three periods: young, middle-aged, retired (each period is 20 years)
income per year: $40,000 when young, $120,000 when middle-aged, $20,000 when retired
let the real interest rate equal 0
PVLR = (20)(40,000) + (20)(120,000) + (20)(20,000)
PVLR = $3,6000,000
Suppose a person wants to consume a constant amount, c, each year:
60c = PVLR
c = $60,000
saving:
young = -$20,000 a year
middle-aged = $60,000 a year
retired -$40,000 a year
The saving rate in Japan is more than 5 times the U.S. saving rate.
long life expectancy and long retirement periods
large proportion of population is middle-aged
fast growing income means current workers save more than retirees dissave
high housing and land prices require lots of saving for down payments
strong bequest motive requires a high saving rate
when r rises, one point on the old budget line is also on the new budget line: the no-borrowing, no-lending point
A rise in the real interest rate makes future consumption cheaper relative to current consumption. This is a substitution effect. Future consumption goes up, current consumption goes down, and saving rises. There is only a substitution effect (no income effect) if a person was planning to consume at the no-borrowing, no-lending point.
An income effect occurs as well if a person was planning to consume at a different point than the no-borrowing, no-lending point.
if the person originally planned to be a lender: a rise in the real interest rate raises future income so current consumption rises (the substitution effect works on the opposite direction)
if the person originally planned to be a borrower: a rise in the real interest rate reduces future income so current consumption falls (same direction as the substitution effect)
substitution and income effects for a lender
substitution and income effects