Question

7 So 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. In this case t1 (marginal propensity to tax) is less than one, because the marginal tax can't be higher than 100%.

b. The equilibrium output is:.

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

c. The multiplier is:

m = 1/(1 - c1).

The economy will respond more to changes in autonomous spending when t1 is zero.