Consider the following functions forms as an extension of the Ramsay model in our slides

F(K(t), N(t), A(t)) = K(t)(A(t)N(t))1 , (0, 1),

A

(

t

)

A

(

t

)

= g > 0, u(c(t)) = ln c(t).

(a) Write down the three fifirst order conditions derived from the current-value Hamiltonian of the detrended

social planner's problem.

(b) Solve the steady state saving rate and prove that it is increasing in g.

(c) Compare the saving rates of U.S. and China via the potentially difffferent values of parameters. Use common

sense to compare the parameters.