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ECON7030 MICROECONOMIC ANALYSIS
TUTORIAL EXERCISE 3
Question 1 Consider the following utility functions (in a world with Good X and
Good Y ):
I. U(x, y) = x
1
2y
1
2
II. U(x, y) = 4x + 3y
III. U(x, y) =
[
x2 + y2
] 1
2
IV. U(x, y) = x
1
2 + y
(a) (Level A – B) Fill out the last 3 columns of Table 1. “MRS” stands for Marginal
Rate of Substitution here. (You would need to copy this table into your answer.)
Some tricky ones have been filled out for you already.
(b) (Level A) Sketch an indifference curve for each of the above utility functions.
(c) (Level A – B) Fill out the the first 4 columns of Table 1 with a Yes/No entry for each
cell. “S. Monotonic” and “S. Convex” means “Strongly Monotonic” and “Strongly
Convex”, respectively.
Table 1. Question 1: Properties of Common Utility Functions
Monotone S. Monotone Convex S. Convex MUx MUy MRS
I. Yes 1
2
x
1
2y−
1
2
II. Yes
III. No x
[
x2 + y2
]− 1
2 y
[
x2 + y2
]− 1
2
IV. Yes
1