Mathematics for Economics and Business 1 (ECON2103)

Faculty of Economics and Management Science (FEMS)

Semester: First Semester

Level: 200

Year: 2015

Answers (200 )
Instructions: answer all questions
Duration: 3 hours
PART ONE
Question one
The demand function for Achu is given as: 400 – 0.5P
x
– 0.75P
y
+ 0.25Y. where x=achu,
P
x
=price of achu, Y=income of individual, P
y
=price of meat. P
x
=200, P
y
=200, Y=100.
Determine and interpret the:
I. Cross elasticity of demand for achu and meat.
II. Income elasticity of demand.
III. Price elasticity of demand.
Question two (20marks)
A monopolistic firm produces and markets two commodities X and Y, with the following
total cost (TC) and total revenue (TR) functions:
TC = X
2
- 2XY – 3Y
2
; TR = 36X – 3X
2
+40Y – 5Y
2
.where X and Y are quantities of
commodity X and Y produced and sold in the market.
Determine:
I. The profit maximizing quantities and the total profit.
II. The marginal cost of producing good X and Y, when profits are maximized.
III. The marginal revenue of goods X and Y when profits are maximized.
IV. Verify that the quantities in (sub one) above actually maximized profits
Question three (5)
The Total Utility (TU) function is given as: TU = 2
+ 1. Find the slope and equation of
the tangent line to the utility function at the point (1, 3)
PART TWO
Question four
A cocoa producing company based in kumba has a production function given
as:
=
√
I. The manager of this company is interested to know how valid this function is.
What assumption must be made about the function to ensure validity?
II. In order to know the production pattern of the company, the foreign partners
requested for the graph of the production function. Plot the graph of the function.
III. Write down the domain and range of the function
IV. Calculate f(3)
THE UNIVERSITY OF BAMENDA
FACULTY OF ECONOMICS AND MANAGEMENT SCIENCES
1st Semester Exam
Course Title: Math for Economics and Business 1
Course Code: ECON203
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V.
What happens if you try to calculate f(-2)
Question five (6marks)
Which of the following functions are polynomial functions?
I.
f(x) = 4
+ 2
II.
= 3
− 2 + √x
III.
= 12 -4
+ 3
IV.
= sin + 1
V.
= 3
12
–
2
VI.
= 3

− 2

Question six
Write down the polynomial function with roots:
I.
1, 2, 3, 4
II.
2, -4
III.
12, -1, -6
Question seven
I.
Find the sum of the first five terms of the GP with first term 3 and common ratio
2.
II.
Find the sum of the first 20 terms of the GP with first term 3 and common ratio
1.5.
III.
The sum of the first 3 terms of a geometric series is 37/8. The sum of the first 6
terms is 3367/512. Find the first term and common ratio.
IV.
How many terms in the GP 4, 3.6, 3.24, . . . are needed so that the sum exceeds
35?
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