Question

Suppose the government decides to reduce transfer payments but increase government

purchase of goods and services by an equal amount i.e. ∆G=-∆TR (5 points)

a. Would equilibrium income rise or fall as a result of this change? Show using the

following data c=0.8, t=0.25, Y 0 =600, ∆G=10=-∆TR. (2)

b. Find the change in equilibrium change in income ∆Y 0 (2)

c. What is the change in budget surplus? Why has it changed? (1)

Answer 1

a

$T_m=\frac{1}{1-c(1-t)}\\ T_m=\frac{1}{1-0.8(1-0.25)}\\ T_m=2.5$

We also know,

$T_m=\frac{\Delta Y}{\Delta TR}\\ 2.5=\frac{\Delta Y}{10}\\ \Delta Y= 2.5*10=25$

Thus, change in equilibrium income due to change in taxes = 25

The expenditure multiplier is given as,

$M=\frac{1}{1-c}\\ M=\frac{1}{1-0.8}\\ M=5$

We also know,

$T_m=\frac{\Delta Y}{\Delta TR}\\ 5=\frac{\Delta Y}{10}\\ \Delta Y= 5*10=50$

Thus, change in equilibrium income due to change in Expenditure = 50

Thus, equilibrium income rises as the expenditure multiplier is stronger than the tax multiplier.

b.

So, Change in Total Income = 50 - 25 = 25

c.

$\Delta BS= \frac{(1-c)(1-t)}{1-c(1-t)} \Delta G\\ \Delta BS= \frac{(1-0.8)(1-0.75)}{1-0.8(1-0.75)} *10\\ \Delta BS=-1.25\\$

Thus, Budget surplus changes because the expenditure multiplier is stronger than the tax multiplier