In the optimal growth model, suppose that U(C_t) = ln C_t and F(K_t, N_t) = K_t^α N_t^1–α, with d = 1(100% depreciation).

(a) Guess that the value function takes the form v(K_t) = A + B ln K_t, where A and B are undetermined constants.

(b) Substitute your guess for the value function on the right side of Equation (A-57), solve the optimization problem, and verify that your guess was correct.

(c) Solve for Aand Bby substituting your optimal solution from part (b) on the right side of Equation (A-57) and equating coefficients on the left- and right sides of the equation.

(d) Determine the solutions for K_t+1 and C_t as functions of K_t, and interpret these solutions.