问答题 关于消费函数的一种观点是,工人的边际消费倾向高,而资本家的边际消费倾向低。为了说明这种观点的含义,假设一个经济,所有的工资收入都用于消费,而所有资本收入都用于储蓄。证明:如果生产要素赚到了自己的边际产量,这个经济就达到了黄金律的资本水平。(提示:从储蓄等于投资这个恒等式开始。然后利用投资正好足够维持折旧和人口增长的稳定状态条件,以及在这个经济中储蓄等于资本收入这一事实。)
   One view of the consumption function is that workers have high propensities to consume and capitalists have low propensities to consume. To explore the implications of this view, suppose that an economy consumes all wage income and saves all capital income. Show that if the factors of production earn their marginal product, this economy reaches the Golden Rule level of capital. (Hint: Begin with the identity that saving equals investment. Then use the steady-state condition that investment is just enough to keep up with depreciation and population growth, and the fact that saving equals capital income in this economy.)
【正确答案】令k=K/L代表人均资本。因此:
   △k=sf(k)-(δ+n)k
   如果生产要素都获得它们的边际产量并且所有的资本收入都被储蓄起来,则人均储蓄等于MPK×k。将它代入上式,得:
   △k=MPK×k-(δ+n)k
   在稳定状态下,△k=0。所以有:
   MPK×k=(δ+n)k或MPK=(δ+n)
   即:    MPK-δ=n
   也就是说,在这个经济的稳定状态中,资本的净边际产出(MPK-δ)等于产出的增长率n,所以,这个经济已经达到了资本积累的黄金规则水平。
【答案解析】