<p>If GDP is measured (as it usually is) for a period such as a year, then number of hours worked (<span class="math-container">$h$</span>) should be measured for the same period.  Thus <span class="math-container">$h$</span> is dimensionless and the dimension of the right hand side is also value / time.</p>

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2019-12-03T13:28:44.093Z
2019-12-03T13:28:44.093Z
Adam Bailey
<p>The GDP is sometimes given by 
<span class="math-container">$$
GDP=P\cdot h\cdot e \cdot F
$$</span></p>

<p>Where <span class="math-container">$P$</span> is the Productivity, <span class="math-container">$h$</span> is the number of hours worked, <span class="math-container">$e$</span> is the employment rate and <span class="math-container">$F$</span> is the size of the labor force. </p>

<p>If we do a dimensional analysis, we see that the left hand side of that equation i <span class="math-container">$\left[ GDP \right]= \text{value / time}$</span></p>

<p>On the right hand side we have:</p>

<p><span class="math-container">$$
[P]=\text{value/time}\\
[h]=\text{time}\\
[e]=\text{dimensionless}\\
[F]=\text{dimensionless}.
$$</span></p>

<p>This analysis yields that the dimension of the RHS is value. </p>

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

<p>Does anyone know why that is?</p>

<econometrics><mathematical-economics><gdp>
Dimensional analysis of GDP
Bobby_Tables
# Dimensional analysis of GDP

(Asked by: username_0 on 2019-12-03)

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?

**Tags:** econometrics, mathematical-economics, gdp

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## 1 answers

### Answer by username_1 on 2019-12-03. Score: 1 | Accepted answer

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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