Question

Suppose that for a particular economy, investment is equal to 200, government purchases are 150, net taxes (that is lump-sum taxes minus transfer) is 100 and consumption is given by C = 100 + 0.75y

(i) What is the level of equilibrium income?

(ii) Calculate the value of the government expenditure multiplier and the tax multiplier.

(iii) If the government expenditure increases by 200, find the change in equilibrium income.

Answer 1

Given,

I = 200

G = 150

T = 100

C = 100+0.75Y

$\overline{C}$ = 100

c = 0.75

(i) Equilibrium level of income

$Y=\frac{1}{1-c}(\overline{C}-cT+I+G)$

$=\frac{1}{1-0.75}(100-0.75\times 100+200+150)$

$=\frac{1}{0.25}\left(375\right)$

$=\frac{375}{25}\times 100=Rs.1500$

(ii) Government expenditure multiplier

$\frac{\Delta Y}{\Delta G}=\frac{1}{1-c}=\frac{1}{1-0.75}=\frac{1}{0.25}$

= $\frac{1}{25}\times 100=4$

Tax multiplier $=\frac{\Delta Y}{\Delta T}=\frac{-c}{1-c}$

$\frac{-0.75}{1-0.75}=\frac{-0.75}{0.25}=\frac{-75}{25}=-3$

(iii) New equilibrium income

$\frac{1}{1-c}[\overline{C}-cT+I+G+\Delta G]$

$=\frac{1}{1-0.75}[100-0.75\times 100+200+150+200]$

$=\frac{1}{0.25}\times 575=\frac{575}{25}\times 100=2300$

Change in equilibrium income = 2300 - 1500 = Rs. 800.