<p>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". </p>

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

<p>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.</p>

CC BY-SA 3.0
2015-06-05T17:38:21.817Z
2015-06-05T17:38:21.817Z
Konstantinos
<p>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?</p>

<p>Model reference: <a href="http://crei.cat/people/gali/pdf_files/monograph/slides-ch3.pdf" rel="nofollow noreferrer">http://crei.cat/people/gali/pdf_files/monograph/slides-ch3.pdf</a></p>

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

<p>Reference: <a href="https://economics.stackexchange.com/questions/1850/why-is-labor-h-t-often-average-working-time-percentage-of-non-sleeping-time-in">why is labor $h_t$ often average working time percentage of non-sleeping time in RBC?</a></p>

<p>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..</p>

CC BY-SA 3.0
2015-06-05T10:29:18.960Z
I do not think is always per person. Where did you find that? Please elaborate on your question. I cannot understand the context.
Konstantinos
CC BY-SA 3.0
2015-06-05T10:48:36.223Z
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
CC BY-SA 3.0
2015-06-05T10:57:57.030Z
Where did you find this for labor? In which book/web material?
Konstantinos
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2015-06-05T14:23:43.823Z
So like: http://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?
capkital
CC BY-SA 3.0
2015-06-05T14:25:29.643Z
and this: http://economics.stackexchange.com/questions/1850/why-is-labor-h-t-often-average-working-time-percentage-of-non-sleeping-time-in this seems to say that labor is working time per worker when the maximum possible working time is 1 per worker..
capkital
CC BY-SA 3.0
2015-06-05T17:34:36.977Z
Now we are on the same page. :) Your question seems simple, but it isn't, since literature seems to lack definitions of "units of measurement" as we were doing for physics in high-school: m/sec in RHS, m/sec in LHS.
Konstantinos
<macroeconomics>
Is $y$ always output per person in DSGE/RBC models?
capkital
# Is $y$ always output per person in DSGE/RBC models?

(Asked by: username_0 on 2015-06-05)

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?

Reference: [why is labor $h\_t$ often average working time percentage of non-sleeping time in RBC?](https://economics.stackexchange.com/questions/1850/why-is-labor-h-t-often-average-working-time-percentage-of-non-sleeping-time-in)

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..

**Tags:** macroeconomics

> **Comments:**
> **username_1**: I do not think is always per person. Where did you find that? Please elaborate on your question. I cannot understand the context.  
> **username_0**: 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 $[0,1]$.  
> **username_1**: Where did you find this for labor? In which book/web material?  
> **username_0**: So like: http://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?  
> **username_0**: and this: http://economics.stackexchange.com/questions/1850/why-is-labor-h-t-often-average-working-time-percentage-of-non-sleeping-time-in this seems to say that labor is working time per worker when the maximum possible working time is 1 per worker..  
> **username_1**: Now we are on the same page. :) Your question seems simple, but it isn't, since literature seems to lack definitions of "units of measurement" as we were doing for physics in high-school: m/sec in RHS, m/sec in LHS.  

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## 1 answers

### Answer by username_1 on 2015-06-05. Score: 1

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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