Econ 100A: Fall 2016
Intermediate Microeconomics
Problem Set 3
The questions below are based on Ch. 5-7
1. If a consumer has a utility function u (x1 ; x2 ) = x1 x42 , what fraction of her income will
spend on good 2?
2. For what kind of preferences (or u
Solution of Problem Set 1
Question 1
(a) The function is given by
x2
f (x) =
x4 :
The FOC is given by
df (x)
=
dx
3
2x
4 (x ) = 0:
Thus, x = 0:
(b) The function is given by
x2 + x:
f (x) =
The FOC is given by
df (x)
=
dx
2x + 1 = 0:
f (x; y) =
x2
Thus, x
Econ 100A: Fall 2016
Intermediate Microeconomics
Problem Set 5
The questions below are based on Ch. 12.
1. A risk-averse individual is oered a choice between a gamble that pays $1000 with a probability of 25% and $100 with a probability of 75%, or a payme
Solution of Problem Set 3
Question 1
The Lagrangian of the problem is given by
4
L = x1 (x2 )
(p1 x1 + p2 x2
@L
4
= (x2 )
p1 = 0
@x1
@L
3
= 4x1 (x2 )
p2 = 0
@x2
@L
= p1 x1 p2 x2 + m = 0
@
m)
From the rst two lines we get
4
(x2 ) =p1
x1
3
=
4x1 (x2 ) =p2
=
Practice Exam Midterm 1: ECON 100A
Instructions. You have 65 minutes to solve these questions. To get full credits you need to provide a
detailed justication of your claims.
1. Suppose a consumer buys clothing for the heat it provides and that each unit o
Econ 100A: Fall 2016
Intermediate Microeconomics
Problem Set 2
The questions below are based on Ch. 2-5.
1. Joe Bob has a utility function given by u (x1 ; x2 ) = x21 + x22 + 2x1 x2 :
(a) Compute Joe Bobs marginal rate of substitution.
(b) Joe Bobs cousin
Solution of Practice Midterm Exam 1
Question 1
(a) The maximization problem is given by
maxH;C fU (H; kC) = min fH; kCg
subject to ph H + pc C = mg :
Then,
H = kC
and ph H + pc C = m:
It follows that C = m= (ph k + pc ) and H = km= (ph k + pc ) :
(b) @C =