THE MACRO ECONOMIC MULTIPLIER Deriving and illustrating

Injections into the circular flow cause changes in the equilibrium level of output The change is sometimes bigger than the injection eg R1 of G spending results in R2 of Y and E in the economy How and why this happens is explained using the macro economic multiplier

Assume the basic model That means only firms and consumers in this economy Therefore E= C + I Y= C + S The economy is in equilibrium: E = Y and L = J

The Keynesian 45 degree diagram

The 45 degree line shows all points where E = Y

The expenditure functions a0

The expenditure function is represented by the line E = C + I this shows total spending by households and firms When either C or I increases it causes the E function to shift up The amount of the shift is illustrated by a0a1 while the increase in output is Y0Y1

Numerical example C = a + bY C = 10 + 0.5Y I = 10 C is made up of 2 parts 10 is the amount they always spend with or without income (autonomous spending) 0.5 represents how much of each Rand of income they spend (b also determines the gradient)

If consumers spend 0.5 of each Rand, it means they save the other 0.5 This number refers to their marginal propensity to consume (mpc) A high mpc means consumers are likely to spend more than save So if C = 10 +0.5 and I = 10 then E = 10 + 0.5 + 10 That means E = 20 + 0.5Y

The gradient of the expenditure function is determined by bY (0.5) The intersection with the 45degree line will show the equilibrium level of real output The value of this amount is calculated as follows: 10 + 0.5Y + 10 = Y Therefore: 20 = 0.5Y thus Y = 40

Assume businesses decide to increase I by 10 This will push E up to 30 + 0.5Y The E curve will shift up and will result in an increase in Y from 40 to 60 Thus an increase in E of just 10 results in the double the increase in Y (20)

Size of the gradient The value of bY (mpc) determines the slope of the gradient If the mpc is 0.7, the E function will have a steeper slope, will cut the 45 degree line higher up and result in larger increases in Y. From previous example: C10 + 0.7Y + I 20 becomes 30 = 0.3Y THUS the equilibrium level of Y here is 90