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San José State University Department of Economics |
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applet-magic.com Thayer Watkins Silicon Valley & Tornado Alley USA |
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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 kY
ID = (kY−1)DD
Now the direct and induced demands have to be converted into jobs. Let aD and aI be, respectively, the proportions of production revenue that goes for labor. Thus aDDD and aIID will be the payments made for labor. The amount of labor secured by these payments will be (aDDD)/wD and (aIID)/wI. Let these amounts of labor employed be denoted by ED and EI. Thus
From the definition of the employment multiplier kE
After substitution of the expressions for ED and EI the above equation becomes
This equation may be solved for (kE−1) as
From the expression for ID it follows that (ID/DD) is equal to (kY−1). Therefore
Finally this reduces to
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