Consider the following finite horizon economy. A decision maker has preferences: \sum_{t=0}^T \beta^t ln(c_t) with \beta < 1, U'(c) > 0, U''(c) < 0, \lim_{c \to 0}U'(c) = + \infty. The production technology is y_t = k_t^\alpha for \alpha < 1. The resource constraint is y_t = c_t + k_{t+1}. Find a solution to the social planner' problem by guessing and verifying that it takes the form k_{t+1} = \gamma_tk_t^\alpha for t = 0, ..., T-1 with unknown \gamma_t and \gamma_T = 0