ECON7150 Assignment 1
All answers must be handwritten clearly, scanned as one pdf document (scanners
are available at the Library) and submitted ONLY ONCE via Turnitin between 13
Sept 12 pm and 15 Sept 12 pm. Multiple submissions are NOT allowed, so
make sure before submitting. If you email me because you cannot resubmit
again, it is highly likely that by the time this gets sorted, it will be a late submission
and you will incur a penalty mark.
You can also handwrite on your ipad and scan it and upload as a pdf. If you do not
have access to a flatbed scanner you can use a phone app such as “Adobe Scan" or
Microsoft Office Lens".
The first page of the assignment should contain Assignment Number, followed by
your given and family name, and lastly, your student number.
Please make sure you do not wait until the last minute to upload your assignment as
this takes up time. So be mindful that you need to start uploading a few hours before
the deadline in case things go wrong or you forget a page here and there. Also,
make sure that you wait until the upload is complete and check that your assignment
has successfully uploaded on Turnitin.
Several students in the past claimed that they submitted on Turnitin and were
shocked to receive no marks because their assignment wasn’t actually uploaded. So
this is a warning that it is your responsibility to ensure that you recheck and see that
the assignment is actually there for marking.
The total mark of 48 will be converted to make up 30% of the final exam mark.
Questions are based on material covered in lectures 1 to 6.
Make sure you show all steps, key formulae, and workings clearly.
Question 1 (8 marks)
A firm has a demand function
100q p= −
and a total cost function
3 21 7 111 50
3
C q q q= − + +
Find an expression in terms of q only for the firm’s
(a) revenue function
(b) marginal revenue function
(c) marginal cost function
(d) profit function
(e) Solve for the profit maximising level of output, explaining which is a local
minimum or maximum.
Question 2 (6 marks)
Let (, ) =
!
(a) Calculate (2,3).
(b) Calculate ∑ (2, )2=0 , ∑ (, 3)3=1 .
(c) Calculate ∑ ∑ (, )=03=1 .
Question 3 (5 marks)
The point (x0, y0) = (1, 0) lies on the curve
2 3 12y xxe y x e −− = −
Show that (x1, y1) = (0, −4) lies on the tangent to the curve at (x0, y0).
Question 4 (10 marks)
(a) Find the third-order Taylor polynomial for the function () = 1
√1−
about = 0.
(b) Use your answer from part (a) to calculate the approximate value of 1
3√11
. To
clarify, the denominator is 3 multiplied by square root of 11. Round your
answer to six decimal places.
(c) Find the domain, range, and inverse of () = 1
√1−
. State your answer using
interval notation.
Question 5 (10 marks)
A firm’s price in a perfectly competitive market is 1000. Its cost function is
3 2( ) 0.01 3 1108 960C x x x x= − + + ,
where x ≥ 0 is the number of units produced and sold.
(a) Find an expression for the profit function π(x) for x ≥ 0.
(b) Find all stationary points and determine the profit maximising level of output.
(c) Using a sign diagram, determine the intervals over which π(x) is increasing
and decreasing.
(d) Determine the intervals over which π(x) is concave and convex.
(e) Where is the point of inflection in C(x)? Give an economic interpretation of
the point of inflection.
Question 6 (5 marks)
Given the demand function 0aQ bP k+ − = , where a, b and k are positive constants,
show that the price elasticity of demand is minus one when marginal revenue is zero.
Question 7 (4 marks)
Let 1( ) , 0.xf x e x= ≠
(a) Compute f ′(x) and f ′′(x).
(b) Determine the intervals where f is concave/convex.