EC 501: Problem Set 1, Solutions
1. (a) The equation of the line is
212 32
F 32
=
.
C 0
100 0
This simplies as follows:
F 32
180
=
C
100
F 32 =
9
C
5
9
F = 32 + C.
5
(b) F = C when
9
F = 32 + F
5
4
F = 32 =
5
F = 40.
1
2. Dierentiating u(y) = y 2 :
u (y)
EC 501: Problem Set 2, Solutions
1. (a) To nd the compensated demand functions, we need to solve the
problem:
M inimize
E = pa A + pb B
1
1
A 2 B 2 = U.
subject to
The Lagrangian for this problem is
1
1
L = pa A + pb B + U A 2 B 2 .
The rst order conditio
EC 501: Problem Set 1
(Due in class on Tuesday, September 9)
1.
(a) Find the relationship between the Centigrade (C) and Fahrenheit (F) temperature scales,
given that (i) the relationship is linear, (ii) water freezes at C = 0 or F = 32, and (iii) water
b
EC 501: Problem Set 5
(Due in class on Tuesday, October 16)
1.
The Widget Co. can produce widgets according to the formula:
q = 5K L
where q is the output of widgets, and K, L are the quantities of capital and labor used.
(a) Are there constant, increasin
EC 501: Problem Set 3, Solutions
1. This follows from the Generalized Engels Law, that the weighted average
of income elasticities must be equal to 1:
n
i i = 1.
i=1
Now a luxury is a good for which i > 1. So if a consumer consumes
only two goods, and the
EC 501: Problem Set 9, Solutions
1. (a) Under perfect competition in the long run, each rm will produce at
the minimum point of the AC curve. Now
AC =
200
+ 0.5q
q
and so AC is at a minimum where
dAC
200
= 2 + 0 .5 = 0
dq
q
q = 20.
When q = 20, AC = 20, s
EC 501: Problem Set 7, Solutions
1. (a) We can nd the ppf by solving the problem:
M aximize Y = 3Ly
subject to X = 3Lx
and Lx + Ly = 66.
In this case, because there is only one factor of production, the constraints
combined become the ppf:
Lx + Ly = 66
Y
EC 501: Problem Set 2
(Due in class on Tuesday, September 25)
1.
Adam's utility function is U = A1/2 B1/2 where A, B represent the number of apples and
bananas respectively that he consumes.
(a) Find Adams compensated demand functions.
(b) Write down Adam
EC 501: Problem Set 1
(Due in class on Tuesday, September 18)
1.
Jack Sprat will eat no fat; his wife will eat no lean. Suppose lean and fat are the only
two goods Jack and his wife consume. Find their (separate) utility functions and draw their
indiffere
EC 501: Problem Set 1, Solutions
1. Suppose Jacks utility function is UJ (LJ , FJ ), where LJ is the amount of
lean and FJ is the amount of fat he consumes. Since he never
actually eats any fat, his utility function must be
UJ (LJ , FJ ) = LJ ,
or any pos
EC 501: Problem Set 4, Solutions
1. (a) A simple way to think about this is to treat Joes income as pa A0
and then nd the demand functions in the usual way. Since the utility
function is Cobb-Douglas, with equal coecients for the two goods, we
can write d
1
Chapter 2
Theory of Consumer Behavior
Consumers or households are the economic agents whose primary economic activity is
consumption of goods and services. This chapter will be concerned with how micro-economists model the
behavior of households. The ap
EC 501: Problem Set #3
(Due in class on Tuesday, October 2)
1. Show that, if a consumer consumes just two goods, they cannot both be luxuries.
2. When the price of gasoline is $1 per gallon, you consume 1,000 gallons per year. Then two
things happen: (1)
Chapter 4
Extensions of Consumer
Theory
In the theory of consumer behavior, our starting point has been the consumers
income or budget constraint, which she then must choose how to spend in order
to maximize her utility. But many decisions a consumer face
EC 501: Problem Set 6, Solutions
1. (a) To solve this problem, we use a discrete version of the formula
dpd
=
dT
We use
s
s
.
d
s
T.
s d
Substituting the values in this case, we get
pd =
pd =
0.8
1.80 = 0.576.
0.8 + 1.7
Therefore the new demand price is
EC 501: Problem Set 5, Solutions
1. (a) To test for returns to scale, suppose capital and labor inputs are xed
at K0 , L0 and output is
1
3
4
4
q0 = 5K0 L0 .
Now lets change capital and labor inputs by a factor to K0 , L0 and
see what happens to output. O
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Chapter 3
Applications of Consumer
Theory
The theory of consumer behavior gives us a powerful tool to analyze a broad
range of issues beyond the obvious one of understanding how consumers might
respond to price changes, i.e. estimating demand functions as
EC 501: Problem Set 8
(Due in class on Tuesday, November 13)
1.
Liz Baylor has a $100,000 ring and keeps $100,000 cash in a checking account that pays no
interest. If the ring is stolen, Liz will be forced to replace it at a cost of $100,000. The chance o
EC 501: Problem Set 9
(Due in class on Tuesday, November 20)
1.
The demand for bread in Munchkinland is given by
Q = 300-5P
where Q: quantity, P: price. The long run cost function of each bakery is given by
C=200+.5q2
a. If the bread industry is perfectly
EC 501: Problem Set 8, Solutions
1. Without insurance, Lizs expected utility is
(EU )0 =
1
99
U (0) +
U (100, 000).
100
100
With insurance at a premium of her expected utility is
(EU )1 = U (100, 000 ).
The largest premium she would be willing to pay woul
EC 501
Final Exam
December 18, 2010
Answer all questions, showing all your work. Try to use diagrams wherever
possible. Time allowed: 2 hours. Good luck! (Each question is worth 20 points.)
1.
The demand for widgets is given by
Q = 100 P.
The cost of prod
Answers to End-of-Chapter
Exercises
Chapter 2: Theory of Consumer Behavior
2I
5pg ,
1. (a) G =
3I
5pM
M=
(b) M = 10,
G = 40.
(c) M = 10,
.
G = 80.
2. X =
I
px +py .
3. False.
4. See Chapter.
5. (a) x =
Ipx
2px ,
(b) x = 2,
(c)
x
A
I+px
2py .
y = 6.
= 1.25
EC 501: Problem Set 2
(Due in class on Tuesday, September 16)
1.
Jack Sprat will eat no fat; his wife will eat no lean. Suppose lean and fat are the only
two goods Jack and his wife consume. Find their (separate) utility functions and draw their
indiffere
Chapter 9
Monopoly and Market Power
The optimality theorems of welfare economics require some stringent conditions
in order to hold, conditions that do not always hold in practice. Starting with
this chapter, we will be looking at various ways in which th
Chapter 7
General Equilibrium and
Welfare Economics
General equilibrium analysis is the study of the whole economy as an aggregate
of all the individual markets, taking into account the relationships between all
the markets. We have been studying individu
EC 501: Problem Set 7
(Due in class on Tuesday, November 6)
1.
In the economy of Ricardia, two consumer goods, X and Y, are produced from a single
factor input, labor, according to the production functions:
Y = 3Ly
and
X = 3Lx
where Ly and Lx are the quan
EC 501: Problem Set 11
(Due in class on Tuesday, December 11)
1.
The Johnsville Co. produces pipe insulation at a cost of $10 per ton. It is also known that for
every ton of insulation it produces it also vents into the air one ounce of asbestos fibers, w
EC 501: Problem Set 10
(Due in class on Tuesday, December 4)
1.
Bigfoot Corp. manufactures shoes in the small town of Here. It is the only employer in town, and
Here is too far from anywhere else for townspeople to work elsewhere. Men and women are equall
EC 501: Problem Set 11, Solutions
1. (a) If Johnsville is not regulated, it will ignore the externality and simply
maximize its prot, using the monopoly solution. Now demand can be
written as
1
Q,
P = 22
120
1
then M R = 22 Q.
60
Setting MR=MC to maximiz