Question

Your local Congressman calls you up excitedly in the middle of the night. Somebody has told him about a model that predicted that increases in government purchases would have a magnified “multiplier” impact on the economy. If the model is correct, then he would be able to spend money on his favorite projects for years to come. However, the Congressman is concerned because he has to operate under a Balanced Budget Amendment, which requires him to keep taxes equal to government purchases, i.e. he has to increase taxes whenever he increases government purchases in order to keep the budget balanced. A model of the economic situation that the Congressman is facing is given by

Y=C+I+G+NX

C=C(bar)+b(Y-T)

G=G(bar)

I=I(bar)

T=G

NX=NX(bar)

a) Solve this simple model and obtain an expression for the equilibrium value of Y in this economy.

b) Derive an equation for the spending multiplier associated with government purchases in this economy. How does it compare to the spending multiplier of 1/(1−b) we derived for a simple economy with an exogenous tax system? Provide some intuition for your answer.

c) Derive an equation for the spending multiplier associated with exogenous consumption (or investment or net exports) in this economy. How does it compare to the multiplier you derived in b)? Provide some intuition for your answer.

d) Based on your answers to b) and/or c) should the Congressman be discouraged? Explain (briefly).

Answer 1

a.

b. The spending multiplier is given by

Differentiating completely the equation for Y:

This is also known as the balanced budget multiplier as the government uses tax revenue to finance the increase in government spending. Comparing it to the standard multiplier, 1/MPS, where the tax rate is exogenous, the government uses other sources to finance the increase in spending. The standard multiplier is stronger than the balanced budget multiplier as MPS is always less than or equal to 1.

c. We need to find

Using the equation for Y in part a.

This is equal to the standard spending multiplier for the government.

d. No, because while maintaining a balanced budget, the government does not have to worry about fiscal deficit. Whereas, when the tax rate is exogenous, the government might have to take measure to reduce fiscal deficit in the long run which arises from increasing government expenditure.