HW XXXXXXXXXXExternalities
XXXXXXXXXXFind a quote from a famous public figure (including ancient or modern
prophets) regarding the proper role of government. Relate the content of the
quote to notions that we have discussed in class, such as externalities or public
goods.
XXXXXXXXXXThis question simply illustrates two ways in which wealth transfers can
increase total utility. In a certain society, individuals are either rich (i.e. wealth
?? = 500) or poor (i.e. ?? = 100). However, the government transfers ?? from the
ich to the poor. After this redistribution, the utility (to any individual) of
consumption ?? is given by ??(??) = √??.
a. (+4) Suppose that individuals are all altruistic, in the sense that they
each seek not to maximize ?? , but to maximize the total welfare ?? =
500√500 − ?? + 500√100 + ?? of the 1000 members of society. What
level ???? of transfer does each prefer in that case? How high is utility in that
case for rich and poor individuals?
. (+4) Suppose that life is sufficiently uncertain, one year to the next, that
each individual perceives an equal probability of being rich or poor next
year. In that case, what level ??∗ of transfer would maximize expected
utility ??[??(??; ??)] = .5√500 − ?? + .5√100 + ?? ? How high is expected
utility in that case?
XXXXXXXXXXConsider an apartment with three roommates, Abe (??), Ben (??), and
Chris (??), who can play loud music or not. Abe and Ben like loud music, but Chris
hates it; if music is played, the three utilities are 10, 4, and -12 (respectively), and
otherwise each receives zero utility. Like many roommates, the three hardly see
each other; if one wishes to bargain with another over anything, he must pay a
cost of 4, reflecting the need to coordinate schedules. If he wishes to hold a
meeting with both of his roommates, he must pay a coordination cost of 8. For
each scenario below, tell whether music plays or not, and who
ibes whom, for
how much. (There will typically be a range of possible
ibes, if any, rather than
a specific
ibe amount).
a. (+2) Abe owns the “right” to listen to music (or not).
. (+2) Ben owns the “right” to listen to music (or not).
c. (+2) Chris owns the “right” to listen to music (or not).
d. (+4) How (if at all) would your answers to parts (a) through (c) change
if coordination with roommates were not costly?
HW XXXXXXXXXXExternalities