Question

Explain the relationship between marginal propensity to save and multiplier.

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 an increase in investment by ΔI. When investment increases, it will lead to an increase in income (ΔY). This induces an 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

`(DeltaY)/(DeltaI) = 1/ (1-c)`

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

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