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. Note c0 is autonomous consumption, c1 is the propensity to consume, and t0 is the part of taxes not dependent on income.

Required:
a. Solve for equilibrium output.
b. What is the multiplier? Does the economy respond more to changes in autonomous spending when t1 is 0 or when t1 is positive? Explain.
c. Why is fiscal policy in this case called an automatic stabilizer?

C) The fiscal policy is called an automatic stabilizer because the taxes are dependent on the level of income and also the output of the multiplier is more stable because it doesn't respond to rapid changes in fiscal policies.

Explanation:

Given data:

C = Co + C1YD

T = t0 + t1Y

YD = Y - T

G and I are both constant

C1 lies between 0 and 1 while T1 lies between 0 and 1

A ) solving for equilibrum output

attached below

B) The multiplier

Multiplier = [tex]\frac{1}{1 -C1 +c1t1}[/tex]

The economy responds to changes in autonomous spending when t1 is 0 but responds less when t1 is positive, this is because the more positive t1 is the lower the multiplier value

c) The fiscal policy is called an automatic stabilizer because the taxes are dependent on the level of income and also the output of the multiplier is more stable because it doesn't respond to rapid changes in fiscal policies.