IS曲线的另一种推导方法

According to the permanent income hypothesis, consumption depends on the
present discounted value of income. An increase in the real interest rate will
aect the discounted value of income. Consider the case where the net present
value of your labor income is negatively related to interest rate
C = acY - bcr
where ac > 0 is the constant consumption propensity. bc > 0 is the sensitivity
to interest rate changes.
 Combining with the investment decision It = aIY - bIr, rederive the IS
curve.
 How and why does it dier from the original IS curve?
 How does this aect the eectiveness of the monetary policy?

IS曲线的数学表达式为I(R)=S(Y) ，它的斜率为负，这表明IS曲线一般是一条向右下方倾斜的曲线。一般来说，在产品市场上，位于IS曲线右方的收入和利率的组合，都是投资小于储蓄的非均衡组合;位于IS曲线左方的收入和利率的组合，都是投资大于储蓄的非均衡组合，只有位于IS曲线上的收入和利率的组合，才是投资等于储蓄的均衡组合。
第一象限是投资需求曲线i=i(r) 由既定利率r得出相应的i的值
第二象限是投资储蓄均衡即i=s 由前面的i的值可得出s的值
第三象限是储蓄函数曲线s=y-c(y) 为向右上方倾斜的曲线 表示储蓄是国民收入的增函数 可由s的值得出y的值
第四象限即产品市场均衡IS曲线 即由最初的既定利率r推出国民收入y的值