Principles of Macroeconomics
Principles of Macroeconomics
7th Edition
ISBN: 9781260110982
Author: Frank, Robert
Publisher: MCGRAW-HILL HIGHER EDUCATION
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Chapter 15, Problem 11P

(a)

To determine

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

(a)

Expert Solution
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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)+0.6Y(2,000r+1,000r)PAE=4,950+0.6Y3,000r

Thus, 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 0.04, the PAE can be calculated as follows:

PAE=4,9503,000r=4,950(3,000×0.04)=4,950120=4,830

Thus, the autonomous expenditure is 4,830.

The equilibrium output in the short run can be calculated by fixing PAE, which is equal to the output (Y). The equilibrium output (Y) can be calculated by substituting the equation PAE=4,830+0.6Y as follows:

PAE=4,830+0.6YY=4,830+0.6YY0.6Y=4,8300.4Y=4,830Y=4,8300.4=12,075

Thus, the equilibrium output in the short run is 12,075.

Similarly, substitute each value of the rate of interest in the equation PAE=4,9503,000r+0.6Y. Table-1 below shows the calculated autonomous expenditure and equilibrium output at each level of rate of interest.

Table 1

Rate of inflationReal inflation rateAutonomous expenditureEquilibrium output
00.044,83012,075
0.010.0454,81512,038
0.020.054,80012,000
0.030.0554,78511,963
0.040.064,77011,925

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

Principles of Macroeconomics, Chapter 15, Problem 11P

In Figure 1, the horizontal axis represents the output, and the vertical axis represents the rate of inflation. The 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.

(b)

To determine

Construction of a table that shows the relation of equilibrium output in the short run and inflation rate when the Fed reduces the real rate of interest.

(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, the PAE can be calculated as follows:

PAE=4,9503,000r=4,950(3,000×0.035)=4,950105=4,845

Thus, the autonomous expenditure is 4,845.

The equilibrium output in the short run can be calculated by fixing PAE, which is equal to the output (Y). The equilibrium output (Y) can be calculated by substituting the equation PAE=4,830+0.6Y as follows:

PAE=4,845+0.6YY=4,845+0.6YY0.6Y=4,8450.4Y=4,845Y=4,8450.4=12,112.5

Thus, the equilibrium output in the short run is around 12,113.

Similarly, substitute each value of rate of interest in the equation PAE=4,9503,000r+0.6Y. Table-2 below shows the calculated autonomous expenditure and equilibrium output at each level of rate of interest.

Table 2

Rate of inflationReal inflation rateAutonomous expenditureEquilibrium output
00.0354,84512,113
0.010.044,83012,075
0.020.0454,81512,038
0.030.054,80012,000
0.040.0554,78511,963

Table-2 shows the autonomous expenditure and equilibrium output at each level of inflation rate with a new real rate of interest. While comparing Tables 1 and 2, it is clear that the autonomous expenditure increases about 15 at each level of inflation rate. In the case of equilibrium output, it is increased about 38.  This increase in aggregate demand will lead to a shift in the AD curve to the right because the Fed adopts easing of monetary policy, which means, the Fed reduced the real rate of interest and thereby cause a downward shift of reaction curve. As a result, AD curve shifts to the right.

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