Econ 429
Sample Exam Problems
1. Does the utility function U(x,y) = x 2 + y 2 yield convex indifference
curves? Why or why not?
2. Victoria consumes only x and y. Her utility function is
U(x, y) = Ax 4 y 2 , A > 0. She is currently consuming 10 units of x
Homework 3 - Solutions
Dr. D. Boyd
Denison University
*
1. a. x =
Econ. 429
I
2I
, y* =
.
3Px
3Py
x *
< 0 The Marshallian demand for x is downward sloping.
b.
Px
x *
= 0 X and Y are neither gross substitutes nor gross complements.
Py
x*
> 0 X is a norm
Homework 2
Dr. D. Boyd
Denison University
Econ. 429
1. Consider the utility function U(x,y) = xy, with 0 < , < 1.
a. Determine the expressions for marginal utility, MUx and MUy.
b. Using your answers to part a, determine an expression for the marginal rat
Homework 7
Dr. D. Boyd
Denison University
Econ. 429
In these two problems, you will derive a perfectly competitive firms long run supply
curve using two different methods. In both cases, the production function governing the
firms production process is gi
Homework 7 - Solutions
Dr. D. Boyd
Denison University
Econ. 429
q2 !1/ 2 1/ 2
q2
*
1. a. K =
and L =
v w
w !1/ 2 v 1/ 2
1600
1600
*
! K * ! L*
b.
,
< 0 . The constant-output input demand functions are downward sloping.
! v !w
! K * ! L*
c.
,
> 0 . Capital
Econ 429
Sample Exam Problems
Solutions
1. MUx = 2x, MUy = 2y
So, MRS = MUx/MUy = x/y
MRS 1
= > 0 . Hence the utility function does not exhibit diminishing
x
y
MRS, so the indifference curves are not convex.
Then,
2.
This question really asks what is the
Homework 3
Dr. D. Boyd
Denison University
Econ. 429
1. Consider the specific Cobb-Douglas utility function U(x,y) = x1/3y2/3.
a. Determine the Marshallian demand functions by maximizing utility subject to the
budget constraint.
!x *
! x*
!x *
? Of
? Of
?
Homework 2 - Solutions
Dr. D. Boyd
Denison University
Econ. 429
! "1 #
" ! #1
1. a. MUx = !x y , MUy = ! x y
b. MRS =
!y
" x
c. y = U1/ ! x "# / !
d. MRS =
! 1/ " #( ! /" )#1
U x
"
e. MRS =
!y
" x
f.
! MRS
# y
="
< 0 . Yes, the utility function does exhib
Homework 5
Dr. D. Boyd
Denison University
Econ. 429
1. The production of foot long Twinkies is governed by the production function
q = f (S, F) = S1/ 2 F1/ 2 , where S = lbs. of sugar used, and F = lbs. of fat used. The price of
sugar is $3 per pound and