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The GDP is sometimes given by $$ GDP=P\cdot h\cdot e \cdot F $$

Where $P$ is the Productivity, $h$ is the number of hours worked, $e$ is the employment rate and $F$ is the size of the labor force.

If we do a dimensional analysis, we see that the left hand side of that equation i $\left[ GDP \right]= \text{value / time}$

On the right hand side we have:

$$ [P]=\text{value/time}\\ [h]=\text{time}\\ [e]=\text{dimensionless}\\ [F]=\text{dimensionless}. $$

This analysis yields that the dimension of the RHS is value.

Hence, the dimension of the left hand side and the right hand side is not equal, which would constitute a contradiction.

Does anyone know why that is?

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If GDP is measured (as it usually is) for a period such as a year, then number of hours worked ($h$) should be measured for the same period. Thus $h$ is dimensionless and the dimension of the right hand side is also value / time.

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  • $\begingroup$ Thanks! That is very helpful. $\endgroup$ – Bobby_Tables Dec 3 '19 at 14:56

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