Consider a consumption function in a simple macro model with government and taxes.Given a marginal propensity to consume out of disposable income of 0.8 and a net tax rate of 20% of national income,the marginal propensity to consume out of national income is
A)0.36.
B)0.64.
C)0.80.
D)0.90.
E)1.00.

Question

Quizplus · Accepted Answer

The marginal propensity to consume out of disposable income (MPCd) is given as 0.8. This means that for every increase in disposable income, consumption increases by 0.8.

Let the gross national income be Y and the net tax rate be t. Then disposable income (Yd) is given as:

Yd = Y(1-t)

The marginal propensity to consume out of national income (MPC) is given as the change in consumption over the change in national income.

MPC = ΔC/ΔY

We can express the change in consumption (ΔC) as a function of the change in disposable income (ΔYd) and the MPCd as follows:

ΔC = MPCd * ΔYd

Substituting for Yd, we get:

ΔC = MPCd * Δ(Y(1-t))

ΔC = MPCd * Y * Δ(1-t)

ΔC = -MPCd * Y * t

The negative sign indicates that taxes reduce disposable income and hence consumption.

Substituting the given values, we get:

MPC = -0.8 * Y * 0.2

MPC = -0.16Y

This means that for every increase in national income, consumption decreases by 0.16. The MPC out of national income is therefore 1 - 0.16 = 0.84.

Alternatively, we could have used the formula for the MPC out of national income directly:

MPC = MPCd / (1-t)

Substituting the given values, we get:

MPC = 0.8 / (1-0.2)

MPC = 0.8 / 0.8

MPC = 1 - 0.2

MPC = 0.8

This confirms our earlier result.

Consider a Consumption Function in a Simple Macro Model with Government