<p>Based on the steady state your production function is Cobb-Douglas.Taking logs and derivatives wrt time of <span class="math-container">$Y$</span>, <span class="math-container">$\frac{Y}{L}$</span> and <span class="math-container">$\frac{Y}{AL}$</span> in the steady state yields the desired result: <span class="math-container">$K$</span> grows with <span class="math-container">$n+g$</span> on the BGP. </p>

<p>It would be interesting to know what the supervisor's objection was.</p>

CC BY-SA 4.0
2020-05-13T22:25:37.123Z
Yes you are correct the production function was standard Cobb Douglas everything was expressed per unit of effective labor so it was $f(k)=k^{\alpha}$ she showed me his email with comments and he literary said that she puts too much effort in deriving steady state but no effort in showing the growth depends on those variables. Should I just tell her to explicitly add the time derivatives?
1muflon1
CC BY-SA 4.0
2020-05-13T22:43:43.613Z
@1muflon1 yes. Showing that there is only one steady state is the first step. The second is to show that this causes the growth rates to be constant
Grada Gukovic
CC BY-SA 4.0
2020-05-13T22:55:35.453Z
okay thanks, also was my explanation/reasoning actually incorrect or do you think he just wants her to show everything explicitly as an exercise
1muflon1
CC BY-SA 4.0
2020-05-13T23:04:12.090Z
@1muflon1 its not wrong. It is just up to the supervisor to decide what level of  informal argumentation he wishes to tolerate
Grada Gukovic
CC BY-SA 4.0
2020-05-13T22:21:00.130Z
2020-05-13T22:21:00.130Z
Grada Gukovic
<p>To provide some context for the question: I was approached by a student needing help for a an empirical thesis based on Solow-Swan model. She had trouble solving the theoretical model she wanted to showcase in her work. She already put a lot of efforts and had a problem just with last steps of derivations so I helped her to solve simplified version of Solow-Swan model where:</p>

<p><span class="math-container">$$ k^*= \left( \frac{s}{d+ n + g} \right)^{\frac{1}{1-\gamma}}$$</span></p>

<p>where <span class="math-container">$k$</span> is the capital per effective labor, <span class="math-container">$n$</span> population growth and <span class="math-container">$g$</span> technology growth and <span class="math-container">$d$</span> depreciation, and told her that this results implies that <span class="math-container">$K$</span> is growing at the rate <span class="math-container">$n+g$</span> which implies due to the assumption of constant returns that <span class="math-container">$Y$</span> grows at the same rate. Since <span class="math-container">$g$</span> and <span class="math-container">$n$</span> are exogenous the growth must be exogenous as well. </p>

<p>But her supervisor told her that the above is not enough to show that economic growth is driven by exogenous factors and she has to expand her model.  </p>

<p>Hence my question is: was my statement incorrect or is her supervisor making mistake? If my advice was incorrect whats the missing link that unambiguously shows that economic growth depends on <span class="math-container">$n+g$</span>? </p>

CC BY-SA 4.0
2020-11-18T01:18:04.367Z
Strange I woulden't expect this comment from an advisor given the model is so canonical.
EconJohn
CC BY-SA 4.0
2020-11-18T01:19:31.670Z
@EconJohn yes I think that her advisor was just being purposely difficult but then my imposter syndrome kicked in so I needed to confirm this
1muflon1
CC BY-SA 4.0
2020-11-18T01:27:30.040Z
Are you sure its not qualms about data?
EconJohn
CC BY-SA 4.0
2020-11-18T01:35:34.327Z
@EconJohn well I never spoken to that advisor directly but afterwards I helped the girl to put there more details (if I recall correctly we added about 3 more equations) and later it was ok and she passed, although she might have also some issues with empirical part the models did had some problems here and there. Like there was likely some overfitting on some subsamples...
1muflon1
<macroeconomics><economic-growth><solow>
Is the steady state of $k$ enough to show $Y$ grows at the rate $n+g$?
1muflon1
# Is the steady state of $k$ enough to show $Y$ grows at the rate $n+g$?

(Asked by: username_0 on 2020-05-13)

To provide some context for the question: I was approached by a student needing help for a an empirical thesis based on Solow-Swan model. She had trouble solving the theoretical model she wanted to showcase in her work. She already put a lot of efforts and had a problem just with last steps of derivations so I helped her to solve simplified version of Solow-Swan model where:

$$ k^\*= \left( \frac{s}{d+ n + g} \right)^{\frac{1}{1-\gamma}}$$

where $k$ is the capital per effective labor, $n$ population growth and $g$ technology growth and $d$ depreciation, and told her that this results implies that $K$ is growing at the rate $n+g$ which implies due to the assumption of constant returns that $Y$ grows at the same rate. Since $g$ and $n$ are exogenous the growth must be exogenous as well.

But her supervisor told her that the above is not enough to show that economic growth is driven by exogenous factors and she has to expand her model.

Hence my question is: was my statement incorrect or is her supervisor making mistake? If my advice was incorrect whats the missing link that unambiguously shows that economic growth depends on $n+g$?

**Tags:** macroeconomics, economic-growth, solow
> **Comments:**
> **username_1**: Strange I woulden't expect this comment from an advisor given the model is so canonical.  
> **username_0**: @EconJohn yes I think that her advisor was just being purposely difficult but then my imposter syndrome kicked in so I needed to confirm this  
> **username_1**: Are you sure its not qualms about data?  
> **username_0**: @EconJohn well I never spoken to that advisor directly but afterwards I helped the girl to put there more details (if I recall correctly we added about 3 more equations) and later it was ok and she passed, although she might have also some issues with empirical part the models did had some problems here and there. Like there was likely some overfitting on some subsamples...  

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## 1 answers

### Answer by username_2 on 2020-05-13. Score: 3 | Accepted answer

Based on the steady state your production function is Cobb-Douglas.Taking logs and derivatives wrt time of $Y$, $\frac{Y}{L}$ and $\frac{Y}{AL}$ in the steady state yields the desired result: $K$ grows with $n+g$ on the BGP.

It would be interesting to know what the supervisor's objection was.

> **Comments:**
> **username_0**: Yes you are correct the production function was standard Cobb Douglas everything was expressed per unit of effective labor so it was $f(k)=k^{\alpha}$ she showed me his email with comments and he literary said that she puts too much effort in deriving steady state but no effort in showing the growth depends on those variables. Should I just tell her to explicitly add the time derivatives?  
> **username_2**: @1muflon1 yes. Showing that there is only one steady state is the first step. The second is to show that this causes the growth rates to be constant  
> **username_0**: okay thanks, also was my explanation/reasoning actually incorrect or do you think he just wants her to show everything explicitly as an exercise  
> **username_2**: @1muflon1 its not wrong. It is just up to the supervisor to decide what level of  informal argumentation he wishes to tolerate  

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