SOLUTIONS MANUAL
** All Chapters included
** Solutions to self-assessment exercises
** Solutions to end-of-chapter exercises
,Table of Contents are given below
Chapter 1 - Introduction (Solutions not available for Ch.1)
Chapter 2 - Consumer Preferences and Utility
Chapter 3 - Consumer Choice
Chapter 4 - Substitution and Income Effects
Chapter 5 - Measuring Welfare Changes
Chapter 6 - Choice under Uncertainty
Chapter 7 - Production Functions
Chapter 8 - Cost Minimization
Chapter 9 - Partial and General Equilibrium
Chapter 10 - Monopoly
Chapter 11 - Price Discrimination and Bundling
Chapter 12 - Simultaneous-move Games
Chapter 13 - Sequential and Repeated Games
Chapter 14 - Imperfect Competition
Chapter 15 - Games of Incomplete Information and Auctions
Chapter 16 - Contract Theory
Chapter 17 - Externalities and Public Goods
,Chapter 2: Consumer Preferences and Utility
2.1 Solutions to self-assessment exercises
1. Self-assessment 2.1. Consider now that Eric prefers bundle A = (1; 1) to B = (2; 1).
Assume that this ranking holds for any two bundles we present to him, where only the
amount of good x increases from bundle A to B. Are Eric’s preferences monotonic?
Are they strictly monotonic? What if he prefers bundle A = (3; 3) to B = (2; 2), and
a similar ranking holds for any two bundles where the amount of both goods decreases
from A to B?
First type of preferences. Since Eric prefers bundle A to B, bundle A has fewer
units of good x than bundle B, and both bundles have the same amount of good
y, his preferences violate monotonicity and strictly monotonicity.
– Recall that, for monotonicity to hold, Eric should weakly prefer (that is,
strictly prefer or be indi¤erent) the bundle that contains more units of either
good (x or y). Since he prefers the bundle with fewer units of x and the same
amount of y, his preferences are non-monotonic. Intuitively, Eric treats good
x as a bad, preferring fewer units of it. As a remark, note that if Eric weakly
preferred bundles with more units of x but the same amount of y, we would
still not be able to say that monotonicity holds. For monotonicity, we would
need Eric to weakly prefer bundles with more units of x or more of y.
– For strict monotonicity to hold, Eric should strictly prefer bundles with more
units of either good (x or y) but, as discussed above, he prefers the bundle with
fewer units of good x (bundle A), implying that his preferences do not satisfy
strict monotonicity either. A similar remark as for monotonicity applies here:
if Eric strictly preferred bundles with more units of x but the same amount
of y, we would still not be able to say that strict monotonicity holds. For
that, we need that Eric strictly prefers bundles with more units of x, more of
y, or both.
Second type of preferences. He now prefers bundle A to bundle B, but in this
case bundle A has more of each good than bundle B. As such, Eric’s preferences
are monotonic, but not strictly monotonic. For his preferences to satisfy strict
monotonicity, we would need Eric to prefer bundle A to B when only good x or
only good y is increased.
1
, 2. Self-assessment 2.2. Assume that Eric prefers bundles with more units of good x
but fewer units of y. If he cannot consume negative amounts of either good, can you
…nd a bliss point, i.e., a bundle where he is satiated? Given your answer, do Eric’s
preferences satisfy non-satiation? What about monotonicity?
Since good y is viewed as a “bad”by Eric, he would prefer to consume zero units
of good y. That being said, Eric would always view a bundle with more of good
x as at least as good as a bundle with less of good x. Thus, there does not exist
a bliss point, as Eric can always identify bundles with higher amounts of good x.
Since there does not exist a bliss point, Eric’s preferences satisfy non-satiation,
but as one of the goods is a “bad,” his preferences do not satisfy monotonicity.
Recall that, for preferences to satisfy monotonicity, we need that the consumer
prefers more units of good x, good y, or both.
3. Self-assessment 2.3. Consider again bundles A = (40; 30) or B = (20; 30) from
Example 2.3, and assume that Chelsea’s utility function is u(x; y) = 2x + 3y. Does she
prefer bundle A, B, or is she indi¤erent between them? What if her preferences are
represented with utility function v(x; y) = 4x + 6y? What if they are represented with
v 0 (x; y) = 4x 6y? Hint: Utility function v 0 (x; y) is not an increasing transformation
of Chelsea’s original utility function u(x; y).
First utility function. With Chelsea’s utility function u(x; y) = 2x + 3y, bundle
A yields a utility level of
u(40; 30) = (2 40) + (3 30) = 80 + 90 = 170
whereas bundle B only yields a utility level of
u(20; 30) = (2 20) + (3 30) = 40 + 90 = 130:
– Since bundle A provides a higher utility level than bundle B, Chelsea prefers
bundle A to bundle B.
Second utility function. We now consider the alternative utility function v(x; y) =
4x + 6y, which is just a monotonic transformation of u(x; y), i.e., v(x; y) =
2 (2x + 3y) = 2u(x; y). In this context, bundle A yields a utility level of
v(40; 30) = (4 40) + (6 30) = 160 + 180 = 340
2
** All Chapters included
** Solutions to self-assessment exercises
** Solutions to end-of-chapter exercises
,Table of Contents are given below
Chapter 1 - Introduction (Solutions not available for Ch.1)
Chapter 2 - Consumer Preferences and Utility
Chapter 3 - Consumer Choice
Chapter 4 - Substitution and Income Effects
Chapter 5 - Measuring Welfare Changes
Chapter 6 - Choice under Uncertainty
Chapter 7 - Production Functions
Chapter 8 - Cost Minimization
Chapter 9 - Partial and General Equilibrium
Chapter 10 - Monopoly
Chapter 11 - Price Discrimination and Bundling
Chapter 12 - Simultaneous-move Games
Chapter 13 - Sequential and Repeated Games
Chapter 14 - Imperfect Competition
Chapter 15 - Games of Incomplete Information and Auctions
Chapter 16 - Contract Theory
Chapter 17 - Externalities and Public Goods
,Chapter 2: Consumer Preferences and Utility
2.1 Solutions to self-assessment exercises
1. Self-assessment 2.1. Consider now that Eric prefers bundle A = (1; 1) to B = (2; 1).
Assume that this ranking holds for any two bundles we present to him, where only the
amount of good x increases from bundle A to B. Are Eric’s preferences monotonic?
Are they strictly monotonic? What if he prefers bundle A = (3; 3) to B = (2; 2), and
a similar ranking holds for any two bundles where the amount of both goods decreases
from A to B?
First type of preferences. Since Eric prefers bundle A to B, bundle A has fewer
units of good x than bundle B, and both bundles have the same amount of good
y, his preferences violate monotonicity and strictly monotonicity.
– Recall that, for monotonicity to hold, Eric should weakly prefer (that is,
strictly prefer or be indi¤erent) the bundle that contains more units of either
good (x or y). Since he prefers the bundle with fewer units of x and the same
amount of y, his preferences are non-monotonic. Intuitively, Eric treats good
x as a bad, preferring fewer units of it. As a remark, note that if Eric weakly
preferred bundles with more units of x but the same amount of y, we would
still not be able to say that monotonicity holds. For monotonicity, we would
need Eric to weakly prefer bundles with more units of x or more of y.
– For strict monotonicity to hold, Eric should strictly prefer bundles with more
units of either good (x or y) but, as discussed above, he prefers the bundle with
fewer units of good x (bundle A), implying that his preferences do not satisfy
strict monotonicity either. A similar remark as for monotonicity applies here:
if Eric strictly preferred bundles with more units of x but the same amount
of y, we would still not be able to say that strict monotonicity holds. For
that, we need that Eric strictly prefers bundles with more units of x, more of
y, or both.
Second type of preferences. He now prefers bundle A to bundle B, but in this
case bundle A has more of each good than bundle B. As such, Eric’s preferences
are monotonic, but not strictly monotonic. For his preferences to satisfy strict
monotonicity, we would need Eric to prefer bundle A to B when only good x or
only good y is increased.
1
, 2. Self-assessment 2.2. Assume that Eric prefers bundles with more units of good x
but fewer units of y. If he cannot consume negative amounts of either good, can you
…nd a bliss point, i.e., a bundle where he is satiated? Given your answer, do Eric’s
preferences satisfy non-satiation? What about monotonicity?
Since good y is viewed as a “bad”by Eric, he would prefer to consume zero units
of good y. That being said, Eric would always view a bundle with more of good
x as at least as good as a bundle with less of good x. Thus, there does not exist
a bliss point, as Eric can always identify bundles with higher amounts of good x.
Since there does not exist a bliss point, Eric’s preferences satisfy non-satiation,
but as one of the goods is a “bad,” his preferences do not satisfy monotonicity.
Recall that, for preferences to satisfy monotonicity, we need that the consumer
prefers more units of good x, good y, or both.
3. Self-assessment 2.3. Consider again bundles A = (40; 30) or B = (20; 30) from
Example 2.3, and assume that Chelsea’s utility function is u(x; y) = 2x + 3y. Does she
prefer bundle A, B, or is she indi¤erent between them? What if her preferences are
represented with utility function v(x; y) = 4x + 6y? What if they are represented with
v 0 (x; y) = 4x 6y? Hint: Utility function v 0 (x; y) is not an increasing transformation
of Chelsea’s original utility function u(x; y).
First utility function. With Chelsea’s utility function u(x; y) = 2x + 3y, bundle
A yields a utility level of
u(40; 30) = (2 40) + (3 30) = 80 + 90 = 170
whereas bundle B only yields a utility level of
u(20; 30) = (2 20) + (3 30) = 40 + 90 = 130:
– Since bundle A provides a higher utility level than bundle B, Chelsea prefers
bundle A to bundle B.
Second utility function. We now consider the alternative utility function v(x; y) =
4x + 6y, which is just a monotonic transformation of u(x; y), i.e., v(x; y) =
2 (2x + 3y) = 2u(x; y). In this context, bundle A yields a utility level of
v(40; 30) = (4 40) + (6 30) = 160 + 180 = 340
2
