A change in tax rate changes the IS equation, LM equation remaining the same. Let same, let us suppose that the government raises the tax rate from 20 percent to 25 percent. The rise in tax rate from t = 0.20 to t = 0.25 would change the IS equation by changing the consumption function with increase in tax rate, the consumption function changes form C = 100 + 100 + 0.60 Y, given in Eq. to
C= 100 + 0.75 [Y - (40 + 0.25Y + 40)]
= 100 + 0.5625Y
With change in the consumption function, the new IS schedule (say, IS2) can be obtained as follows.
Y = C + I + G + ?G
= 100 + 0.5625Y + 250 - 4i +200
= 1257.14 - 9.14i
Given the new IS function (IS2) in Eq. the new equilibrium interest rate can be worked out as follows.
Is2 = LM
1257.14 - 9.14i = 800 + 80i
89.14i = 457.14
I = 5.13 (percent)
Once interest rate is known equilibrium income with tax effect can be computed by substituting the interest rate (5.13%) into the IS2 or LM equation. By using IS2 function, we get
Y = 1257.14 - 9.14i = 1257.14 - 9.14 (5.13)
The negative effect of increase in tax rate on the equilibrium income equals income before tax - rise less income after tax-rise that is
Tax effect = $1311.10 bn - $1210.25 bn
This calculation shows that increasing tax rate form t = 0.20 to I = 0.25 decreases equilibrium income by $100.85 billion.