Rs 100 to inventory (ex ante investment) may end up adding only Rs 70 if unexpected demand draws down stocks (ex post investment).

The consumption function is C = C̄ + cY, where C̄ is autonomous consumption (the level of consumption when income is zero) and cY is induced consumption. The term c is the marginal propensity to consume (MPC), which shows how much consumption rises for each unit rise in income.

MPC = ΔC/ΔY and lies between 0 and 1 inclusive. MPC = 0 means a consumer does not increase consumption at all when income rises; MPC = 1 means the entire increment in income is spent on consumption; values between 0 and 1 mean only part of the extra income goes to consumption.

Since savings S = Y − C, MPS = ΔS/ΔY = 1 − c (i.e., 1 − MPC). Therefore MPC + MPS = 1. A higher MPC automatically implies a lower MPS.

Autonomous consumption (C̄) is the level of consumption expenditure that takes place even when household income is zero. It is independent of income and is shown as the intercept of the consumption function on the vertical axis.

Equilibrium requires ex ante aggregate demand to equal ex ante aggregate supply: C̄ + Ī + cY = Y. Solving for Y gives the equilibrium income formula Y* = (C̄ + Ī)/(1 − c). Graphically, this is the intersection of the AD line with the 45° aggregate supply line.

The investment multiplier = ΔY/ΔA = 1/(1 − c) = 1/MPS, where ΔA is the initial change in autonomous expenditure. When autonomous spending rises by ΔA, producers raise output by ΔA, which raises income and hence consumption in successive rounds (each round adds c times the previous increment), creating a convergent geometric series that sums to ΔA/(1 − c).

The Paradox of Thrift states that if all households simultaneously increase their propensity to save (MPS rises, MPC falls), the equilibrium level of income and output falls, but the total value of savings in the economy remains unchanged (or declines). Individual thriftiness, collectively applied, does not raise aggregate savings.

Deficient demand occurs when the equilibrium level of output is less than the full employment level of output — demand is not sufficient to employ all factors of production. The chapter states this leads to a decline in prices in the long run.

Excess demand occurs when the equilibrium level of output exceeds the full employment level of output — aggregate demand is greater than what can be produced at full employment. The chapter states this leads to a rise in prices (inflation) in the long run.

With unused resources and fixed prices, any level of output can be supplied without a rise in marginal cost. Whatever quantity is produced (GDP, Y) becomes the income of the economy. The 45° line captures this because every point on it has equal horizontal and vertical coordinates, meaning output supplied always equals income generated.

When ex ante aggregate demand differs from planned output, firms involuntarily accumulate or draw down stocks. If demand falls short of output, unsold goods pile up as unplanned (unintended) positive inventory investment. If demand exceeds output, firms run down existing stocks, which is unintended negative inventory investment. These unintended changes in inventories signal to producers to adjust output in the next period.

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