Therefore, a vertical line represents the GDP in the graph. Note that a change in employment or output implies a direct positive impact on the GDP and thus there will be a horizontal shift in the vertical line representing GDP in such cases. However, like the level of interest rate, changes in the price level also has no direct impact on the GDP and thus, the GDP line would remain stationary if there was a change in the price level. Figure 1: Graphical representation of GDP The next step is to add the APE into this set up. Assuming a simple linear form under typical assumptions, we can have the following expression: Note that a, b and c are all positive fractions. ‘a’ represents the autonomous part of planned expenditure, while b represents the marginal propensity to expend out of income and c represents the marginal expenses induced by interest rate changes. Figure 2: Adding in the APE – the horizontal intercept of the APE line is a+b(GDP0) as i=0 along the horizontal axis by definition. To graph this relationship into the set up introduced previously, first note that the interest rate has an inverse relationship with APE implying that the graph will slope upwards to the left, i.e., the APE wil fall (rise) following an increase (decrease) in the interest rate. ...

expression clearly implies that the IS relationship can be plotted as a straight line which has a horizontal intercept equal to which lies to the right of a+b(GDP0) and rises upwards to the left with a flatter incline compared to the APE line (since the coefficient on I is c for the APE line while it is c/(1-b) for the IS line. This is shown in the diagram below (figure 3) Figure 3: Adding in the IS line Observe that due to the particular specifications of each of these lines, there will always be an intersection or a common point were the lines cross. Suppose that if there is a change in GDP, the GDP line will move horizontally to the right in case of an increase or to the left in case of a decrease and the APE line will also shift in the same direction but by a smaller magnitude. The shift will be b times the shift in the GDP line. The IS line will remain unchanged. Alternatively if there is a change in the APE line, then the GDP line will remain stationary but the IS line will shift upwards or downwards in accordance to the direction of the change in the APE line. However, the crucial point to note here is that due to these coordinated movements, that these lines will intersect is necessarily ensured. Since by definition the IS line is the locus of combinations of the interest rate and the GDP such that APE=GDP, we can trace the IS line by allowing the GDP to change, letting the APE curve shift in accordance and connecting the new intersection points. The final point to note in this context is that if the GDP shifts first, then the APE will also shift in response and the IS line shall remain stationary. However, if the APE line shifts by itself (say due to a change in a), then the GDP line remains stationary, while the IS line shifts. ASF which is defined as the
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