Student Number:
Name:
Quiz 2 A
1. Consider the utility function U(x,y)=3x2+5y with MUx=6x and MUy=5
a) (1 mark) Is the assumption that ‘more is better’ satisfied for both goods? Explain
Yes, since the marginal utility is greater that zero for both goods, increasing consumption of
either good will increase total utility
b)
(2 marks) what is MRSx,y for this utility function? Is the MRSx,y diminishing, constant, or
increasing as the consumer substitute x for y along an indifference curve?
MRSx,y=MUx/MUy=6x/5
MRSx,y is increasing as the consumer substitutes towards more x and less y since x appears in
the numerator of MRS
2. Olivia likes to eat both apples and bananas. At the grocery store, each apple costs P A and each
banana cost PB. Olivia’s utility function for apples and bananas is given by U(A,B)=6
where MUA=3 B A and MUB=3
AB
A B . If Olivia has income of I to spend on apples and
bananas, how many of each should she buy to maximize her utility?
a) (5 marks) Derive the demand functions for apples and bananas in terms of PA, PB and I .
MU A PA

MU B PB
3 B A
3 AB

PA
PB
P
B
 A
A PB
B=
PA
A
PB
Now plug this into the budget constraint to find the optimal B
PB B  PA A  I
PB
A
I
2 PA
PA
A  PA A  I
PB
B
I
2 PB
b) (2 marks) If PA=0.2, PB=0.25 and I=4, please derive the optimal consumption bundle.
A
I
2 PA
B
B=8
A=1.25*8=10
I
2 PB