Chapter 2. A Theory of Preferences
 

1. Look at textbook questions #:  5, 6, 7, 8, 19.

2. True/False

1. An indifference curve is defined as a set of bundles that a consumer with a given income can afford, and among which she or he is indifferent.

2. More is preferred to less means that if the total number of goods in bundle A exceeds the total quantity in B, than A is preferred to B.

3. The assumptions of completeness, two-term consistency, transitivity and continuity are necessary for constructing a utility function over a set of preferences.

4. The utility function V(x₁, x₂) = 5[U(x₁, x₂)]/2+7 represents the same preference ordering as the utility function U(x₁, x₂).

5. A diminishing marginal rate of substitution implies that an individual requires increasing amounts of one good as he gives up more and more of the other good to remain at the same utility level.

6. More is preferred to less implies that two bundles with different amounts of either good 1 or good 2 and the same amount of the other good cannot be on the same indifference curve.

7. Since utility is ordinal and not cardinal, interpersonal comparisons cannot be made.

8. The MRS for indifference curve x₁ + x₂ =c is diminishing.

9. The indifference curve between garbage and ice cream would be positively sloped.

10. If Alfred's indifference curve between income and leisure is positively sloped and convex, then the additional income required to induce Alfred to work additional hours is constant and equal to his current wage.

Answers:  1.F     2.F    3.T    4.T    5.T
                6.T     7.T    8.F    9.T  10.F
 

3. Short Questions.

1. Draw an indifference curve which is not convex.

2. Consider the following list of statements. Each statement in the list means the same thing as one of the other statements. Identify the pairs of statements which are equivalent:
a) Consumers always prefer to have more of a good
b) Consumers' preferences are complete
c) Consumers' preferences are transitive
d) Every market basket has an indifference curve associated with it
e) Indifference curves are convex
f) Indifference curves are downwards sloping
g) Indifference curves do not cross
h) A diminishing marginal rate of substitution is a characteristic of consumer preferences

Answers: 2.f) and h),  c) and g), b) and d), a) and e).
 

4. Long Questions

1. Consider the following utility function:

U(x₁, x₂) = 2x₂ + x₁^1/3

a) Draw the indifference curve associated with utility numbers 8, 27 and 64.
b) How does MRS changes as you move from one indifference curve to another along the vertical line x₁=2? Or x₁=3?

2. Consider the following utility functions:

(i) U(x₁, x₂) = x₁ x₂^1/3
(ii) U(x₁, x₂) = 10x₁x₂
(iii) U(x₁, x₂) = 3x₁+4x₂
(iv) U(x₁, x₂) = 2x₁+ln(x₂)
(v) U(x₁, x₂) = x₁³

a) Construct an indifference curve for each of these functions.
b) Calculate the MRS for each of these functions.
 

Answers:  1. b).MRS = (1/6)x₁^(-2/3)  doesn't change  as you move along a vertical line because does not depend on x₂.
                2. b). i) MRS=3x₂/x₁; ii) MRS=x₂/x₁; iii) MRS=3/4; iv) MRS=2x₂ ;  v) MRS=infinity