Mathematics for Economics and Business 2 (ECON2204)

Faculty of Economics and Management Science (FEMS)

Semester: Second Semester

Level: 200

Year: 2016

Answers (200 )
Duration: 3 hours
Instructions: answer all questions
Question one (10 marks)
The demand and supply of achu in Bambui are given as:
=16 − while the
=
10 + .
is the demand function and
is the supply function with respect to quantity
. Determine (a) the consumer surplus. (b) the producer surplus
Question two (15 marks)
a) A project has an initial cost of 100,000 FRS and a continuous income stream of 30,000
FRS, what is the present value of the income stream if the investment project last for 4
years and the discount rate is 10% per year? Is this investment project profitable?
b) The marginal cost function is given as =2− 40, while the price per unit is 100
I. Determine the total cost function if total fixed cost equals 1,000frs
II. Determine the profit maximizing output and hence the total profit/loss of the firm
Question three (10 marks)
Assume that the rate of investment is described by the function
=24
√
and that
0
=
500; find the time path of capital stock, K and hence find the capital accumulated between
the intervals [0,3] and [1,3]
Question four (20 marks)
Tambi production company (TPC) established by the different variety of goods to be produced in
the following matrix order
=
1 −2 0
−2 2 −2
0 −2 3
!
From this matrix, column one represent cosmetic goods, column two represent detergent
products, column three is communication products
(a) Given that the production is to begin with a reversal concentration on column 3, as a
business student, determine
"#
to show how the products will be classified
(b) The engineers later realize that collective or combine production is not the best, they then
decided to now produce in vector format by applying the Eigen procedure; determine the
Eigen values of this company.
THE UNIVERSITY OF BAMENDA
FACULTY OF ECONOMICS AND MANAGEMENT SCIENCES
2nd Semester Exam
Course e: Maths for Econs and Business 2
Course Code: ECON204
www.schoolfaqs.net
(c) What are the Eigen vectors attributed to the Eigen values above that can permit the
engineers to develop a new production strategy?
(d) Determine the new production model also known as the passage matrix (P) derive from
the Eigen vectors above.
(e) To determine the future effect of the company, the engineers decided to multiply out the
various production possibilities such that: $=%
&
%; where by $= future production
possibilities, %
&
= transpose of the passage matrix, = the initial given production
matrix and %=the passage matrix
(f) What economic/business advice can you give to TPC
Question five(5marks)
Following president Biya emergence plan and considering the present trend of activities and
economic situation of Cameroon, the engineers of TPC decided to increase their production
by raising the number of rows to four while maintaining the columns. Determine the possible
determinant of this TPC if the production matrix is increase as indicated below
'
1 −1 2 1
−1 2 3 2
−2 1 0 −1
2 1 −1 1
(
Question 6 (5 marks)
Consider the following matrix
3 −4 4
−1 −1 −8
0 0 −3
!
From above calculate the following;
(a)
*
(b)
&
− −
*
(c)
&
+
www.schoolfaqs.net