Part 3 – Public Expenditure:
Social Insurance and Income Maintenance
Chapter 12 – Income Redistribution:
Conceptual Issues
1.
Utilitarianism suggests that social welfare is a function of individuals’ utilities.
Whether
the rich are vulgar is irrelevant, so this part of the statement is inconsistent with
utilitarianism.
On the other hand, Stein’s assertion that inequality
per se
is unimportant is
consistent with utilitarianism.
2.
a.
To maximize W, set marginal utilities equal; the constraint is I
s
+ I
c
= 100. So, 400
- 2I
s
= 400 - 6I
c
, substituting I
c
= 100 - I
s
gives us 2I
s
= 6 (100 – Is).
Therefore, I
s
=
75, I
c
= 25.
b.
If only Charity matters, then give money to Charity until MU
c
= 0 (unless all the
money in the economy is exhausted first). So,400-6 I
c
= 0; hence, I
c
= 66.67.
Giving any more money to Charity causes her marginal utility to become
negative, which is not optimal.
Note that we don’t care if the remaining money
($33.33) is given to Simon or not.
If only Simon matters, then, proceeding as above, MU
s.
0 if I
s
= 100; hence, giving
all the money to Simon is optimal.
(In fact, we would like to give him up to
$200.)
c.
MU
s
= MU
c
for all levels of income.
Hence, society is indifferent among all
distributions of income.
3.
Suppose the government is initially providing an in-kind benefit of 10 units of free public
transportation, worth $2 each, so the cost of the subsidy is $20.
Without the subsidy,
income is $40.
With no subsidy, the consumer maximizes utility at point A, and with an
in-kind benefit of 10 units of free public transportation, the consumer maximizes utility at
point B.
A cash subsidy equal to $20 would allow the consumer to reach point B as well,
so the government could convert an in-kind subsidy valued at $20 to a cash subsidy of
$20 and leave people equally well off.