(a)
Equation that relate planned spending to output and real rate of interest.
(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
(b)
Construction of a table shows the relation of equilibrium output in the short run and inflation rate.
(b)
Explanation of Solution
The equation for PAE is derived as
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
Thus, the equilibrium output in the short run is 12,225.
Similarly, substitute each values of the rate of interest in the equation
Table 1
Rate of inflation | Real inflation rate | Autonomous expenditure | Equilibrium output |
0 | 0.02 | 4,890 | 12,225 |
0.01 | 0.03 | 4,860 | 12,150 |
0.02 | 0.04 | 4,830 | 12,075 |
0.03 | 0.05 | 4,800 | 12,000 |
0.04 | 0.06 | 4,770 | 11,925 |
With the equilibrium output, the aggregate demand curve is graphically represented as below:
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)
Impact of increasing government purchases and construction of a table shows the relation of equilibrium output in the short run and inflation rate.
(c)
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:
Thus, the equation for PAE is derived as
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
Thus, the equilibrium output in the short run is 12,475.
Similarly, substitute each values of the rate of interest in the equation
Table 1
Inflation Rate | Real Interest Rate | Autonomous Expenditure | Equilibrium Output |
0 | 0.02 | 4,990 | 12,475 |
0.01 | 0.03 | 4,960 | 12,400 |
0.02 | 0.04 | 4,930 | 12,325 |
0.03 | 0.05 | 4,900 | 12,250 |
0.04 | 0.06 | 4,870 | 12,175 |
With the equilibrium output, the aggregate demand curve is graphically represented as below:
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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Chapter 15 Solutions
PRINCIPLES OF MACROECONOMICS(LOOSELEAF)
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