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
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.)
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。