Microeconomics: Theory & Analysis
Tutorial 1 - Consumer choice
Multiple choice questions
Q1
Consider the following consumption bundles:
- Bundle A contains 5 units of good 1 and 8 units of good 2
- Bundle B contains 15 units of good 1 and 6 units of good 2
- Bundle C contains 10 units of good 1 and 7 units of good 2
A consumer is indifferent between bundles A and B. The consumer has well-behaved preferences.
It must be the case that:
a) Bundle A is better than bundle C
b) Bundle A is as good as bundle C
c) Bundle A is worse than bundle C
d) Cannot answer this without knowing the utility function
Q2
The relation “is preferred to” between commodity bundles is just one example of a binary relation.
Another example is the relation “is a full brother of” defined over the set of all human beings. Let xRy
mean person x is a full brother of person y. Which of the following statements is correct?
a) The relation R is reflexive, transitive, and complete.
b) The relation R is transitive and complete but not reflexive.
c) The relation R is transitive but not complete or reflexive.
d) The relation R is complete but not transitive or reflexive.
e) The relation R is not reflexive, transitive, or complete.
Q3
Imagine (or draw) a figure with good F on the horizontal axis and good C on the vertical axis. In this
figure, an increase of the price of good F from 15 to 20 and of good C from 30 to 40 will lead to:
a) A parallel outward shift of the budget line
b) A parallel inward shift of the budget line
c) A flatter budget line that is also shifted inwards
d) A flatter budget line that is also shifted outwards
,The following figure is used for Q4, Q5 and Q6
The following indifference curves represent the preferences of Daan:
𝑥
𝑥
Q4
What happens with the absolute value of the MRS of Daan when x1 increases?
a) The absolute value of the MRS increases
b) The absolute value of the MRS decreases
c) The absolute value of the MRS stays the same
Q5
What happens with the absolute value of the MRS of Daan when x2 increases?
a) The absolute value of the MRS increases
b) The absolute value of the MRS decreases
c) The absolute value of the MRS stays the same
Q6
What happens with the absolute value of the MRS of Daan along an indifference curve?
a) The absolute value of the MRS increases
b) The absolute value of the MRS decreases
c) The absolute value of the MRS stays the same
Q7
Angela has preferences represented by the utility function U(x, y) = 2x + 2y. She consumes 10 units of
good x and 6 units of good y. If her consumption of good x is lowered to 4, how many units of y must she
have in order to be exactly as well off as before?
, a) 14
b) 13
c) 12
d) 15
Q8
Mariska has the following utility function: 𝑢(𝑥 , 𝑥 ) = 𝑥 + 𝑥 and prices are given by 𝑝 = 1 and 𝑝 =
2. How will Mariska spend her budget?
a) She will only buy good 1
b) She will only buy good 2
c) She will spend 1/3 of her budget on good 1 and 2/3 on good 2
d) She will spend 2/3 of her budget on good 1 and 1/3 on good 2
Q9
Which of the following utility functions does NOT represent the same preferences as Mariska’s (Q8)?
a) 𝑢(𝑥 , 𝑥 ) = 2𝑥 + 2𝑥
b) 𝑢(𝑥 , 𝑥 ) = (𝑥 + 𝑥 )(𝑥 + 2𝑥 𝑥 + 𝑥 )
c) 𝑢(𝑥 , 𝑥 ) = 1 +
d) 𝑢(𝑥 , 𝑥 ) = 𝑥 + 𝑥 − 100
Q10
Wanda Littlemore’s utility function is U(x, y) = x + 47y − 3y2. Her income is 107. If the price of x is 1 and
the price of y is 23, how many units of good x will Wanda demand?
a) 11
b) 19
c) 18
d) 15
Exercises
E1
If good X is measured on the horizontal axis and good Y on the vertical, what can you say about the
preferences of someone whose indifference curves are
a) parallel to the Y axis?
b) positively sloped with more desirable indifference curves as one moves to the right?
c) negatively sloped with more desirable indifference curves as one moves to the left?
, E2
Anna is choosing buying cookies for herself and Bram. Suppose that the following utility function
describes the preferences of Anna:
𝑢 (𝑥 , 𝑥 ) = 𝑥 + 2√𝑥 ,
where 𝑥 denote the amount of cookies for Anna and 𝑥 denote the amount of cookies for Bram.
Anna’s budget is denoted by 𝑚 and the price of a cookie for herself and Bram is denoted by 𝑝 and 𝑝
respectively.
a) Suppose Anna has a budget of 𝑚 = 6 and 𝑝 = 𝑝 = 1. How many cookies does she buy for
herself and for Bram?
b) Suppose Anna has a budget of 𝑚 = 6 and 𝑝 = 1 and 𝑝 = . How many cookies does she
buy for herself and for Bram?
c) Derive Anna’s optimal bundle as a function of the parameters 𝑚, 𝑝 and 𝑝 .
d) Show for each of the following utility functions whether they describe the same preferences
as Anna’s.
1. 𝑣(𝑥 , 𝑥 ) = 𝑥 + √𝑥
2. 𝑣(𝑥 , 𝑥 ) = 2𝑥 + 4 √𝑥
3. 𝑣(𝑥 , 𝑥 ) = 𝑥 + 4𝑥
4. 𝑣(𝑥 , 𝑥 ) = 𝑥 + 4𝑥 √𝑥 + 4𝑥
Tutorial 1 - Consumer choice
Multiple choice questions
Q1
Consider the following consumption bundles:
- Bundle A contains 5 units of good 1 and 8 units of good 2
- Bundle B contains 15 units of good 1 and 6 units of good 2
- Bundle C contains 10 units of good 1 and 7 units of good 2
A consumer is indifferent between bundles A and B. The consumer has well-behaved preferences.
It must be the case that:
a) Bundle A is better than bundle C
b) Bundle A is as good as bundle C
c) Bundle A is worse than bundle C
d) Cannot answer this without knowing the utility function
Q2
The relation “is preferred to” between commodity bundles is just one example of a binary relation.
Another example is the relation “is a full brother of” defined over the set of all human beings. Let xRy
mean person x is a full brother of person y. Which of the following statements is correct?
a) The relation R is reflexive, transitive, and complete.
b) The relation R is transitive and complete but not reflexive.
c) The relation R is transitive but not complete or reflexive.
d) The relation R is complete but not transitive or reflexive.
e) The relation R is not reflexive, transitive, or complete.
Q3
Imagine (or draw) a figure with good F on the horizontal axis and good C on the vertical axis. In this
figure, an increase of the price of good F from 15 to 20 and of good C from 30 to 40 will lead to:
a) A parallel outward shift of the budget line
b) A parallel inward shift of the budget line
c) A flatter budget line that is also shifted inwards
d) A flatter budget line that is also shifted outwards
,The following figure is used for Q4, Q5 and Q6
The following indifference curves represent the preferences of Daan:
𝑥
𝑥
Q4
What happens with the absolute value of the MRS of Daan when x1 increases?
a) The absolute value of the MRS increases
b) The absolute value of the MRS decreases
c) The absolute value of the MRS stays the same
Q5
What happens with the absolute value of the MRS of Daan when x2 increases?
a) The absolute value of the MRS increases
b) The absolute value of the MRS decreases
c) The absolute value of the MRS stays the same
Q6
What happens with the absolute value of the MRS of Daan along an indifference curve?
a) The absolute value of the MRS increases
b) The absolute value of the MRS decreases
c) The absolute value of the MRS stays the same
Q7
Angela has preferences represented by the utility function U(x, y) = 2x + 2y. She consumes 10 units of
good x and 6 units of good y. If her consumption of good x is lowered to 4, how many units of y must she
have in order to be exactly as well off as before?
, a) 14
b) 13
c) 12
d) 15
Q8
Mariska has the following utility function: 𝑢(𝑥 , 𝑥 ) = 𝑥 + 𝑥 and prices are given by 𝑝 = 1 and 𝑝 =
2. How will Mariska spend her budget?
a) She will only buy good 1
b) She will only buy good 2
c) She will spend 1/3 of her budget on good 1 and 2/3 on good 2
d) She will spend 2/3 of her budget on good 1 and 1/3 on good 2
Q9
Which of the following utility functions does NOT represent the same preferences as Mariska’s (Q8)?
a) 𝑢(𝑥 , 𝑥 ) = 2𝑥 + 2𝑥
b) 𝑢(𝑥 , 𝑥 ) = (𝑥 + 𝑥 )(𝑥 + 2𝑥 𝑥 + 𝑥 )
c) 𝑢(𝑥 , 𝑥 ) = 1 +
d) 𝑢(𝑥 , 𝑥 ) = 𝑥 + 𝑥 − 100
Q10
Wanda Littlemore’s utility function is U(x, y) = x + 47y − 3y2. Her income is 107. If the price of x is 1 and
the price of y is 23, how many units of good x will Wanda demand?
a) 11
b) 19
c) 18
d) 15
Exercises
E1
If good X is measured on the horizontal axis and good Y on the vertical, what can you say about the
preferences of someone whose indifference curves are
a) parallel to the Y axis?
b) positively sloped with more desirable indifference curves as one moves to the right?
c) negatively sloped with more desirable indifference curves as one moves to the left?
, E2
Anna is choosing buying cookies for herself and Bram. Suppose that the following utility function
describes the preferences of Anna:
𝑢 (𝑥 , 𝑥 ) = 𝑥 + 2√𝑥 ,
where 𝑥 denote the amount of cookies for Anna and 𝑥 denote the amount of cookies for Bram.
Anna’s budget is denoted by 𝑚 and the price of a cookie for herself and Bram is denoted by 𝑝 and 𝑝
respectively.
a) Suppose Anna has a budget of 𝑚 = 6 and 𝑝 = 𝑝 = 1. How many cookies does she buy for
herself and for Bram?
b) Suppose Anna has a budget of 𝑚 = 6 and 𝑝 = 1 and 𝑝 = . How many cookies does she
buy for herself and for Bram?
c) Derive Anna’s optimal bundle as a function of the parameters 𝑚, 𝑝 and 𝑝 .
d) Show for each of the following utility functions whether they describe the same preferences
as Anna’s.
1. 𝑣(𝑥 , 𝑥 ) = 𝑥 + √𝑥
2. 𝑣(𝑥 , 𝑥 ) = 2𝑥 + 4 √𝑥
3. 𝑣(𝑥 , 𝑥 ) = 𝑥 + 4𝑥
4. 𝑣(𝑥 , 𝑥 ) = 𝑥 + 4𝑥 √𝑥 + 4𝑥
