# Is $y$ always output per person in DSGE/RBC models?

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: http://crei.cat/people/gali/pdf_files/monograph/slides-ch3.pdf

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

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..

• I do not think is always per person. Where did you find that? Please elaborate on your question. I cannot understand the context. 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 $[0,1]$. Jun 5 '15 at 10:48
• Where did you find this for labor? In which book/web material? Jun 5 '15 at 10:57
• So like: crei.cat/people/gali/pdf_files/monograph/slides-ch3.pdf 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? Jun 5 '15 at 14:23
• and this: economics.stackexchange.com/questions/1850/… this seems to say that labor is working time per worker when the maximum possible working time is 1 per worker.. 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.