(a)
Construction of a table that shows the relation of equilibrium output in the short run and inflation rate.
(a)
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:
Thus, the equation for PAE is derived as
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
Thus, the equilibrium output in the short run is 12,075.
Similarly, substitute each value of the rate of interest in the equation
Table 1
Rate of inflation | Real inflation rate | Autonomous expenditure | Equilibrium output |
0 | 0.04 | 4,830 | 12,075 |
0.01 | 0.045 | 4,815 | 12,038 |
0.02 | 0.05 | 4,800 | 12,000 |
0.03 | 0.055 | 4,785 | 11,963 |
0.04 | 0.06 | 4,770 | 11,925 |
With the equilibrium output, the aggregate demand curve is graphically represented below:
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)
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)
Explanation of Solution
The equation for PAE is derived as
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
Thus, the equilibrium output in the short run is around 12,113.
Similarly, substitute each value of rate of interest in the equation
Table 2
Rate of inflation | Real inflation rate | Autonomous expenditure | Equilibrium output |
0 | 0.035 | 4,845 | 12,113 |
0.01 | 0.04 | 4,830 | 12,075 |
0.02 | 0.045 | 4,815 | 12,038 |
0.03 | 0.05 | 4,800 | 12,000 |
0.04 | 0.055 | 4,785 | 11,963 |
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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Chapter 15 Solutions
PRINCIPLES OF MACROECONOMICS(LOOSELEAF)
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