ECON3010 Advanced Microeconomics
Metin Uyanık
Tutorial #2 Questions
Semester 1, 2021
1.
A binary relation
R
on a set
X
is called
reflexive
if
xRx
for all
x
in
X
. The relation
R
is
transitive
if
xRy
and
yRz
implies
xRz
for all
x, y, z
in
X
. The relation
R
is called
complete
if
xRy
or
yRx
for all
x, y
in
X
. Which of the following would you expect to be
reflexive? transitive? complete?
(a)
xRy
is interpreted as ”
x
is less than or equal to
y
”.
(b)
xRy
is interpreted as ”
x
is heavier than
y
”.
(c)
xRy
is interpreted as ”
x
is the mother of
y
”.

2.
Jack strictly prefers wine (
w
) to beer (
b
), but is indifferent between beer and coke (
c
).
(a)
Write down a preference ordering
%
(representing at least as good as) for Jack that is
complete and transitive and respects what is written above about his strict preference of
wine over beer and his indifference between beer and coke.
(b)
Define the strict preference (better than) by
x
y
iff
x
%
y
and not
y
%
x
. What is
included in
?