a. Yt = Kt^.5 * Nt^.5
ln(Yt) = .5ln(Kt) + .5ln(Nt)
dYt/dt/Yt = .5dKt/dt/Kt + .5dNt/dt/Nt
gY = .5gK + .5gN
b. gY = .02
gK = .04 b/c N=1, whose growth rate = 0
c. Kt/Yt
ln(Kt/Yt) = ln(Kt) - ln(Yt) = .5ln(Kt) - .5ln(Nt)
dln(Kt/Yt)/dt = .5dKt/dt/Kt - 0 = .02
d(Kt/Yt)/dt = exp(.02)
d. impossible
b/c KT/YT = exp(.2)(T-t)
which implies that Kt is explosive in the infinite time. the economy can grow at .02 in finite time but cannot maintain the growth rate forever不好意思 我不知道你指哪本宏观教材 上面是我随手帮你做的A里面的是用到微积分的知识吗？具体是什么微积分之后得什么？x = x(t)d ln(x(t)) / dt = (d x(t)/dt ) / x = (dx/x) /dt 也就是微小时间段里x的百分比变化 一般我们把这个记作增长率 g_x你如果没有学过微积分 需要看一下ln的求导和链式法则