Derivation of Multiplier
Another way to derive multiplier is based on the functional relation between consumption and income.
We start with the basis equilibrium condition, i.e.,
Y = C + I (1)
We known that consumption (C) is the function of income (Y). This functional relationship can be expresses as
C = a + bY (2)
Substituting equation (2) in equation (1), we get
Y = a + bY + I
or, Y - bY = a + I
or, (1 - b) Y = a + I
If we denote change in investment by ?I and change in income by ?Y, the equilibrium condition becomes
Dropping brackets, the first and last terms cancel out,
For a given change in investment, the change in income is equal to 1/(1 - b) times the change in investment. Thus 1/(1 - b) is the value of multiplier. If we divide both sides of the Equation (3) by ?I, we get
The ratio ?Y/?I is the ratio of change in income to the change in investment which is the definition of the multiplier.
In equation (4), b =MPC
We know MPC+MPS = 1
K = 1 - MPC = 1 - b
Multiplier = K = 1/MPS
Services: - Derivation of Multiplier Homework | Derivation of Multiplier Homework Help | Derivation of Multiplier Homework Help Services | Live Derivation of Multiplier Homework Help | Derivation of Multiplier Homework Tutors | Online Derivation of Multiplier Homework Help | Derivation of Multiplier Tutors | Online Derivation of Multiplier Tutors | Derivation of Multiplier Homework Services | Derivation of Multiplier