Question

‘The size of multiplier varies directly with the size of MPC and inversely with MPS’. Elucidate.

Answer 1

The multiplier formula can be derived by using the simple equilibrium condition for the two-sector model.

Recall that the equilibrium level of income in two-sector model is given by

Y = C + I

Now, let there be increase in investment by ΔI. When investment increases, it will lead to increase in income (ΔY). This induces increase in consumption (ΔC). This will lead to a change in the equilibrium level of income. Moving from one equilibrium to another, it is necessary that change in Y is equal to change in AE (i.e., ΔC + ΔI).

∴ ΔY = ΔC + ΔI

⇒ ΔY = c ΔY + ΔI

(because change in total consumption equals change in income multiplied by MPC).

⇒ ΔY − c ΔY = ΔI

⇒ ΔY (1 − c) = ΔI

Dividing both the sides by (1 - c), we get

ΔY = `1/(1-c).ΔI`

Dividing both the sides by ΔI, we get

`(ΔY)/(ΔI)=1/(1-c)`

or k = `1/(1-c)`

Thus, the term `1/(1-c)` gives the value of investment multiplier.

The multiplier's formula clearly shows that its magnitude is determined by the marginal propensity to consume (c). K has a direct relationship with the marginal propensity to consume. The multiplier size grows in proportion to the MPC value. A greater MPC implies that the induced consumption spending caused by any initial rise in income is larger at each cycle, leading in a proportionately larger ultimate increase in national income. In contrast, when MPC decreases, so does the size of the multiplier. The consumer spending triggered by the initial increase in income decreases with each round, and the eventual growth in national income is proportionally lower.

For example, when MPC is .8, the multiplier will be `5(1/(1-c)=1/(1-0.8)=1/0.2=5)`, and when MPC is .75, the value of the multiplier will be 4.

We also know that MPC + MPS = 1, i.e., MPS = 1 − MPC (s = 1 − c).

Therefore,

K = `(1/"MPS") = 1/s`

The multiplier (K) is the reciprocal of the Marginal Propensity to Save (MPS), showing an inverse relationship: higher MPS means a smaller multiplier, and lower MPS means a larger multiplier. The multiplier works both ways – an increase in investment leads to a multiple rise in income, while a decrease causes a multiple fall in income.