Question

Assume that MPC = $\frac{4}{5}$when answering the following questions.

a. If government expenditures rise by \( 1 billion, by how much will the aggregate expenditure curve shift upward?

b. If taxes rise by \) 1 billion, by how much will the aggregate expenditure curve shift downward?

c. If both taxes and government expenditures rise by $ 1 billion, by how much will the aggregate expenditure curve shift? What will happen to the equilibrium level of real GDP?

d. How does your response to the second question in part (c) change if MPC = $\frac{3}{4}$? If MPC =$\frac{1}{2}$?

Short answer

a. by$\$5$trillion

b. by$\$4$billion

c. by $\$5$trillion

d. by $1$

Step-by-step solution

introduction

Tax multiplier addresses sway on Real Output because of progress in the Tax rate.

Government Multiplier addresses change in Real GDP because of progress in Government Expenditure

explanation part (a)

Given,

government expenditures rise by$∆G$=$\$1$billion

MPC = $0.8$

Now, government multiplier =

$\begin{array}{r}\frac{\mathrm{\Delta }Y}{\mathrm{\Delta }G}=\frac{1}{1-MPC}\\ \frac{\mathrm{\Delta }Y}{1}=\frac{1}{1-0.8}\end{array}$

$\mathrm{△}Y=5$trillion

aggregate expenditure curve shift upward by$\$1$billion

explanation part (b)

Given,

MPC = $0.8$

MPS = $0.2$

Tax multiplier =

$\frac{\mathrm{△}Y}{\mathrm{△}T}=\frac{-MPC}{MPS}$

role="math" localid="1651986364126" $∆Y=\frac{-0.8}{0.2}=-4$billion

explanation part (c)

Given,

MPC =$0.8$

MPS = $0.2$

Overall impact = increased output due to government expenditure - reduced output due to government expenditure

$$\begin{gathered} \Rightarrow 5-4 \\ =1 \end{gathered}$$

There is an increase in output by$\$1$trillion

explanation part (d)

Given,

MPC = $\frac{3}{4}$

MPS = $1-\frac{3}{4}=\frac{1}{4}$

Now calculating,

$\frac{-MPC}{1-MPC}+\frac{1}{1-MPC}=1$

$\Rightarrow \mathrm{\Delta }G+\mathrm{\Delta }T=1$

Adding tax and government multiplier,

$\frac{-MPC}{1-MPC}+\frac{1}{1-MPC}$

$\frac{-MPC+1}{1-MPC}=\frac{1-MPC}{1-MPC}=1$

$\Rightarrow \mathrm{\Delta }G+\mathrm{\Delta }T=1$

increase in the output remains the same i.e$1$