Microeconomics I
Homework#2 Answer Key
Fall 2009
I. Multiple choice question
1
2
3
4
5
6
7
8
9
10
A
A
A
C
A
C
C
D
D
D
11
12
13
14
15
A
D
C
B
A
1) The assumption of completeness means that
A) the consumer can rank all possible consumption bundles.
B) more of a good is always better.
C) the consumers can rank all affordable consumption bundles.
D) all preferences conditions are met.
Answer: A
2) Measuring "y" on the vertical axis and "x" on the horizontal axis, convexity
of indifference curves implies that the MRS of "y" for "x"
A) decreasing as "x" increases.
B) is increasing as "x" increases.
C) is constant as "x" increases.
D) cannot be calculated for large levels of "x".
Answer: A
3) If two goods, "x" and "y", are perfect substitutes, then which of the following
best represents the utility function for the two goods?
A) U = x + y
B) U = x ∗ y
C) U = x2 + y2
D) Any of the above.
Answer: A
4) Clifford lives by the motto "Eat drink and be merry today, for tomorrow
doesn't matter." If today's consumption is represented by "x" and tomorrow's
consumption is represented by "y", then which of the following best represents
Clifford's utility function?
A) U = x - y
B) U = x/y
C) U = x
D) U = y
Answer: C
5) Assume the price of beer is $4, the price of pizza is $10 and the consumer's
income is $250. Which consumption bundle will NOT be the consumer’s choice?
A) A (5 Beers, 5 Pizzas)
B) B (0 Beers, 25 Pizzas)
C) C (25 Beers, 15 Pizzas)
D) None of the above bundles will be chosen.
Answer: A
6) The above figure shows Bobby's indifference map for juice and snacks. Also
shown are three budget lines resulting from different prices for snacks. Bobby's
demand for snacks is
A) unit elastic.
B) elastic.
C) inelastic.
D) perfectly elastic.
Answer: C
7) Suppose a graph is drawn to show a consumer's preferences for football
tickets and basketball tickets. The quantity of football tickets is measured on the
horizontal axis. If the price-consumption curve is horizontal when the price of
football tickets changes, then
A) football tickets are an inferior good.
B) the demand for football tickets is perfectly elastic.
C) the demand for football tickets is unit elastic.
D) the demand curve for football tickets will be horizontal.
Answer: C
8) An inferior good exhibits
A) a negative income elasticity.
B) a downward-sloping Engel curve.
C) a decline in the quantity demanded as income rises.
D) All of the above.
Answer: D
9) The above figure shows Larry's indifference map and budget lines for ham
and pork. Which of the following statements is TRUE?
A) Larry's demand curve for pork shifts rightward when his income
increases.
B) Larry's income elasticity of demand for pork is greater than zero.
C) Pork is a normal good.
D) All of the above.
Answer: D
10) If consumer income and prices increase by the same percentage
A) the consumer will buy more of both goods.
B) the consumer will buy more of both goods if they are both normal goods.
C) the consumer will buy less of both goods if they are both inferior goods.
D) the consumer's utility maximizing bundle stays the same.
Answer: D
11) The above figure shows Bobby's indifference map for soda and juice. B 1
indicates his original budget line. B2 indicates his budget line resulting from a
decrease in the price of soda. What change in quantity best represents his
substitution effect?
A) 3
B) 10
C) 15
D) 7
Answer: A
12) The above figure shows Bobby's indifference map for soda and juice. B 1
indicates his original budget line. B2 indicates his budget line resulting from a
decrease in the price of soda. What change in quantity best represents his income
effect?
A) 3
B) 10
C) 15
D) 7
Answer: D
13) The above figure shows Bobby's indifference map for soda and juice. B 1
indicates his original budget line. B2 indicates his budget line resulting from an
increase in the price of soda. From the graph, one can conclude that
A) Bobby views soda as an inferior good.
B) Bobby's demand for soda is perfectly inelastic.
C) Bobby views soda as a normal good.
D) the income elasticity of demand for soda is one.
Answer: C
14) Under which of the following conditions will there be no substitution bias in
the CPI?
A) Indifference curves are convex.
B) Indifference curves are L-shaped.
C) Indifference curves are linear.
D) Indifference curves are downward sloping.
Answer: B
15) Suppose the quantity of x is measured on the horizontal axis. If the income
consumption curve is vertical, then the income elasticity of demand for x is
A) 0.
B) 1.
C) -1.
D) There is not enough information to determine the income elasticity of
demand for x.
Answer: A
II. Problem
1)(Ch3 Q27)
Ann’s utility function is U=q1q2/(q1+q2). Solve for her optimal values of q1 and q2
as function of p1, p2, and Y.
Ans:
q22
U q2  q1  q2   q1q2


2
2
q1
 q1  q2 
 q1  q2 
q12
U q1  q1  q2   q1q2


.
2
2
q2
 q1  q2 
 q1  q2 
Equating MRS with relative price:
q22 P1

q12 P2
and substituting into the budget constraint:
1
 P 2
Y  P1q1  P2 q1  1  .
 P2 
Solving for q1:
q1 
and by symmetry:
Y
1
P1   P1 P2  2
q2 
Y
P2   P1P2 
1
2
.
2)(Ch4 PA4)A consumer faces prices for hot dogs and hamburgers of $1 each.
Consumption of the two commodities at various weekly income levels are shown
below.
(a) Use the information to sketch the income consumption curve on a graph.
(b) Draw the Engel curves for hot dogs and hamburgers.
Income
Hot Dogs
Hamburgers
$10
3
7
15
6
9
20
10
10
(c) What is the income elasticity of hot dogs for this consumer as income
increases from $10 to $15?
Ans:
4.
a.
See Figure 4.2
b. See Figures 4.3 and 4.4
c.
  (3/5)(10/3)  2
Figure 4.2
Figure 4.3
Figure 4.4
3)(Ch4 Q27,28)
Ryan has a constant elasticity of substitution (CES) utility function U=q1ρ+ q2ρ.
(a)Derive his Engel curve. (b)Derive Ryan’s demand curve for q1 and q2.
Ans:
(a)
The tangency condition is
p1 q21 

p2 q11 
which implies
1/1 
p 
p2 q2  q1  1 
 p2 
Substituting into the budget constraint:
.
p 
Y  p1q1  q1  1 
 p2 
1/1 
1/1 


 p1 

 q1  p1    


p2 



(b)
1/1 


p 
,
Y  q1  p1   1 


p2 



so
1/1 


 p1 

q1  Y  p1    


p2 



and by symmetry:
1/1 


 p2 

q2  Y  p2    


p1 



1
1