Question

Suppose the consumption function is C=100+0.95YD. If the tax rate changes from t=0 to t=30%, then the increase in govt spending that leaves equilibrium income unaffected is what ?

YD= disposable income

The answer is 570 , but can you help explain how they got to this?
Tks

Answer 1

If t = 0, then T = 0, so C = 100 + 0.95(Y - T) = 100 + 0.95Y.

If t = 0.3, then T = t*Y = 0.3Y, so C = 100 + 0.95(Y - 0.3Y) = 100 + 0.665Y, so the consumption will decrease by 0.285Y and government spending should increase by this amount to leave equilibrium income unaffected.