# Endogenous technology

Given the following endogenous knowledge (technology) model where production function is as follows -

Can anyone tell me - For what values of φ does this model get closer to a Solow model of growth?

Note: In solow growth model, knowledge is assumed to be an exogenous variable and assumed to grow at constant rate g.

My hunch is φ should approach to 0 then A˙(t) will be 1 (constant) and A˙(t)/A(t) will be constant. But this doesn't seem right. Can someone please help me with it.

Also, can anyone also help me with

Can you obtain expressions for g˙A(t) and in terms of gA(t) and the parameters? Draw the phase diagram in (gA, gK)

How do we draw phase diagram and I am stuck with derivation of g˙A(t) in terms of gA(t)

Note: gA(t) is growth rate of knowledge given by A˙(t)/A(t).