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Consider an economy described by the following:

C = \(3.25 trillion

I = \)1.3 trillion

G = \(3.5 trillion

T = \)3.0 trillion

NX = -$1.0 trillion

f = 1

mpc = 0.75

d = 0.3

x = 0.1

l = 1

r = 1

a. Derive expressions for the MP curve and the AD

curve.

b. Assume that p = 1. Calculate the real interest

rate, the equilibrium level of output, consumption,

planned investment, and net exports.

c. Suppose the Fed increases r to r = 2. Calculate the

real interest rate, the equilibrium level of output,

consumption, planned investment, and net exports

at this new level of r.

d. Considering that output, consumption, planned

investment, and net exports all decreased in part (c),

why might the Fed choose to increase r?

Short Answer

Expert verified

A. The ADequation isY=16.4-1.6

B. The value of net export is -$1.2trillion.

C. The value of net export is -$1.3trillion.

D. The Fed affect the real interest rate through increase or drop in r

Step by step solution

01

Concept Preface 

Monetary policy is used by the central bank to control the liquidity of plutocrat from frugality to bring the frugality to stablecondition.This is done through operation of interest rate and the plutocrat force. Objects of a financial policy are high employment and affair stability, profitable growth, stability of fiscal requests, interest rate stability, and stability in foreign exchange requests. Aggregate demand is the total demand of goods and services in an frugality. Aggregate claim is the aggregate of consumption, investment, administration charge and net exports.

affectedness is the overall increase in general price position of an frugality. affectedness causes increase in the price of goods and services which decreases exports and fall in aggregate demand.

02

:Explanation of Solution

A.

Given,

Cis $3.25trillion.

Iis $1.3trillion.

Gis $3.5trillion.

Tis $3trillion.

NXis -$1trillion.

fis 1

mpcis 0.75.

dis 0.3.

xis 0.1.

ris 1.

is 1.

MP curve equation is:

r=r+(1)

AD curve equation is as,

Y=[C+I-df+G+NX-mpcT]11-mpc-d+x1-mpc(r+)(2)

Where,

- Yis the Aggregate demand.

- Cis autonomous consumption.

- Iis the investment expenditure .

- dis investment responsiveness to real interest rate.

- fis financial frictions.

- Gis Government expenditure.

- NXis net export.

- mpc is marginal propensity to consume.

- Tis the tax.

- xis net export responsiveness to real interest rate.

- ris autonomous component of real interest rate.

- is the responsiveness of real interest rate to inflation rate.

- is the inflation rate .

Substitute the values of rand in the equation (1),

r=1+

Hence, the MP curve equation is r=1+.

Substitute the values in equation (2),

Y=[3.25+1.3-0.31+3.5-1-0.753]11-0.75-0.3+0.11-0.75(1+)Y=[4.5]10.25-0.40.25(1+)Y=18-1.6(1+)Y=16.4-1.6

Hence, the ADequation is localid="1648505220881" Y=16.4-1.6.

03

:

B.

Given,

Cis $3.25trillion.

Iis $1.3trillion.

Gis $3.5trillion.

Tis$3trillion.

NXis -$1trillion.

fis 1.

mpcis 0.75.

dis 0.3.

xis 0.1.

ris 1.

is 1.

is 1 .

The MP curve equation isr=1+

Substitute value of to determine real interest rate in the above equation,

Real interest rate=1+1=2

Hence, the value of real interest rate is 2%when inflation is given as 1%in the economy.

The ADequation isY=16.4-1.6

Substitute value of to determine equilibrium level of output in the above equation,

Equilibrium level of output=16.4-1.61

=14.8

Hence, the value of equilibrium level of output is $14.8trillion.

The formula of consumption expenditure is:

C=C+mpc(Y-T)

Substitute the value of equilibrium output level and the given value of autonomous consumption, tax and marginal propensity to consume role="math" localid="1648503381445" mpcin the above formula,

role="math" localid="1648503473900" C=3.25+0.75(14.8-3)C=$12.1

Hence, the value of consumption expenditure is $12.1trillion.The formula for planned investment is:

I=I-d(r+f)

Substitute, the value of real interest rate with the given values of fixed investment, dand fin the above formula,

I=1.3-0.3(2+1)I=$0.4

Hence, the value of planned investment is $0.4trillion.

The formula for net export is:

NX=NX-xr

Substitute the value of real interest rate in the above formula,

NX=-$1-0.12=-$1.2

Hence, the value of net export is -$1.2trillion.

04

:Explanation of Solution

C.

Given,

Cis $3.25trillion.

Iis $1.3trillion.

Gis $3.5trillion.

Tis $3trillion.

NXis -$1trillion.

fis 1.

mpcis 0.75.

dis 0.3.

x is0.1.

ris 2.

is 1.

is 1 .

The MP curve equation isr=1+

Substitute the value of to determine real interest rate in the above formula,

Real interest rate=2+1

=3

Hence, the value of real interest rate is 3%as the value of rchange from 1%to 2%in the economy.

AD curve equation is:

Y=[C+I-df+G+NX-mpcT]11-mpc-d+x1-mpc(r+)

Where,

- Yis the Aggregate demand.

-Cis autonomous consumption.

- lis the investment expenditure.

- d is investment responsiveness to real interest rate.

- fis financial frictions.

-Gis Government expenditure.

-NXis net export.

- mpc is marginal propensity to consume.

- Tis the tax.

- xis net export responsiveness to real interest rate.

- sautonomous component of real interest rate.

- is the responsiveness of real interest rate to inflation rate.

- is the inflation rate.

Substitute, value of changed rto determine equilibrium level of output.

Y=3.25+1.3-0.31+3.5-1-0.753\rrbracket11-0.75-0.340.11-0.75=[4.5]10.25-0.40.25(2+)=18-1.6(2+)=14.8-1.6

05

:Explanation of Solution 

Substitute the value ofpin the above formula,

Equilibriumlevelofoutput=14.8-1.61=13.2

Hence, the value of equilibrium level of output is $13.2trillion.

The Consumption expenditure is:

C=C+mpc(Y-T)

Substitute, the value of equilibrium output level and the given value of autonomous consumption, tax and marginal propensity to consume ( mpc) to determine the value of consumption expenditure.

C=3.25+0.75(13.2-3)=$10.9

Hence, the value of consumption expenditure is $10.9trillion.

The planned investment is:

I=I-d(r+f)

Substitute, the value of real interest rate with the given values of fixed investment, dand fto determine the value of planned investment.

I=1.3-0.3(3+1)I=$0.1

Hence, the value of planned investment is$0.1 trillion.

The net export isNX=NX-xr

Substitute the value of real interest rate to determine the value of net export.

NX=-1-0.13=-$1.3

Hence, the value of net export is -$1.3trillion.
06

:Explanation of Solution

D.

The Fed may believe that the frugality will strengthen in the future and there is a threat that affectedness will raise in the future, so they increased r. A change in independent element of real claim rate will affect real claim rate directly. Real claim rate increases with an increase inr. Fed can only control r, thus, Fed affect the real claim rate through increase or drop in r.

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Most popular questions from this chapter

A measure of real interest rates can be approximated by the Treasury Inflation-Indexed Security, or TIIS. Go to the St. Louis Federal Reserve FRED database, and find data on the five-year TIIS (FII5) and the personal consumption expenditure price index (PCECTPI), a measure of the price index. Choose 鈥淨uarterly鈥 for the frequency setting of the TIIS, and download both data series. Convert the price index data to annualized inflation rates by taking the quarter-to-quarter percent change in the price index and multiplying it by 4. Be sure to multiply by 100 so that your results are percentages.

a. Calculate the average inflation rate and the average real interest rate over the most recent four quarters of data available and the four quarters prior to that.

b. Calculate the change in the average inflation rate between the most recent annual period and the year prior. Then calculate the change in the average real interest rate over the same period.

c. Using your answers to part (b), compute the ratio of the change in the average real interest rate to the change in the average inflation rate. What does this ratio represent? Comment on how it relates to the Taylor principle.

How does an autonomous tightening or easing of monetary policy by the Fed affect the aggregate demand curve?

Suppose the MP curve is given by r = 2 + p, and the IS curve is given by Y = 20 - 2r.

a. Derive an expression for the AD curve, and draw a

graph labeling points at p = 0, p = 4, and p = 8.

b. Suppose that l increases to l = 2. Derive an expression

for the new AD curve, and draw the new AD

curve using the graph from part (a).

c. What does your answer to part (b) imply about the

relationship between a central bank鈥檚 distaste for

inflation and the slope of the AD curve?

Why does the aggregate demand curve shift when 鈥渁nimal spirits鈥 change?

Suppose that government spending is increased at the same time that an autonomous monetary policy tightening occurs. What will happen to the position of the aggregate demand curve?

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