Principles of Macroeconomics
Principles of Macroeconomics
7th Edition
ISBN: 9781260110982
Author: Frank, Robert
Publisher: MCGRAW-HILL HIGHER EDUCATION
Question
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Chapter 15, Problem 10P

(a)

To determine

Equation that relate planned spending to output and real rate of interest.

(a)

Expert Solution
Check Mark

Explanation of Solution

The planned aggregate expenditure is the sum of consumption, planned investment, government spending, and net export. The equation that connects the planned spending to output and real rate interest can be derived as follows:

PAE=C+IP+G+NXPAE=(1,600 + 0.6(Y2,000) 2,000r)+(2,5001,000r)+2,000+50=1,600+0.6Y1,2002,000r+2,5001,000r+2,000+50=(1,6001,200+2,500+2,000+50)(2,000r1,000r)+0.6YPAE=4,9503,000r+0.6Y

Thus, the equation for PAE is derived as PAE=4,9503,000r+0.6Y.

(b)

To determine

Construction of a table shows the relation of equilibrium output in the short run and inflation rate.

(b)

Expert Solution
Check Mark

Explanation of Solution

The equation for PAE is derived as PAE=4,9503,000r+0.6Y. The autonomous expenditure is not related to the output (Y). Hence, the equation can be rewritten as PAE=4,9503,000r. If the inflation rate is 0.0 and real interest rate is 0.02, then the PAE is calculated as follows:

PAE=4,9503,000r=4,950(3,000×0.02)=4,95060=4,890

Thus, the autonomous expenditure is 4,890.

The equilibrium output in the short run can be calculate by fix PAE equal to the output (Y). When the inflation rate is 0.0 and rate of interest is 0.02, Y is calculated by substituting the equation PAE=4,8900.6Y as follows:

PAE=4,890+0.6YY=4,890+0.6YY0.6Y=4,8900.4Y=4,890Y=4,8900.4=12,225

Thus, the equilibrium output in the short run is 12,225.

Similarly, substitute each values of the rate of interest in the equation PAE=4,9503,000r+0.6Y. The table below shows the calculated autonomous expenditure and equilibrium output at each level of the rate of interest.

Table 1

Rate of inflationReal inflation rateAutonomous expenditureEquilibrium output
00.024,89012,225
0.010.034,86012,150
0.020.044,83012,075
0.030.054,80012,000
0.040.064,77011,925

With the equilibrium output, the aggregate demand curve is graphically represented as below:

Principles of Macroeconomics, Chapter 15, Problem 10P , additional homework tip  1

In Figure 1, the horizontal axis represents output and the vertical axis represents the rate of inflation. Curve AD is the aggregate demand curve, which refers to the total value of the goods and services that are demanded at each price or inflation rate in a given period of time.

(c)

To determine

Impact of increasing government purchases and construction of a table shows the relation of equilibrium output in the short run and inflation rate.

(c)

Expert Solution
Check Mark

Explanation of Solution

The planned aggregate expenditure is the sum of consumption, planned investment, government spending, and net export. The equation that connects the planned spending to output and real rate interest is derived as follows:

PAE=C+IP+G+NXPAE=(1,600 + 0.6(Y2,000) 2,000r)+(2,5001,000r)+2,100+50=1,600+0.6Y1,2002,000r+2,5001,000r+2,100+50=(1,6001,200+2,500+2,100+50)(2,000r1,000r)+0.6Y=5,0503,000r+0.6Y

Thus, the equation for PAE is derived as PAE=5,0503,000r+0.6Y. The autonomous expenditure is not related to output (Y). Hence, the equation can be rewritten as PAE=5,0503,000r. If the inflation rate is 0.0 and real interest rate is 0.02, the PAE is calculated as follows:

PAE=5,0503,000r=5,050(3,000×0.02)=5,05060=4,990

Thus, the autonomous expenditure is 4,990.

The equilibrium output in the short run is calculated by fix PAE equal to the output (Y). When the inflation rate is 0.0 and rate of interest is 0.02, Y is calculated by substituting equation PAE=5,0503,000r as follows:

PAE=4,990+0.6YY=4,990+0.6YY0.6Y=4,9900.4Y=4,990Y=4,9900.4=12,475

Thus, the equilibrium output in the short run is 12,475.

Similarly, substitute each values of the rate of interest in the equation PAE=5,0503,000r+0.6Y. The table below shows the calculated autonomous expenditure and equilibrium output at each level of the rate of interest.

Table 1

Inflation RateReal Interest RateAutonomous ExpenditureEquilibrium Output
00.024,99012,475
0.010.034,96012,400
0.020.044,93012,325
0.030.054,90012,250
0.040.064,87012,175

With the equilibrium output, the aggregate demand curve is graphically represented as below:

Principles of Macroeconomics, Chapter 15, Problem 10P , additional homework tip  2

In Figure 2, the horizontal axis represents output and the vertical axis represents the rate of inflation. Curve AD is the aggregate demand curve, which refers to the total value of the goods and services that are demanded at each price or inflation rate in a given period of time.

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