二、簡答題
1. Consider a Ramsey model in which the social planner weighs future consumption according to the number of people who will be alive in the following manner: \( V = \int_{0}^{\infty} e^{-\theta t} U(c_t) N(t)^{\pi} dt \), where \( 0 < \pi < 1 \). Population grows exogenously at rate \( n > 0 \), \( \dot{N} = nN \). At time zero, population is \( N_0 \). The rest of the problem is standard. There is no technological progress. The deprecation rate is zero. The production function is \( y = k^{\alpha} \), and the differential equation for capital stock is \( \dot{k} = f(k) - c - nk \).