AEB 6106: Problem Set 2 Due Sept. 12 at the start of class (9:35AM) Instructions: 1. Please use your UF ID as the only identifying information on your problem set. Please do not include your name. 2. Please write your answers on separate paper, instead of squeezing answers into the margins of this paper. For the following utility functions in questions 1 - 4, maximize utility subject to a budget constraint to derive demand functions for goods x and y. 1) 𝑈 = 𝑥 4 5𝑦 1 5 2) 𝑈 = 3𝑥 + 10𝑦 3) 𝑈 = min{5𝑥, 6𝑦} 4) 𝑈 = 4𝑥 1 4 + 3𝑦 For all four utility functions in questions 5 - 8, maximize utility subject to a budget constraint when: 𝑃𝑥 = 2, 𝑃𝑦 = 1,𝐼 = 12 5) 𝑈 = 𝑥 1 5𝑦 4 5 6) 𝑈 = 2𝑥 + 3𝑦 7) 𝑈 = min{2𝑥, 7𝑦} 8) 𝑈 = 2𝑥 1 2 + 2𝑦 For questions 9 through 12, derive the indirect utility functions for each utility function using your answers to questions 1 through 4. 9) 𝑈 = 𝑥 4 5𝑦 1 5 10) 𝑈 = 3𝑥 + 10𝑦 11) 𝑈 = min{5𝑥, 6𝑦} 12) 𝑈 = 4𝑥 1 4 + 3𝑦 AEB 6106: Problem Set 3 Due Oct. 10 at the start of class 1. In problem set 2, you worked with the following utility function: 𝑈 = 𝑥 4 5𝑦 1 5 You derived the Marshallian demand functions: 𝑥 = 4 5 𝐼 𝑃𝑥 , 𝑦 = 1 5 𝐼 𝑃𝑦 And the indirect utility function: 𝑉 = ( 4 𝑃𝑥 ) 4 5 ( 1 𝑃𝑦 ) 1 5 𝐼 5 From this we can derive the expenditure function: 𝐸 = 5𝑈 ( 4 𝑃𝑥 ) − 4 5 ( 1 𝑃𝑦 ) − 1 5 And compensated demand for x: 𝑥𝑐 = 𝑈 ( 4𝑃𝑦 𝑃𝑥 ) 1 5 a. Derive the own-price Slutsky equation for this utility function for good x. b. Explain what the terms in the Slutsky equation mean. 2. In problem set 2, you worked with the following utility function: 𝑈 = 3𝑥 + 10𝑦 You derived the Marshallian demand functions: If 3 10 > 𝑃𝑥 𝑃𝑦 , then x = 𝐼 𝑃𝑥 , y = 0 If 3 10 < 𝑃𝑥 𝑃𝑦 , then y = 𝐼 𝑃𝑦 , x = 0 And the indirect utility function: 𝑉 = max {3 ( 𝐼 𝑃𝑥 ) , 10 ( 𝐼 𝑃𝑦 )} From this you could derive the expenditure function: 𝐸 = 𝑈 min { 𝑃𝑥 3 . 𝑃𝑦 10 } And the compensated demand functions: If 3 10 > 𝑃𝑥 𝑃𝑦 , then 𝑥𝑐 = 𝑈 3 , 𝑦 𝑐 = 0 If 3 10 < 𝑃𝑥 𝑃𝑦 , then 𝑦 𝑐 = 𝑈 10 , 𝑥𝑐 = 0 a. Derive the own-price Slutsky equation for this utility function for good x, assuming that 3 10 > 𝑃𝑥 𝑃𝑦 and that this remains the case after the price change. b. Discuss the terms in the Slutsky equation for this utility function and the assumed scenario. (Note- this discussion should vary considerably from your discussion in part a) c. Derive the own-price Slutsky equation for this utility function for good x, assuming that originally 3 10 > 𝑃𝑥 𝑃𝑦 but after the price change, 3 10 < 𝑃𝑥 𝑃𝑦 . Note that you will not be able to take partial derivatives to derive the terms in the Slutsky equation, but will instead have to consider discrete changes from the

1. AEB 6106: Problem Set 2
Due Sept. 12 at the start of class (9:35AM)
Instructions:
1. Please use your UF ID as the only identifying information on
your problem set. Please do
not include your name.
2. Please write your answers on separate paper, instead of
squeezing answers into the
margins of this paper.
For the following utility functions in questions 1 - 4, maximize
utility subject to a budget constraint
to derive demand functions for goods x and y.
1)
� = �
4
5�
1
5
2)

2. � = 3� + 10�
3)
� = min{5�, 6�}
4)
� = 4�
1
4 + 3�
For all four utility functions in questions 5 - 8, maximize utility
subject to a budget constraint
when:
�� = 2, �� = 1,� = 12
5)
� = �
1
5�
4
5
6)
� = 2� + 3�
7)
� = min{2�, 7�}
8)
� = 2�

3. 1
2 + 2�
For questions 9 through 12, derive the indirect utility functions
for each utility function using your
answers to questions 1 through 4.
9)
� = �
4
5�
1
5
10)
� = 3� + 10�
11)
� = min{5�, 6�}
12)
� = 4�
1
4 + 3�
AEB 6106: Problem Set 3

4. Due Oct. 10 at the start of class
1. In problem set 2, you worked with the following utility
function:
� = �
4
5�
1
5
You derived the Marshallian demand functions:
� =
4
5
�
��
, � =
1
5
�
��
And the indirect utility function:

5. � = (
4
��
)
4
5
(
1
��
)
1
5 �
5
From this we can derive the expenditure function:
� = 5� (
4
��
)
−
4
5
(
1

6. ��
)
−
1
5
And compensated demand for x:
�� = � (
4��
��
)
1
5
a. Derive the own-price Slutsky equation for this utility
function for good x.
b. Explain what the terms in the Slutsky equation mean.
2. In problem set 2, you worked with the following utility
function:
� = 3� + 10�
You derived the Marshallian demand functions:
If
3

7. 10
>
��
��
, then x =
�
��
, y = 0
If
3
10
<
��
��
, then y =
�
��
, x = 0
And the indirect utility function:
� = max {3 (
�
��

8. ) , 10 (
�
��
)}
From this you could derive the expenditure function:
� = � min {
��
3
.
��
10
}
And the compensated demand functions:
If
3
10
>
��
��
, then �� =
�
3

9. , � � = 0
If
3
10
<
��
��
, then � � =
�
10
, �� = 0
a. Derive the own-price Slutsky equation for this utility
function for good x, assuming that
3
10
>
��
��
and that this remains the case after the price change.
b. Discuss the terms in the Slutsky equation for this utility
function and the assumed scenario.

10. (Note- this discussion should vary considerably from your
discussion in part a)
c. Derive the own-price Slutsky equation for this utility
function for good x, assuming that
originally
3
10
>
��
��
but after the price change,
3
10
<
��
��
. Note that you will not be able to take partial
derivatives to derive the terms in the Slutsky equation, but will
instead have to consider discrete
changes from the original price to the new price.
3. In problem set 2, you worked with the following utility

11. function:
� = min{5�, 6�}
You derived the Marshallian demand functions:
� =
6�
6�� + 5��
, � =
5�
6�� + 5��
And the indirect utility function:
� =
30�
6�� + 5��
From this, we could get the following expenditure function:
� =
�(6�� + 5��)
30
And the compensated demand function for x:
�� =
�

12. 5
a. Derive the own-price Slutsky equation for this utility
function for good x.
b. Explain the terms in the Slutsky equation specifically for this
utility function (Note- your
discussion should be different from the two previous
discussions).
4. In problem set 2, you worked with the following utility
function:
� = 4�
1
4 + 3�
You derived the Marshallian demand functions:
� = (
��
3��
)
4
3
, � =
�

13. ��
− (
1
3
)
4
3
(
��
��
)
1
3
If you worked through the additional practice problems, you
derived the indirect utility function:
� = 3
2
3 (
��
��
)
1
3

14. +
3�
��
For this utility function, Hicksian and Marshallian demand for
good x are the same:
�� = (
��
3��
)
4
3
Derive the own-price Slutsky equation for this utility function
for good x.
5. For both goods x and y in each of the four problems above,
indicate whether the goods are
normal or inferior goods.
6. For the utility functions in questions 1 – 4, determine if
goods x and y are gross substitutes,
gross complements, or gross independent (Note- this requires 2
calculations) and determine if they

15. are net substitutes, net complements, or net indepent.
7. For the demand functions for good x contained in questions 1
– 4, derive the price, income, and
cross-price elasticities of demand.