Question

State the formula for the investment 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 ΔI expand its investment. Increased investment will result in higher revenue (ΔY). This causes an increase in consumption (ΔC). This will cause a shift in the equilibrium level of income. To transition from one equilibrium to another, the change in Y must match the 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 the investment multiplier.