Question

In: Economics

The Abbott government is concerned about the growing budget deficit, so it decides to cut government...

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?

Expert Solution

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.

Rahul Sunny answered 8 months ago

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