P R I C E T H E O R Y
A S S I G N M E N T 1
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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:
1. Answer all questions.
2. Show all working.
3. All answers and equations must be typed.
4. All graphs must be computer generated.
5. Your assignment must be your own work.
6. Submit your assignment through Turnitin.
Following the submission of your assignment:
7. Check that you received a Turnitin receipt at your RMIT student email address. If
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
grade of zero.
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
contributes 25% of your nal grade.
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)
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