Please provide detailed and readable solution for the Macroeconomics exercise:

I. Consider the planning problem s.t.max{kt+1}t=0Tt=0Ttu[f(kt)kt+1]0kt+1f(kt),t,givenk0. a. Write down the Lagrangian and characterize the solution. b. Obtain the Euler equation when f(k)=k and u(c)=ln(c). Convert the Euler equation from a second-order difference equation into a first-order difference equation using the change of variable zt+1=kt+1/kt