Public Sector Economics

1
Public Sector Economics

• Social Security, Voting, and Chain Letters

2
Voting Version

• elderly are not a majority, or even a majority of
  a majority
• US aged 65 are 13 of population
• approaching 20 in Europe
• coalition with the poor?
• Browning coalition with the middle-aged
• equal numbers of young, middle-aged, and old
• election between doing nothing or taxing T
  forever to finance paygo SS for the old
• with r 0, old gain 2T, middle-aged gain T,
  young gain nothing
• with r gt 0 (but not too large), old and
  middle-aged gain and young lose

3
Voting Version (contd)

• subgame perfection
• young and middle-aged both favor temporary
  suspension
• Kotlikoff et al use Folk Theorem

4
Efficiency Version

• just young and old
• taxes are proportional to aggregate labor income,
  which grows at rate g gt 0
• budget time series is T, (1g)T, (1g)2T, etc.
• initial old gain T
• initial young lose T - (1g)T/ (1r) (r-g)T/
  (1r)
• later young lose the same, except scaled by
  growth factor
• this loss is a gain if r lt g

5
Efficiency Version (contd)

• although r may appear less than g, the economy is
  in fact dynamically efficient because the
  business sector creates more resources than it
  uses
• even if r lt g, this analysis ignores dwcs of
  taxes and spending
• more general condition is
• g gt ??(1?)r/(1-?)