International Foundation Programme in Humanities and Social Sciences
IFP3804 MATHEMATICS FOR ECONOMICS
12 MAY 2015 14:30
Duration: 2 hours 30 minutes
YOU ARE NOT PERMITTED TO READ THE CONTENTS OF THIS QUESTION PAPER UNTIL
INSTRUCTED TO DO SO BY AN INVIGILATOR
Answer ALL SIX questions
Calculators are permitted in this examination. Please state on your answer book the name and
type of machine used.
Complete all rough workings in the answer book and cross through any work that is not to be
assessed.
Possession of unauthorised material at any time when under examination conditions is an
assessment offence and can lead to expulsion from QMUL. Check now to ensure you do not
have any notes, mobile phones, smartwatches or unauthorised electronic devices on your
person. If you do, raise your hand and give them to an invigilator immediately. It is also an
offence to have any writing of any kind on your person, including on your body. If you are found
to have hidden unauthorised material elsewhere, including toilets and cloakrooms it will be
treated as being found in your possession. Unauthorised material found on your mobile phone
or other electronic device will be considered the same as being in possession of paper notes. A
mobile phone that causes a disruption in the exam is also an assessment offence.
EXAM PAPERS MUST NOT BE REMOVED FROM THE EXAM ROOM
Examiners:
Elmina Homapour
Dr Y. G. Makedonis
© Queen Mary, University of London, 2015
Page 2 of 4
IFP3804 (2015)
Question 1
For a firm with the following total revenue (TR) and total cost (TC) functions:
TR(Q) = 150Q – 10Q2
TC(Q) = 2Q3 – 3Q2 + 10Q +49
where Q is the quantity produced
(a) Construct a profit function (π)
(b) By calculating the vertex of the parabola find:
(i) the optimal quantity (Q) to produce
(ii) the level of profit (π) obtained
(c) Sketch the profit function. Ensure that you identify any points where the curve cuts the axis
and label any maximum or minimum points.
[20 marks]
Question 2
1. A toy maker has a supply equation P = Q2 + 300 and equilibrium observed as Pe = 700,
Qe = 20.
a. Calculate the producers’ surplus for the toy maker
b. Sketch this supply equation, Make sure you label the points at which this equation
meets both the x and y axis. Share in the area that represents producer surplus.
[20 marks]
Question 3
For the economy described below:
C = 89 + 0.7Y
Consumption Function
I = 120 – 100i
Investment Function
Mt= 0.1Y
Transaction-Precautionary Demand for Money
Mw = 240 – 250i
Speculative Demand for Money
MS =275
Money Supply
(a) find the level of income Y and the rate of interest i that simultaneously bring equilibrium
(b) estimate the level of consumption C, investment I, the speculative demand for money Mw
and the transaction-precautionary demand for money Mt
[20 marks]
IFP3804 (2015)
Page 3 of 4
Question 4
For a class of twenty students their scores out of 100 in an in class test for Mathematics were as
follows:
55,63,40,80,82,96,21,55,64,69,77,73,90,65,53,55,70,60,74,86
(a) Use the above data to construct a suitable frequency table
(b) Represent the data in a suitable graph
(c) Calculate the mean and mode test score
(d) Calculate the standard deviation for the test score
(e) Calculate the Pearson’s first and second coefficients of skewness
(f) Using the results from (b) and (d) does the degree of skewness observed in the data suggest
that the teacher set a paper that was rather easy for the students?
[20 marks]
Question 5
The table below shows the number of days, f, in a 40-day period during which X automobile
accidents occurred in a city. Fit a Poisson distribution to the data
Number of Accidents (x)
0
1
2
3
4
Number of Days (f)
15
10
7
5
3
Total = 40
[10 marks]
Turn Over
Page 4 of 4
IFP3804 (2015)
Question 6
On a final examination in statistics marked out of 100, the mean was 75 and the standard
deviation was 10. If the scores were normally distributed,
a) determine the proportion of the students who scored at least 63
b) determine the proportion of the students who scored between 58 and 80
[10 marks]
End of Paper – An appendix of 1 page follows
______________________________________________________________________________