Income Tax (2): Static Analysis

02/04/2014 Revised

Recall the Keynesian cross, where there's one consumer and no producer.

The equilibrium of the aggregate economy: Y (aggregate supply) = E (aggregate demand) .....(1)

where Y= (constant).

The aggregate demand is: E = C (consumption) + I (investment) .....(2)

where I = (constant) .

The aggregate consumption is assumed to be the Keynesian version: C = a(Y-T) + c .....(3)

where a and c are both constant.
a is greater than 0 and less than 1. c is greater than 0. T is a tax.

The income tax t1: T=t1Y, C=a(1-t1)Y + c, E=Y .....(4)

The consumption tax t2 : T=0, E=(1+t2)Y.....(5)

The size of the effect of each tax on the demand:

income tax t1: 1/(1-a(1-t1)) .....(6)

consumption tax t2: 1/(1-a+t2)  .....(7)

If t1=t2, then 1/(1-a(1-t1)) is greater than 1/(1-a+t2). Then, the effect of income tax is greater than that of consumption tax.