We consider endogenous growth without scale effect. The model setting is the same

as Romer $(1990)$ done in class except two points. First, population grows at the

rate of $n.$ Second, knowledge production follows

$A_t=$

$u{L}_{At}{A}_t^{},in(0,1)$

where $$ stands for the fishing$-$out effect, i$.$e$.,$ it is getting more difficult to come up

wit a new idea after a lot of ideas have been already created. $($see Jones $(1995).)$

$($a$)$ Derive the value of technology, $q,$ on a balanced growth path.

$($b$)$ What is the growth rate of per$-$capita output?

$($c$)$ Consider a policy such that it leads to more employment in the research sector

$($e$.$g$.$ R&D subsidy$).$ Do yo think that such a policy stimulates economic

growth in the long run? Explain.