Chapter 12, Problem 3NP

a.

To determine

To calculate: The equilibrium values of price level, expected price level, expected inflation, output and unemployment rate.

Answer to Problem 3NP

The equilibrium value of price level is $\text{4}$ , expected price level is 4, expected inflation is zero percent, output is $\text{6,000}$ and an unemployment rate is $\text{5\%}$ .

Explanation of Solution

Given the following data:

AD	$\text{Y=4000+2}\left(\frac{\text{M}}{\text{P}}\right)$
SRAS
Okun’s law

And, $\text{M=4000}$ , $\left(\text{<mover accent="true"><mo> Y </mo><mo>¯</mo></mover>}\right)\text{ =6000}$ , $\text{(ū) = 0}\text{.05}$

The given aggregate demand and short run aggregate supply equations are as follows:

$\begin{array}{l}\text{AD:Y=4000+2}\left(\frac{\text{M}}{\text{P}}\right)\\ \text{SRAS:Y=}\overline{\text{Y}}{\text{+100(P-P}}^{\text{e}}\text{)}\end{array}$

Substituting the given values and equate both the equations as follows:

$\begin{array}{l}\overline{\text{Y}}{\text{+100(P-P}}^{\text{e}}\text{)=4000+2}\left(\frac{\text{M}}{\text{P}}\right)\\ \text{6000=4000+2}\left(\frac{\text{4000}}{\text{P}}\right)\\ {\text{P=4=P}}^{\text{e}}\end{array}$

Thus, the equilibrium price level is 4, and also showing that is the same for the equilibrium expected price level.

$\begin{array}{l}\text{Y=4000+2}\left(\frac{\text{4000}}{\text{4}}\right)\\ \text{Y=6000}\end{array}$

Thus, equilibrium output is $6000$ .

$\begin{array}{l}\frac{\text{(Y-}\overline{\text{Y}}\text{)}}{\overline{\text{Y}}}\text{=-2(u-}\overline{\text{u}}\text{)}\\ \text{0=-2(u-0}\text{.05)}\\ \text{u=0}\text{.05}\end{array}$

$\frac{{\text{P-P}}^{\text{e}}}{{\text{P}}^{\text{e}}}\text{=}\frac{\text{4-4}}{\text{4}}\text{=0\%}$

Economics Concept Introduction

Introduction: Okun’s Law graph representation helps in defining relationship between unemployment and lossesin the GDP of an economy. It explains the link between unemployment and output levels. Output is directly dependent on the amount of labor used in the production. This law explains how much of a country’s GDP may be lost when the unemployment is above its natural rate. Therefore, okun’s law explains the negative correlation between GDP growth and unemployment.

b.

To determine

To calculate: The new short run equilibrium values of the price level, expected price level, output, value of cyclical unemployment and unanticipated inflation.

Answer to Problem 3NP

The short run equilibrium values of the price level $4.4$ , expected price level is $4$ , output is $6,040$ , unemployment rate is $0.047$ , decrease in cyclical unemployment by $0.3\%$ and unanticipated inflation is $10\%$ .

Explanation of Solution

Given that,

Y= $6000$ ,

P^e =4,

M= $4000$

Substitute above values to the equation,

$\begin{array}{l}\overline{\text{Y}}{\text{+100(P-P}}^{\text{e}}\text{)=4000+2}\left(\frac{\text{M}}{\text{P}}\right)\\ \text{6000+100(P-4)=4000+2}\left(\frac{\text{4000}}{\text{P}}\right)\\ \text{6000+100P-400=4000+}\frac{\text{8000}}{\text{P}}\\ \text{1600=}\frac{\text{8000}}{\text{P}}\text{-100P}\\ \text{1600=}\frac{{\text{8000-100P}}^{\text{2}}}{\text{P}}\\ {\text{1600P=8000-100P}}^{\text{2}}\\ {\text{100P}}^{\text{2}}\text{-1600P-8000=0}\end{array}$

Or, ${\text{P}}^{\text{2}}\text{-16P-80=0}$

On solving this equation,

$\text{P=4}\text{.4}$

And, substitute above value to the equation,

$\begin{array}{l}\text{Y=6000+100(4}\text{.4-4)}\\ \text{Y=6040}\end{array}$

Therefore, the short-run equilibrium level output is $6040$ .

$\begin{array}{l}\frac{\text{6040-6000}}{\text{6000}}\text{=-2(u-0}\text{.05)}\\ \frac{\text{40}}{\text{6000}}\text{=-2u+0}\text{.10}\\ \text{0}\text{.006667=-2u+0}\text{.10}\\ \text{u=}\frac{\text{0}\text{.10-0}\text{.006667}}{\text{2}}\\ \text{u=}\frac{\text{0}\text{.093333}}{\text{2}}\\ \text{u=0}\text{.047}\end{array}$

Change in cyclical unemployment $0.047-0.05=0.003$ or $0.3\%$

And,

The unanticipated inflation is represented by the percentage change in price of the economy and will be calculated as follows:

$\frac{{\text{P-P}}^{\text{e}}}{{\text{P}}^{\text{e}}}\text{=}\frac{\text{4}\text{.4-4}}{\text{4}}\text{=0}\text{.1}$

Or, $\text{10\%}$

Therefore, the economy will face $\text{10\%}$ unanticipated inflation.

Economics Concept Introduction

Introduction: Okun’s Law graph representation helps in defining relationship between unemployment and losses in the GDP of an economy. It explains the link between unemployment and output levels. Output is directly dependent on the amount of labor used in the production.This law intended to tell us how much of a country’s GDP may be lost when the unemployment is above its natural rate. Therefore, okun’s law explains the negative correlation between GDP growth and unemployment.

c.

To determine

To describe: The slope of the expectations-augmented Philips curve in this economy.

Answer to Problem 3NP

The slope of the expectations-augmented Philips curve in this economy (h) is - $\text{33}\text{.33}$ and the curve is negative.

Explanation of Solution

Given data,

$\begin{array}{l}{\text{π-π}}^{\text{e}}\text{= 0}\text{.1}\\ \text{u = 0}\text{.047}\\ \overline{\text{u}}=0.05\end{array}$

The equation for Philips curve of expectations-augmented is as follows:

${\text{π-π}}^{\text{e}}\text{=-h(u-}\overline{\text{u}}\text{)}$

Substitute the values given above in the equation,

$\begin{array}{l}{\text{π-π}}^{\text{e}}\text{=-h(u-}\overline{\text{u}}\text{)}\\ \text{0}\text{.1=-h(0}\text{.047-0}\text{.05)}\\ \text{h=33}\text{.33}\end{array}$

Economics Concept Introduction

Introduction: Okun’s Law graph representation helps in defining relationship between unemployment and losses in the GDP of an economy. It explains the link between unemployment and output levels. Output is directly dependent on the amount of labor used in the production. This law explains how much of a country’s GDP may be lost when the unemployment is above its natural rate. Therefore, okun’s law explains the negative correlation between GDP growth and unemployment.