Multi-period Consumption II

Life Cycle model

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

Japanese Saving

The saving rate in Japan is more than 5 times the U.S. saving rate.

• 1. long life expectancy and long retirement periods

  2. large proportion of population is middle-aged

  3. fast growing income means current workers save more than retirees dissave

  4. high housing and land prices require lots of saving for down payments

  5. strong bequest motive requires a high saving rate

Changes in the Real Interest Rate

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

Supply of Labor

• • substitution and income effects