Intermediate Microeconomic Analysis (Econ 173)
Drake University, Fall 2009
William M. Boal
Signature:
Printed name:
MIDTERM EXAMINATION #2 VERSION B
“Consumers and Demand”
October 5, 2009
INSTRUCTIONS: This exam is closed-book, closed-notes, and calculators are NOT permitted.
Point values for each question are noted in brackets.
I. MULTIPLE CHOICE: Circle the one best answer to each question. Feel free to use
margins for scratch work [2 pts each—18 pts total]
assumption of "diminishing marginal rate of
substitution," bundle C must be
a. equally preferred to bundle A.
b. equally preferred to bundle B.
c. equally preferred to bundle D.
d. equally preferred to bundle E.
e. more preferred than bundle B.
f. more preferred than bundle D.
The next two questions refer to the
following graph of consumer bundles.
7
B
A
6
Food
5
E
4
C
3
D
2
1
0
0
1
2
3
4
5
6
7
Other Goods
(1) According to the assumption of
"monotonicity" or "more is better," which
bundle must be preferred by any consumer
to bundle E?
a. Bundle A only.
b. Bundle B only.
c. Bundle C only.
d. Bundle D only.
e. Bundles A, B, and C.
f. All of the above.
g. None of the above.
(2) Suppose that bundles A and D are
equally preferred. According to the
(3) Which utility function below violates the
assumption of "monotonicity" or "more is
better"?
a. U(q1,q2) = 4 q1 q2 .
b. U(q1,q2) = 4q2 – 5q1 .
c. U(q1,q2) = –4q1–1/2 – 5q2–1/2 .
d. U(q1,q2) = 4 q14 q25 .
e. U(q1,q2) = 4 q11/5 + 5 q21/2 .
f. U(q1,q2) = (–4/q1) + (–5/q2) .
Intermediate Microeconomic Analysis (Econ 173)
Drake University, Fall 2009
A
Health
care
D
B
C
Other goods
(4) Which indifference curve above violates
the assumption of monotonicity?
a. Curve A.
b. Curve B.
c. Curve C.
d. Curve D.
e. All of the above.
f. None of the above.
The next question refers to the following
graph of four possible indifference curves.
D
C
Health
care
B
A
Other goods
(5) Which indifference curve above violates
the assumption of diminishing marginal rate
of substitution?
a. Curve A.
b. Curve B.
c. Curve C.
d. Curve D.
e. All of the above.
f. None of the above.
(6) Which utility function below violates the
assumption of "diminishing marginal rate of
substitution"? Assume that q1 > 4 and that
q2 > 5.
a. U(q1,q2) = (q1–2)(q2–3) .
b. U(q1,q2) = q12 q23 .
c. U(q1,q2) = –2/q1 – 3/q2 .
d. U(q1,q2) = 2q1 + 3q2 .
e. All of the above.
f. None of the above.
The next question refers to the following
graph of a budget line.
Housing
The next question refers to the following
graph of four possible indifference curves.
Midterm Examination #2 Version B
Page 2 of 9
Other goods
(7) In the graph above, the shift in the
budget line could be caused by
a. an increase in income.
b. a decrease in income.
c. an increase in the price of housing.
d. a decrease in the price of housing.
e. an increase in the price of other goods.
f. a decrease in the price of other goods.
Intermediate Microeconomic Analysis (Econ 173)
Drake University, Fall 2009
The next two questions refer to the
following graph of a consumer's budget line
and indifference curves. Suppose the
consumer is currently at bundle A for some
reason.
Other
goods
= q1
A
Energy = q2
Midterm Examination #2 Version B
Page 3 of 9
(8) This consumer could enjoy higher utility,
without increasing total spending, by
a. purchasing less energy and more other
goods.
b. purchasing more energy and fewer other
goods.
c. purchasing less energy and fewer other
goods.
d. any of the above.
e. none of the above.
(9) Let MU1 denote the marginal utility of
other goods and MU2 the marginal utility of
energy for this consumer. Let p1 denote the
price of other goods and p2 denote the price
of energy. At bundle A,
a. MU2 = MU1 and p2 = p1 .
b. MU2/MU1 = p2/p1 .
c. MU2/MU1 < p2/p1 .
d. MU2/MU1 > p2/p1 .
e. cannot be determined from information
given.
II. SHORT ANSWER: Please write your answers in the boxes on this question sheet. Feel free
to use margins for scratch work.
(1) [Budget line: 6 pts] Suppose the price of food is $3 and the price of other goods is $2.
Suppose a consumer has $120 to spend on these two goods. Consider the consumer's budget
line, with food on the vertical axis and other goods on the horizontal axis.
a. What is the budget line's intercept on the food axis?
units of food
b. What is the budget line's intercept on the other-goods axis?
c. What is the slope of the budget line with food on the vertical
axis and other goods on the horizontal axis?
units of
other goods
Intermediate Microeconomic Analysis (Econ 173)
Drake University, Fall 2009
Midterm Examination #2 Version B
Page 4 of 9
(2) [Slutsky equation: 8 pts] Suppose Consumer X buys a bundle of consumer goods including
10 pounds of hamburger per month. Then the price of hamburger rises from $2 to $4.
a. Assume that the partial derivative of Consumer X's demand
pounds
for hamburger with respect to the price of hamburger is –3.
Compute the approximate total decrease in hamburger
purchased by Consumer X due to the price increase.
b. How much would Consumer X's income have to increase so
$
that Consumer X could still just afford the old bundle?
c. Assume that the partial derivative of Consumer X's demand
pounds
for hamburger with respect to income is 0.025. Compute the
approximate decrease in hamburger purchased due to the
income effect alone.
d. Compute the approximate decrease in hamburger purchased
pounds
due to the substitution effect alone.
Other goods
(3) [Substitution and income effects: 12 pts] Consider the indifference-curve diagram below.
Assume the consumer has $30 income.
10
9
8
7
6
5
4
3
2
1
0
Old budget line
New budget
line
Parallel to new
budget line
0
1
2
3
4
5
6
7
8
9 10
Energy
a. What was the price of energy on the old budget line?
b. Given the old budget line, how much energy does the
consumer demand?
c. What is the price of energy on the new budget line?
d. Given the new budget line, how much energy does the
consumer demand?
e. Compute the change in quantity of energy demanded due to
the substitution effect:  qsub .
f. Compute the change in quantity of energy demanded due to
the income effect:  qinc .
$
units
$
units
units
units
Intermediate Microeconomic Analysis (Econ 173)
Drake University, Fall 2009
Midterm Examination #2 Version B
Page 5 of 9
(4) [Cost-of-living indexes: 6 pts] Suppose we are given the following data on prices and
quantities consumed of food and other goods.
Food
Price
$5
$5
Old period
New period
Other goods
Price
Quantity
$5
4 units
$8
5 units
Quantity
6 units
15 units
a. Compute the Laspeyres cost-of-living index in the new period.
b. Compute the Paasche cost-of-living index in the new period.
c. Give a formula for the Fisher cost-of-living index in the new
period.
(5) [Consumer welfare: 6 pts] The following graph shows the ordinary and compensated
demand for a good.
$9
$8
$7
Price
$6
$5
Ordinary demand
$4
$3
Compensated
demand
$2
$1
$0
0
10
20
30
40 50
60
70
80
90
Quantity
Suppose the price of the good rises from $1 to $7.
a. Are consumers better off or worse off?
b. Compute the change in consumer surplus.
$
c. Compute the compensating variation in income.
$
Intermediate Microeconomic Analysis (Econ 173)
Drake University, Fall 2009
Midterm Examination #2 Version B
Page 6 of 9
(6) [Price elasticity of demand: 10 pts] Suppose the price elasticity of demand for electricity is
–1.2, and the electric utility raises its rates by 5 %.
a. Is the demand for electricity elastic or inelastic ?
b. Will the quantity demanded of electricity increase or
decrease?
c. By about how much?
%
d. Will the revenue received by the electric utility increase or
decrease?
e. By about how much?
%
(7) [Income elasticity of demand: 10 pts] Suppose that a consumer's income rises by 5%, and the
income elasticity of demand for entertainment is 1.8 .
a. Is entertainment an inferior good, a necessary good, or a
luxury or superior good?
b. Will the quantity demanded of entertainment increase or
decrease?
c. By about how much?
%
d. Will the share of the consumer's budget devoted to
entertainment increase or decrease?
e. By about how much?
%
Intermediate Microeconomic Analysis (Econ 173)
Drake University, Fall 2009
Midterm Examination #2 Version B
Page 7 of 9
IV. PROBLEMS: Please write your answers in the boxes on this question sheet. Show your
work and circle your final answers.
(1) [Budgets and choice: 12 pts] A consumer has the following utility function:
U(q1,q2) = q12 (q2 + 5), where q1 denotes the quantity of hamburgers and q2 denotes the
quantity of other goods. The price of hamburgers is $6 and the price of other goods is $5. The
consumer has $155 in income to spend on these items.
a. [4 pts] Give an equation for the consumer’s budget line. The variables q1 and q2
should be the only unknowns.
b. [4 pts] Find a formula for the consumer’s marginal rate of substitution of other goods for
hamburgers—that is, the |slope| of the consumer’s indifference curve with hamburgers on
the vertical axis and other goods on the horizontal axis. The variables q1 and q2 should
be the only unknowns. Circle your final answer.
c. [4 pts] Solve for the quantities of hamburgers (q1*) and other goods (q2*) that this
consumer will choose. Circle your final answers.
Intermediate Microeconomic Analysis (Econ 173)
Drake University, Fall 2009
Midterm Examination #2 Version B
Page 8 of 9
(2) [Individual demand: 9 pts] A consumer has the following utility function:
U(q1,q2) = (q1  2) q2 , where q1 denotes the quantity of energy and q2 denotes the quantity of
other goods.
a. [3 pts] Find a formula for the consumer’s marginal rate of substitution of other goods for
energy—that is, the |slope| of the consumer’s indifference curve with energy on the
vertical axis and other goods on the horizontal axis. The variables q1 and q2 should be
the only unknowns. Circle your final answer.
Let p1 denote the price of energy and let p2 denote the price of other goods. Let I denote
the consumer's income.
b. [3 pts] Solve for the consumer's demand function for energy—that is the formula
showing q1* as a function of p1, p2, and I. Show your work and circle your final
answer. [Hint: check that your answer is homogeneous of degree zero.]
c. [3 pts] Solve for the consumer's demand function for other goods—that is the formula
showing q2* as a function of p1, p2, and I. Show your work and circle your final
answer. [Hint: check that your answer is homogeneous of degree zero.]
Intermediate Microeconomic Analysis (Econ 173)
Drake University, Fall 2009
Midterm Examination #2 Version B
Page 9 of 9
III. CRITICAL THINKING: Answer just one of the questions below (your choice). [3 pts]
(1) Suppose a consumer's demand function for good 1 takes the following form:
q1 *  27 p1 p2 I  ,
where p1 is the good's own price, p2 is the price of another good, and I is the consumer's
income. If the demand for good 1 is homogeneous of degree zero in all prices and income,
then what must be the value of the sum of the exponents: ( + α + ) ? Justify your answer
with algebra.
(2) Suppose a consumer normally buys 20 gallons of gasoline per month at a price of $3. Which
would this consumer prefer: a reduction in price from $3 to $1, or an increase in income of
$40 ? Justify your answer with a graph of a demand curve.
Circle the question you are answering and write your answer below. Full credit requires good
grammar, accurate spelling, and correct reasoning.
[end of exam]