# a question on the endogenous growth model

I have such a question on the endogenous growth mode”:

In the macroeconomics literature there are various ways in which the growth process in the Ransey-Cass- Koopmans model has been endogenized. For this question you are required to incorporate one of these endogenous growth mechanisms into the model. You can select the mechanism, but make sure that you explain and/or show how it will generate growth endogenously. Setup the optimization problems faced by the various types of agents in your model. Derive and interpret the first order conditions (or efficiency conditions) in these optimization problems. Finally, to the best of your ability use the model to explain the stylized facts of economic growth and development.

What I want is exactly not to give an answer. I just want to be explained this question. Summarize it. Give hint! especially on dark statement. For example can I explain something like AK MODEL Or ROMER MODEL, LEARNING BY DOING ...? What means endogenous growth mechanism?

I just try to understand the question. Thus I’m asking here.

"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)

• Thanks a lot! Can you suggest a book or a link on the net to learn what you said? – mnm123 May 30 '18 at 4:25
• I'm not good at growth theory, but the textbook my prof used in class was Barro "Economic Growth". Old but reliable. It deals with growth models in continuous time. The Rebelo model above was from Barro 5.2.1 and Learning-by-doing was from 4.3.1 – T. G. Jun 1 '18 at 9:52

TG's explanation is great. I do not have enough reps so I can't put this as a reply to the comment by OP on TG's post.

On The Mechanics Of Economic Development - Lucas (JME,1988) might be useful for the OP (he solves a Solow model with exogenous growth and his own model with endogenous growth on similar setup) and Introduction to Modern Economic Growth by Acemoglu (apparently the MWG of growth) might be useful as well.