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P R I C E T H E O R Y
A S S I G N M E N T 1
0 x
y
I
Py
I
Px
BL1
U1
A
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I N S T R U C T I O N S & Q U E S T I O N S
Assignment Instructions
Prepare your assignment in accordance with the following instructions:
2. Show all working.
3. All answers and equations must be typed.
4. All graphs must be computer generated.
6. Submit your assignment through Turnitin.
Following the submission of your assignment:
you have not received a Turnitin receipt then your assignment was NOT successfully
submitted. If you do not successfully submit your assignment, you will receive a
8. Review your assignment on Turnitin to ensure that you have uploaded the correct
le, and that your le appears as you intend.
9. Retain your email receipt as proof of a successful submission.
Failure to follow these instructions will result in the loss of marks.
In accordance with RMIT University policy, late assignments will be penalised 10%
per day, or part thereof. Assignments that are more than ten (10) days late will not
be marked. Note: The timestamp on your assignment will be the time at which you
successfully complete the Turnitin submission process.
There are a total of twenty (20) marks available on this assignment. This assignment
1
Assignment Questions
Suppose that Sally’s preferences over baskets containing milk (good x), and coee (good
y ), are described by the utility function U(x; y ) = xy +2x. Sally’s corresponding marginal
utilities are,
MUx = y + 2 and MUy = x:
Use Px to represent the price of milk, Py to represent the price of coee, and I to represent
Sally’s income.
Question 1: Suppose that the price of milk is Px = \$1 per litre, the price of coee is
Py = \$4 per cup, and Sally’s income is I = \$40. Without deriving the optimal consumption
basket, show that the basket with x = 16 litres of milk, and y = 6 cups of coee, is NOT
optimal. (2 Marks)
Question 2: Derive the expression for Sally’s marginal rate of substitution. (1 Mark)
Question 3: Derive Sally’s demand for coee as a function of the variables Px , Py and
I. (i.e. Do NOT use the numerical values for Px , Py and I, from question 1.) For the
purposes of this question you should assume an interior optimum. (3 Marks)
Question 4: Derive Sally’s demand for milk as a function of the variables Px , Py and I. (i.e.
Do NOT use the numerical values for Px , Py and I, from question 1.) For the purposes
of this question you should assume an interior optimum. (1 Mark)
Question 5: Describe the relationship between Sally’s demand for milk and,
(a) Sally’s income;
(b) the price of milk;
(c) the price of coee.
Your answers must reference the demand function that you derived in question 4, AND
use the correct term to describe the relationship. (6 Marks)
Question 6: Suppose that Px = \$1 and I = \$40. Find the equivalent variation for an
increase in the price of coee from Py1 = \$4 to Py2 = \$5. (7 Marks)
2

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