Economics- Math Question?

Question

Assume that the government runs a balanced budget (G=T) and that the equilibrium GDP is $400 billion.

Assume the MPC = 0.6 and the MPS= 0.4

Now suppose the government wants to increase spending by $10 billion (G increases by 10). But, in order to balance its budget, it raises taxes by $10 billion to pay for the increased spending.

What effect will this have on the equilibrium GDP? By how much will it rise?

Answer 1

ΔY/ΔG=1/MPS

ΔY=10/0.4=+ $25 billion

ΔY/ΔT= -MPC/MPS

ΔY = -10 * 0.6/0.4 = -$15 billion

Net result = +25 - 15 = + $10 billion

Answ: Equilibrium GDP will increase by + $10 billion

Answer 2

dY=dG-dT

T=tY

10=dtY+dYt

10=dG

Operating with the last two expressions

0=dG-dtY-dYt

dY=(dG-dtY)/t=10/t  (1-40dt)

The effect on Y will depend on t and dt,

dY=0   dt=1/40

dY>0   dt>1/40    

dY<0   dt<1/40

Of course dY will not vary much as dG=dT and that means that the rise would be exactly zero if dt=1/40.