a question on the endogenous growth model
"Endogenous Growth" is actually the short version of saying "Endogenous Technology Growth"


Exogenous (Technology) Growth Models


The rate technological progress $g$ is Exogenously given.

In both Solow and RCK, we can find $A_t = (1 + g)^t A_0 \ \ $(or $A(t) = A(0) e^{gt}$ if in continuous time). $Y$ increases over time because $A$ increases over time. This assumption of growth rate is very strong.


Endogenous (Technology) Growth Models


The rate of technological progress is Endogenously determined.

For example in Two-Sector Growth Model (Rebelo), we have

production $Y = C + I_K =  A \ (vK)^\alpha \ (uH)^{1-\alpha}$ and education $I_H = B \ ((1-v)K)^\alpha \ ((1-u)H)^{1-\alpha}$

Now $v$ and $u$ are endogenously determined, and thus $H$ is endogenously determined. $A$ doesn't change, but $Y$ will increase over time due to increase in $H$.

Another example will be the Learning-by-Doing Model.

Recall in Exogenous Models $A_t$ is exogenously given by $A_t = (1+g)^t A_0$

But now we want $A_t$ to be determined endogenously. Thus we assume technological progress is due to knowledge creation, and knowledge is a side-production of investment. And thus we let $A_t \equiv \sum_{i=0}^N K_{it}$ (there are N identical firms)