So far we have been assuming that the fiscal policy variable T is independent of

the level of income. In the real world, however, this is not the case. Taxes typically

depend on the level of income, so tax revenue tends 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 model of the economy:

C = c0 + c1YD

T = t0 + t1Y

YD = Y T

where G and I are both constant.

(a) Is t1 greater or less than one? Explain.

(b) Solve for equilibrium output.

(c) What is the multiplier? Does the economy respond more to changes

in autonomous spending when t1 is zero or when t1 is positive? Explain.

(d) Why is fiscal policy in this case called an "automatic stabilizer"?