Need help understanding the walk through of the equations

t Econ 505 (Tan) DERIVING THE CANONICAL NEOCLASSICAL GROWTH REGRESSION This is a set Of brief notes to complement the class discussion on the above topic. We start with the Cobb-Douglas production function. In per efficiency units, we have 9 = rca ae (0,1) Recall also the Neoclassical Fundamental Equation (FE): skal (R As you know, this economy converges (globally) to a unique Ste dy state given by k Now, define (Astu AZ/nI- z In(k)) o x) y A. and rewrite the FE as Verify that the above is true: (e Notice that what we have here is a (nonlinyr) differential squation in one variable (z): Note also that when = 0 at steady state. Now, let's consider a log-linearization of r (z) around the steady state. That is, take a First Order Taylor Series expansion about the value z = 0: ( F.H- orL,_