Macroeconomics
Macroeconomics
10th Edition
ISBN: 9780134896441
Author: ABEL, Andrew B., BERNANKE, Ben, CROUSHORE, Dean Darrell
Publisher: PEARSON
Question
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Chapter 11, Problem 6NP

a.

To determine

To describe: The full employment values of real interest rate, consumption, investment and the price level.

a.

Expert Solution
Check Mark

Answer to Problem 6NP

The full employment value of real interest rate is 10% , consumption is 700 , investment is 150 and the price level is 15 .

Explanation of Solution

Given data,

    Desired ConsumptionC=325+0.5(Y-T)-500r
    Desired InvestmentI=200-500r
    Government purchasesG=150
    TaxesT=150
    Full employment outputY¯ =1000
    Money supplyM=6,000
    Real money demandL=0.5Y-1000r

Whereas, the formula used is as under:

Y=Cd+Id+G

Substitute the values from above to the equation, we get:

1000=325+0.5(1000-150)-500r+200-500r+1501000=325+425-1000r+3501000=1100-1000r1000r=100r=0.10

And,

Formula used to calculate price level is as under:

MP=L

Substitute M=6000 and L=0.5Y-1000r , we get:

6000P=0.5Y-1000r6000P=0.5X1000-1000X0.106000P=500-1006000P=400P=6000400P=15

Calculation of desired consumption is as under:

Cd=325+0.5(Y-T)-500r

Substitute, the value of Y=1000, T=150 and r= 0.10, in the above equation:

=325+0.5(1000-150)-500X0.10=325+425-50=700

And,

Id=200-500r=200-500X0.10=200-50=150

b.

To determine

To compute: The values of the αISISLMLM and lr for the proposed economy.

b.

Expert Solution
Check Mark

Answer to Problem 6NP

The values of the αIS is 0.6,βIS is 0.0005, αLM is zero, βLM is 0.0005 and lr is 1000. for the proposed economy

Explanation of Solution

Given data,

co=325io=200G =150cY=0.5to=150cr=500ir=500

Using these equations,

αIS=co+io+G-cYtocr+irβIS=[1-(1-t)cY]cr+irαLM=l0lr-peβLM=lYly

αIS=co+io+G-cYtocr+irαIS=325+200+150-(0.5×150)500+500αIS=0.6

And,

βIS=[1-(1-t)cY]cr+irβIS=[1-(1-0)0.5]500+500βIS=0.51000βIS=0.0005

Then,

αLM=l0lr-peαLM=01000-0αLM=0

And,

βLM=lYlrβLM=0.51000βLM=0.0005

c.

To determine

To describe: The values under short run equilibrium for output and real interest if the price level is fixed at $ 15 .

c.

Expert Solution
Check Mark

Answer to Problem 6NP

The value under short run equilibrium for output is 1,000 and real interest rate is 10% .

Explanation of Solution

Given data,

    Desired ConsumptionC=325+0.5(Y-T)-500r
    Desired InvestmentI=200-500r
    Government purchasesG=150
    TaxesT=150
    Full employment outputY¯ =1000
    Money supplyM=6,000
    Real money demandL=0.5Y-1000r

Whereas, the formula used is as under:

Y=Cd+Id+G

Substitute the values from above to the equation, we get:

1000=325+0.5(1000-150)-500r+200-500r+1501000=325+425-1000r+3501000=1100-1000r1000r=100r=0.10

And,

Formula used to calculate price level is as under:

MP=L

Substitute M=6000 and L=0.5Y-1000r , we get:

6000P=0.5Y-1000r6000P=0.5X1000-1000X0.106000P=500-1006000P=400P=6000400P=15

d.

To determine

To describe:

The short-run equilibrium level of output and αIS if price level unchanged at 15 and G will be 250 instead of 150 .

d.

Expert Solution
Check Mark

Answer to Problem 6NP

The short-run equilibrium level of output is 1,100 and αIS=0.7 .

Explanation of Solution

Given data,

co=325io=200G = 250cY=0.5to=150cr=500ir=500βLM=0.0005βIS=0.0005P = 15M = 6000

The formula used here is,

αIS=co+io+G-cYtocr+irαIS=325+200+250-(0.5×150)500+500αIS=0.7

Therefore,

MP=600015=400

And,

To calculate equilibrium output the following formula is used:

Y=[αISLM+(1/lr)(M/P)]/[βISLM]

Substitute the values from above:

Y=[0.7-0+(400/1000)]/(0.0005+0.0005)Y=1.1/0.001Y=1100

e.

To determine

To describe:

The government purchases multiplier, given that G=150 to G=250 .

e.

Expert Solution
Check Mark

Answer to Problem 6NP

The government purchases multiplier is 1 .

Explanation of Solution

Formula for purchases multiplier:

dYdG=1/[(cr+ir)(βISLM)]

Given information as calculated above,

cr=500ir=500βLM=0.0005βIS=0.0005

Substitute the above information in the equation:

dYdG=1/[(cr+ir)(βISLM)]=1/[(500+500)(0.0005+0.0005)]=1

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