Download Quant I Dist Assignment 2006

HARAMAYA UNIVERSITY
COLLEGE OF CONTINNING AND DISTANCE EDUCATION
DEPARTMENT OF ECONOMICS
ASSIGNMENT FOR
QUANTITATIVE METHODE FOR ECONOMICS – I
STUDENT INFORMATION:
NAME: _______________________________________
I.D. No: ______________________________________
Centre: _______________________________________
Department: __________________________________
Part I: choose the best answer from the alternatives given (1 Point each)
1) Which of the following is true
a. Limit of all rational functions always exist.
b. If the function has limit at infinity then the limit of the function is said to be existing.
c. Limit of all non continuous function does not exist.
d. A function is said to be continuous if only the limit of the function exist.
e. None of the above
2) A function f(x) is continuous at c if
a. F(x) at c exist
b. The limit of f(x) as x approaches to c exist and equals to f(c)
c. If f is non differentiable at c
d. All of the above
e. None
3) Which of the following is correct?
a. All differentiable functions are continuous
b. All continuous functions are differentiable
c. If the limit of the function exists then necessarily its derivative also exists.
d. Derivative is the method of calculating average rate of change
e. All of the above
4) If the function f(x) has maximum point at x=x0 ,then one of the following is necessarily
true except,
a. f’(x=x0) is equals with zero
b. f’(x) changes its sign from positive to negative
c. f’ (x=x0) is negative
d. all except D
e. none
5) Given cost function constrained by output as
C= x2+2y2+ 5xy+700
Subject to x+ y =500
Then one of the following is true
a. The auxiliary function could be F(x,y,ì)= x2+2y2+5xy+700 +  (500-x-y)
b. The stationary points could be (375,125)
c. The objective function could have minimum point at (125, 375)
d. The stationary points of auxiliary function could be the critical points
e. All except B
6) Which one of the following is odd
A. Exponential functions
C. Rational functions
B. Linear functions
D. quadratic functions
E. None
7) Which of the following is true
A. All polynomial functions are rational
D) All of the above
B. All constant functions are polynomial
E) None
C. Rational functions are the ratio of two quadratic functions
8) All of the following are false about the linear functions, Except
A. Graphs of all linear functions are line
E) A & D are answer
B. Linear functions are polynomial function of degree two F) None
C. Slope of linear functions vary at each points
D. Constant functions are linear functions
9) Given two points (1, 2) and (-1, -1) on the line , all of the following are true , except
A. The slope of the line is 3
C. Y intercept is 2
B. The equation of the line is
D. X intercept is 2
y=3x+2
E. None
10) Which of the following is true about line
A. Lines with positive slopes are up warding
B. Lines with equal slopes are parallel
C. Horizontal lines has no slope
D. All except
PART II FILL THE BLANK ON THE SPACE PROVIDED (2 pts each)
1. The equation of a line that passes through (1 ,7) and (6 , -3) is _________
2. Suppose TC=33+2Q and the per unit output price fixed at birr 13 then the break-even
output level is ___________
(V  2) 3  8
3. Given Q=
then
V

a.
b.
lim
V 0
Q is__________
lim
V a

Q is__________
dy
4. f(x) = 4 4 x 2  1 then
at x=1 is equal to________________
dx
5. Given y=f(x)=2x 2 + x then
a. Average rate of change of f(x) for x changes 1 to 3 is equal to _____________
b. Marginal rate of change of f(x) at x=2 is equal to____________________
Part III Workout (show all the necessary stapes for each question)
1. The demand function of a given commodity X is estimated as
Qx  10,000  1,500Px  2 y  200Pc where Qx is quantity of product x, Px price of
product X, Pc ifs price of related good and y is per capita income of the consumer. If the
current price of x is Birr 5, the price of the competitor product is Birr 8 and the per capita
income is Birr 5000 then(4 pts)
a. Calculate the cross price elasticity of demand and state the two products relation
b. Calculate the income elasticity of demand and the type of good
2. Assume the demand function of wheat for Dire Dawa Food Complex Company is given
by P= 1500-10Q and its total cost is also C= Q3 – 10Q2 +300Q+1000. Then find (3 pts)
a. Profit maximizing level of output & price, assuming Dire Dawa Food Complex
Company is the only company in our country and maximum profit.
b. Profit maximizing level of output & price, assuming perfectly competitive market s
and maximum profit.
3. A firms unit cost of capital and labor are 1 birr and 2 birr respectively and the production
function of the firm is Q=4KL+L2 with total fixed cost of 105 birr then,(3 pts)
a. The output maximizing level of labor and capital
b. The maximum level of out put
Answer sheets
Part I
1
2
Part II
1._____________
2._____________
3
4
5
3. a.____________
b. ____________
6
7
4. ______________
8
9
10
4|Page
5. a.____________
b.____________