Question

For a given economy, investment is 100, government spending is 150 and taxes are 90. the consumption function is C=120+.75 YD

Calculate the government expenditure multiplier and the tax multiplier.

A. 3, 4

B. -3, 4

C. 4, -3

D. 4, 3

Answer 1

Given: C = 120+ 0.75 YD, G = 150 and T = 90.

In the consumption funtion, C, 0.75 is marginal propensity to comsume (mpc), m.

YD = Y-T: Disposable income = Income - Taxes.

Therefore, C can also be written as C = 120+0.75 (Y -T)

Equilibrium is:

Y = C+ I + G + X - M. Here, I is investment, X are exports, M are imports.

On substitution:

Y = 120+0.75 (Y-T) + I + G + X -M

Y = 120 + 0.75Y - 0.75T + I + G + X - M

Y - 0.75 Y = 120 - 0.75T + I + G + X - M

Y (1-0.75) = 120 - 0.75 T + I + G + X - M

Y = (120 - 0.75T + I + G + X - M ) / (1-0.75)

Government expenditure multiplier is the change in Y per unit (dollar) change in G. It is given by:

1/ (1-0.75) = 1/0.25 = 4. Note this is same as 1/ (1-mpc) or 1/(1-m).

Tax multiplier is the change in Y per unit (dollar) change in T. It is given by:

- 0.75/(1-0.25) = -0.75/0.25 = -3. Note this is same as -mpc/(1-mpc) or -m/(1-m).

Therefore, the correct answer is C. 4, -3.