In: Economics
The Abbott government is concerned about the growing budget
deficit, so it decides to cut government expenditures by $10
billion. They also decide the economy needs a boost so they decide
to cut income tax by $30 billion. Would this simply mean a net
increase in aggregate demand of $20 billion? Why or why
not?
Let the consumption fumction is,
C = a + c(Y - T)... where, T = income tax, Y = income, a = autonomous consumption
Investment, I = I0
Govenment Expenditure, G = G0
Tax, T = T0
Total demand, Y = C + I + G = a + c(Y - T0) + I0 + G0
or, Y = a + I0 + G0 + cY - cT0
or, (1 - c)Y = a + I0 + G0 - cT0
or, Y = (a + I0 + G0 - cT0) / (1 - c)
Now, Government expenditure is reduced by $10 billion
New Government expenditure, G = G1 = G0 -10
Tax is decreased by $30 billion
New tax, T1 = T0 - 30
New demand, Y1 = a + c(Y - T1) + I0 + G1 = a + c[Y - (T0 -30)] + I0 + G0 -10
or, Y1 = a + cY - cT0 +30c + I0 + G0 -10
or, (1 - c)Y1 = a - cT0 +30c + I0 + G0 -10
or, Y1 = (a + I0 + G0 - cT0 +30c -10) / (1-c)
Y1 - Y = [(a + I0 + G0 - cT0 +30c -10) / (1-c)] - [(a + I0 + G0 - cT0) / (1 - c)] = (30c -10) / (1-c)
now, mpc = c and 0< c <1
So, the change in aggregate demand will be the sum of the tax multiplier effect and the government expenditure multiplier effect and the change will depend on the value of c. The net increase will be equal to $20 billion if,
(30c -10) / (1-c) = 20
or, 30c -10 = 20 - 20c
or, 50c = 30
or, c = 30/50
or, c = 0.6
So, the change in government expenditure and income tax will not lead to a change of $20 billion as the net increase is the sum of both tax multiplier effect and government expenditutre multiplier effect. The change in tax will have effect on consumption which in turn will have effect on aggregate demand. So, this will depend on the mpc.