As shown in the figure. This is a finite-period deterministic RBC model with lumpsum tax. For simplification, I set initial value B(-1) = 0, terminal value B(T) = 0, Wage W_t is fixed all the time. Interest rate R_t and wage tax Tau^w_t are fixed too. All parameters be calibrated. No government tranferring, G_t = 0 all the time.

Can Dynare numerically solve the model to find the optimal path for consumption? Thanks for your attention.

Yes, Dynare can do that type of perfect foresight simulation.