The consumption function:  C = Co + MPC (Yd)

C = total consumption

Co = autonomous consumption whose amount is independent of disposable income

MPC = marginal propensity to consume. This is a fraction between 0 and 1; and MPC is equal to change in consumption brought about by a change in disposable income.

(MPC = change in C / change in Yd )

Yd = disposable income.

A similar concept as MPC is MPS: marginal propensity to save. It is equal to change in savings (S) brought about by a change in disposable income.

(MPS = change in S / change in Yd)

Since all income must be either consumed or saved, then any change in income must also be consumed or saved. Therefore: MPC + MPS = 1

The average propensity to consume (APC) is the portion of income spent on consumption.

(APC = C / Yd)

The average propensity to save (APS) is the portion of income saved. 

(APS = S / Yd)

Again, APC + APS = 1

EQUILIBRIUM GDP

Equilibrium GDP is the level of output whose production will create total spending just sufficient to purchase that output. If the economy produces an amount of goods that differs to the amount that the four sectors of the economy buy (AE), AE and aggregate production ( AP) are not equal; then the economy is in disequilibrium.

When AE < AP, firms will involuntarily accumulate inventory. This will signal firms that they have overproduced. As a result, firms will cut back on production and/or prices. This will decrease the total value of output, moving the economy towards the equilibrium GDP.

When AE > AP, inventories will be depleted unexpectedly. This will signal firms that they have not produced enough. As a result, firms will increase productions and/or prices. This will increase the total value of output, moving the economy towards the equilibrium GDP.

MULTIPLIER

Keynes observed that changes in autonomous expenditures (those expenditures independent of income) could create even larger changes in national income. For example, a technological break through has increased the autonomous investment by $50million, this $50M will become the income of the resources market. Workers who may have higher income are willing to spend more in the market. Their spending becomes the income of producers who will again spend in the market, and create extra income. This process repeats itself, creating a multiplier effect. If the Multiplier (M) = 2.5, then the aggregate expenditure will increase by $50M X 2.5 = $ 125M.

M = 1 / MPS is commonly used to calculate the expenditure multiplier.

An individual may increase the aggregate expenditure if he took $100 from his shoebox and spent on goods and services. His initial expenditure could be multiplied if the retailers who received the $100 spent part of the $100 to buy more supplies from the wholesalers, and the wholesalers might buy more from the manufacturers. This process continues to create a multiplier effect in the economy. The aggregate expenditure would be increased by a multiple amount. Obviously, if an individual took $100 and put into his shoebox, he would decrease the aggregate expenditure by a multiple of that amount.