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