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As title says, is $y$ output per person in DSGE/RBC model? If so, why did macroeconomics decide not using Solow/Cobb-Douglas style of using full labor to characterize economy?

Model reference:

For Gali's model, would $y$ represent output per worker? Or the whole output of the economy represented by representative household?

Reference: why is labor $h_t$ often average working time percentage of non-sleeping time in RBC?

this for me seems to say that full maximum working time is assumed to be 1 with $h_t$ representing working time per labor unit. Thus it seems to be that $y$ is output per person..

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I do not think is always per person. Where did you find that? Please elaborate on your question. I cannot understand the context. – pidosaurus Jun 5 '15 at 10:29
I don't really have context, but in general RBC models, what do $y$ mean? Often texts just say output, which isn't clear to me, given that labor $n$ is in $[0,1]$. – capkital Jun 5 '15 at 10:48
Where did you find this for labor? In which book/web material? – pidosaurus Jun 5 '15 at 10:57
So like: I am not really sure what y actually means - does it mean output per worker, as it is representative household? Or because it's representative household, it represents the whole output of the economy? – capkital Jun 5 '15 at 14:23
and this:… this seems to say that labor is working time per worker when the maximum possible working time is 1 per worker.. – capkital Jun 5 '15 at 14:25

As far as Gali is concerned he defines (on page 16 of his book) $N$ as "hours of work or employment", noting that "$N_t$ can be interpreted as the number of household members employed, assuming a large household and ignoring integer constraints".

Then on chapter 3 he talks about a continuum of firms $Y_t(i), \ \ i \in [0,1]$ producing the aggregate output: $$ Y_t \equiv \left( \int_0^1 Y_t(i)^{1 - \frac{1}{\epsilon}}\mathrm{d}i\right)^\frac{\epsilon}{\epsilon -1}$$

But small-case $y_t$ refers to the output of the log-linearized equations. Somebody can use $y_t$ as the logarithm of the Gross National Product, so as I perceive it that, this is not output per person.

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