Chapter 11, Problem 14E

To determine

Assume that the equilibrium real GDP is $\$800$ billion, a potential real GDP is $\$950$ billion, the MPC is $.80$ and the MPI is $.40$.

The change to eliminate the recessionary gap when government spending and taxes both change by the same amount.

Explanation of Solution

To calculate recessionary gap when government spending and taxes both change by the same amount follow the steps

Step-1

Calculate the gross domestic product gap

Given Information:-

Real Gross Domestic Product $\$800$ billion.

Potential Gross Domestic Product $\$950$ billion.

Substitute the value in the mentioned formula:-

  $\begin{array}{c}\text{Gross}\text{Domestic}\text{Product}\text{Gap}=\text{Potential}\text{Gross}\text{Domestic}\text{Product}-\text{RealGross}\text{Domestic}\text{Product}\\ =950-800\\ =150\end{array}$ The Gross Domestic Gap is $\$150$ billion

Step-2

Calculate the tax multiplier for the given data

  $\text{Tax}\text{Multiplier}=-\left(\text{MPC}-\text{MPI}\right)\times \frac{1}{\text{MPS}+\text{MPI}}$

Where MPS is marginal propensity to save that means the amount the consumers save from their income rather spending on goods and services.

MPI stands for marginal prosperity to invest.

MPC stands for marginal propensity to consume.

Here, given information:-

MPC is $.80$ and the MPI is $.40$

MPS can be calculated as

  $\begin{array}{c}MPS=1-MPC\\ MPS=1-0.80\\ =0.20\\ \end{array}$

Now substitute the value in the given formula in tax multiplier formula

  $\begin{array}{c}\text{Tax}\text{Multiplier}=\left(\text{MPC}-\text{MPI}\right)\times \frac{1}{\text{MPS}+\text{MPI}}\\ =\left(0.8-0.4\right)\times \frac{1}{0.20+0.40}\\ =\frac{0.4}{0.6}\\ =\frac{2}{3}\end{array}$

The value of tax multiplier is $\frac{2}{3}$

Step 3

Calculate the government spending multiplier

Now, formula for calculating multiplier is:-

  $\text{Multiplier}=\frac{\text{1}}{\text{MPS+MPI}}$

Where MPS is marginal propensity to save that means the amount the consumers save from their income rather spending on goods and services.

MPI is stands for marginal propensity to invest.

Here, MPI is $.40$ given

MPS can be calculated as

  $\begin{array}{l}MPS=1-MPC\\ MPS=1-0.80\\ =0.20\\ \end{array}$

Now substitute the value in the formula:-

  $\begin{array}{c}\text{Multiplier}=\frac{\text{1}}{\text{MPS+MPI}}\\ =\frac{1}{\begin{array}{l}0.20+0.40\\ =\frac{1}{0.60}\end{array}}\end{array}$

The value of multiplier is $\frac{1}{0.60}$

Step 4

Now to close the gap the combined effect of both government spending and tax cut will be

  $\frac{1}{0.60}\text{increase}\text{in}\text{government}\text{spending}+\frac{2}{3}\text{tax}\text{cut}=\text{Gross}\text{Domestic}\text{Gap}$

According to the question increase in government spending is of same amount as of Tax cut

Let's consider government spending as x, therefore tax cut will also be x

Substitute the value in the above equation:-

  $\begin{array}{c}\frac{1}{0.60}\text{increase}\text{in}\text{government}\text{spending}+\frac{2}{3}\text{tax}\text{cut}=\text{Gross}\text{Domestic}\text{Gap}\\ \frac{1}{0.60}x+\frac{2}{3}x=150\\ \frac{5}{3}x+\frac{2}{3}x=150\\ \frac{7}{3}x=150\end{array}$

Calculate for x

  $\begin{array}{l}x=150\times \frac{3}{7}\\ x=64.28\end{array}$

Now to calculate the recessionary gap, add both the values of government spending and tax cut

  $\begin{array}{c}\text{Recessionary}\text{gap}=64.28+64.28\\ =128.56\end{array}$

Therefore, $\$128.56$ billion gap should be closed to close the Gross Domestic Product Gap.

Economics Concept Introduction

Concept Introduction:

Gross Domestic Product is the total amount of finished products and services produced with in the country. It majorly calculates the economic growth of a country. The dissimilarity between potential Gross Domestic Product and real Gross Domestic Product is known as Gross Domestic Product gap.

When real GDP is lower than the potential GDP, there occurs a recessionary gap. When an economy is forthcoming recession, recessionary gap occurs.