Proofs to review for midterm 1:
1. A preference relation on X is monotone if x; y 2 X and y > x implies
y
x: A preference relation
on X is strongly monotone if x; y 2 X,
y x and y =
6 x implies that y x: (MWF def 3.B.2).
(a) Prove that if
is strongly mono
Suggested solution to review midterm 1
Question 1 (30 points) (Consumer Theory)
Toby consumes two goods x1 and x2 : The price of good 1 is p1 > 0; the price of
good 2 is p2 = 1: His income is m = 120. Tobys preferences for the two goods are
represented by
Midterm 1
Question 1 (30 points)
Mason consumes two goods x1 and x2 : The price of good 1 is p1 > 0; the
price of good 2 is p2 = 1: His income is w. Masons preferences for the
two goods are represented by the utility function
u(x1 ; x2 ) = f (x1 ) + x2 :
Econ6201, Problem set 1
Let X = RL
+ in all questions, unless otherwise noted.
In addition to the relevant material on the budget set, preferences and utility, you
might nd useful reviewing logarithm rules, derivative rules including the chain rule and
LH