growth rate in potential GDP - labor vs. labor forece

growth rate in potential GDP =

long-term growth rate of technology + α (long-term growth rate in capital) + (1 – α) (long-term growth rate in labor )

growth rate in potential GDP =

long-term growth rate of _ labor force _ + long-term growth rate in labor productivity

What’s the relationship between labor and labor force here? Thanks.

Same thing, I believe.

+1 same thing

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Thanks. But how to derive the formula from first to second?

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Same here, are we supposed to use one or the other formula depending of the inputs given ?

2 different formulas and have to know both in order to calculate potential GDP growth rate depending on the inputs given in the exam

Thanks


Sorry for digging up this old post but I just want to confirm that labor and labor force are not the same thing in the two equations.

If using the 1st equation, long term growth rate = 3.75%
If using the 2nd equation, long term growth rate = 3.4% + 1.7% = 5.1%

Can anyone confirm? Appreciate it!

From @Mitchi (the green sheet)

The components of growth can be determined using Solow’s growth accounting equation

\frac{\Delta Y}{Y} =\frac{\Delta A}{A}+\alpha\frac{\Delta K}{K}+(1-\alpha)\frac{\Delta L}{L}

where \frac{\Delta Y}{Y} = GDP percentage growth
\frac{\Delta A}{A} = percentage growth from total factor productivity (TFP)
\frac{\Delta K}{K} = percentage growth in capital
\frac{\Delta L}{L} = percentage growth in labor
\alpha = share of income paid to capital factor
1-\alpha = share of income paid to labor factor

TFP = Labor productivity growth - Growth in capital deepening,

If we assume
(i) \alpha=0 so all income is paid to labor factor
and (ii) there is no capital deepening,so that TFP = Labor productivity growth,
then
\frac{\Delta A}{A} = percentage growth from labour productivity

\frac{\Delta Y}{Y}= percentage growth from labor productivity +\frac{\Delta L}{L}

which answers @FrankCFA 's question from 10 years ago about how to derive the first equation from the second