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the Income Multiplier and the Employment Multiplier |
Let DD stand for Direct Demand and ID for Induced Demand. From the definition of the income multiplier k_{Y}
Now the direct and induced demands have to be converted into jobs. Let a_{D} and a_{I} be, respectively, the proportions of production revenue that goes for labor. Thus a_{D}DD and a_{I}ID will be the payments made for labor. The amount of labor secured by these payments will be (a_{D}DD)/w_{D} and (a_{I}ID)/w_{I}. Let these amounts of labor employed be denoted by E_{D} and E_{I}. Thus
From the definition of the employment multiplier k_{E}
After substitution of the expressions for E_{D} and E_{I} the above equation becomes
This equation may be solved for (k_{E}−1) as
From the expression for ID it follows that (ID/DD) is equal to (k_{Y}−1). Therefore
Finally this reduces to
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