Answer to Question #112284 in Macroeconomics for Kgothatso

Question

3.7So far, we have been assuming that the fiscal policy variable T is independent of the level of income (exogenous). 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
G and I are both constant (exogenous).
a. Is t1 (marginal propensity to tax) 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? Demonstrate.

Answer 1

a. marginal propensity to tax less than one:

1 multiplier= MPS + MPM + MPT

b. Y=C+I+G

Y=C0+c1Yd+I+G

Y=C0+c1(Y-T)+I+G

Y=C0+c1((Y-(t0 +t1Y))+I+G

Y=C0+c1(Y-t0-t1Y)+I+G

Y=C0+c1Y-c1t0-c1t1Y+I+G

Y-c1Y+c1t1Y=C0-c1t0+I+G

c.multiplier= MPS + MPM + MPT

t1=0

Y-c1Y=C0-c1t0+I+G

Y(1-c1)=C0-c1t0+I+G

Y(1-c1)+c1t0-I-G=C0

t1=0.3

Y-c1Y-0.3c1Y=C0-c1t0+I+G

Y(1-c1-0.3c1)=C0-c1t0+I+G

Y(1-c1-0.3c1)+c1t0-I-G=C0

Y(1-1.3c1)+c1t0-I-G=C0

increased propensity to tax reduces disposable income