Question

In this chapter we have assumed that the fiscal policy variables G and T are independent of the level of income. In the real​ world, however, this is not the case. Taxes typically depend on the level of income and so tend to be higher when income is higher. In this​ problem, we examine how this automatic response of taxes can help reduce the impact of changes in autonomous spending on output.

Consider the following behavioral​ equations:

C​ = c0​ + c1YD

T​ = t0​ + t1Y

YD​= Y−T

G and I are both constant. Assume that t1 is between 0 and 1. c0 is autonomous​ consumption, c1 is the propensity to​ consume, and t0 is the part of taxes not dependent on income.  

Because of the effect of taxes on the​ economy, it responds (less, the same, more) to changes in autonomous spending than when taxes are independent of income.

Answer 1

Because of the effect of taxes on the economy,it responds the same to changes in autonomous spending than when taxes are independent of income.

Explanation-------

Autonomous spending ( autonomous consumption Co) is that part of consumption expenditure which is independent of change in income.

This amount is spent even if the income is zero.It is the minimum spending which people make to survive.

When govt imposes taxes on income Y, the disposable income decreases, likewise ,the consumption expenditure also reduces but a part of consumption expenditure is dependent upon disposable income as well as on marginal propensity to consume ( mpc), while Co remains the same.

Let me explain algebraically------

C=C0+mpc(y)

Here y is disposable income.,which means income left after tax payment(t)

Because,y=Y-t ,where Y is income before tax

Similarly, t= t0+ t1Y

Where t0 is autonomous tax ( which is imposed on consumers irrespective of income level)& t1 is tax depending upon income level.

If we substitute this in consumption function-----

C= Co+mpc{y--(to+t1Y)}

Hence we find that though total consumption and taxes depend upon income, autonomous consumption is independent of income level and taxes.