It would be a silly question. In a model, I have found the BGP (balanced growth path) for all key variables.
As expected, these variables are constant variables ;
$$\mu^{BGP}=\frac{\alpha+\rho+\pi}{\epsilon\left(1+\pi\right)^{2}}$$
All paramaters on the right hand side are exogeneous constant parameters. Let's say $\mu$ is a variable for technological progress level.
For another variable, let's say capital accumulation $k$,I find a constant growth rate which is ;
$$g_{k}=\frac{\alpha\left(\rho+\pi-\delta\left(\frac{1-\alpha}{\alpha}\right)\right)}{1-\alpha}$$
The parameters on the RHS are again exogenous parameters.
My question is : Is it possible to see the effect of the variable $\mu$ on the growth rate of capital $g_k$ ?
My way of doing seems to me a little bit weird. I firstly put
$$\rho=\mu^{BGP}\epsilon\left(1+\pi\right)^{2}-\alpha-\pi$$
and replace it in $g_k$. So, I have
$$g_{k}=\frac{\alpha\left(\mu^{BGP}\epsilon\left(1+\pi\right)^{2}-\alpha-\delta\left(\frac{1-\alpha}{\alpha}\right)\right)}{1-\alpha}$$
After, I say that technological progress level at BGP affects positevly the growth rate of capital.
Do you think that it is correct to say that ? Making this kind of comparative statics analysis ?
Or any other way to do it in a more appropriate way ?