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: $$V=\int{0}^{\infty}e^{-dt}U(c{t})N(t)^{\frac{1}{2}}dt$$, 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 $$y=k^{n}$$, and the differential equation for capital stock is $$\dot{k}=f(k)-c-nk$$.