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Aec 201: Mathematics Of Economics Question Paper

Aec 201: Mathematics Of Economics

Course: Bachelor Of Arts In Economics

Institution: Pwani University question papers

Exam Year:2012

PWANI UNIVERSITY COLLEGE
A CONSTITUENT COLLEGE OF KENYATTA UNIVERSITY
UNIVERSITY EXAMINATIONS 2008/2009 ACADEMIC YEAR
2
ND YEAR 1ST SEMESTER EXAMINATION FOR THE DEGREEOF
STREAM: BACHELOR ARTS AND BACHELOR OF EDUCTION
AEC 201: MATHEMATICS OF ECONOMICS
END SEMESTER: I TIME: 3 HOURS
DAY/TIME: TUESDAY: 11.00 A.M – 2.00 P.M DATE: 24/2/2009
INSTRUCTIONS
i) Question ONE is COMPULSORY
ii) Attempt any other THREE questions
Q.1) a) Differentiate the following.
i) f(x) = x3
+ 2x2
+ 8 (4 mks)
ii) f(x) = x2
+ (x + 4)2
b) Intergrate the following:-
i) ?(x3
+ 5)dx
3 (4 mks)
ii) ? (x2
+2x + 3)dx
2
c) The cost of an item consists of fixed cost of Ksh.500/= and a
variable cost of Ksh.2/= per unit. Derive the total cost function and
find the total cost of producing 60 units of the item. (4 mks)
d) A manufacturer estimates that Q(thousand) radial tyres will be
purchased (demanded) by wholesalers when the price is
P = D(Q) = -0.1Q + 90 per tyre and the same number of tyres will
be supplied when the price is P = 5(Q) = Q + 50. Find the
equilibrium price and quantity demanded. (4 mks)e) A manufacturer of digital cameras estimates that when X hundred
cameras are provided, the total profit will be
P(x) = -0.003 x 3x3
+ 0.07x2
+ 25x -200 thousand shillings.
Determine the marginal profits when x = 10; x = 50 and x = 80
(6 mks)
Q.2) Electrical Equipment limited is engaged in the production of power transformers
and traction transformers. Both of these transformers pass through three processes
which are core preparation, core-to-coil assembly and vapour-phase drying. The
power transformers yields a contribution of Ksh.50,000/= per unit and a traction
transformer yields Ksh.10,000/= per unit. The time required in terms of hours for
each of these processes is given below:-
Power transformer Traction Transformer
Core-preparation 75 15
Core-to-Coil assembly 160 30
Vapour-Phase drying 45 10
The capacities of the core preparation shop, assembly shop and
vapour-phase drying are as under.
Process Available Capacity
Core preparation 1000
Core-to-Coil assembly 1500
Vapour-phase drying 750
Required: How many units of each type of transformers should be produced to
maximize profits. (16 mks)
Q.3) Determine the outputs primary inputs and secondary inputs for products A. B,
C produced in industries XYZ whose input-output matrix and final demand are
given as below. (16 mks)
A B C final Demand
X 0.3 0.2 0.1 40
Y 0.1 0.4 0.2 50
Z 0.2 0.3 0.4 60

Aec 201: Mathematics Of Economics Question Paper

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