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Aec304: Operations Research 1 Question Paper
Aec304: Operations Research 1
Course:Bachelor Of Arts In Education
Institution: Kenyatta University question papers
Exam Year:2009
QUESTION ONE "
KENY ATT A UNIVERSITY
UNIVERSITY EXAMINATIONS 2007/2008
FIRST SEMESTER EXAMINATION FOR THE DEGREE OF BACHELOR
- OF ARTS, BACHELOR OF COMMERCE AND BACHELOR OF
EDUCATION
AEC 101: INTRODUCTORY MATHEMATICS FOR ECONOMISTS
INSTRUCTIONS:
Answer Question One and any other TWO
DATE: Friday 30th November 2007 TIME: 2.00 - 4.00 p.m.
(a)Using the following national income model:
Y=C+I+G+X-:M
C=a+byd
I=ro+rIR
T=to+tIY
•. G=Go
X=Xo
M=mO+mIY
Where, C= Consumption, I= Investment, G= Government expenditure, X=Exports, M=Imports
(i) Find the equilibrium income (5marks)
(ii) What does a, b, tl, mo and mr stand for? (5marks)
(iii) Find the rate of change of equilibrium income with respect to G and R (4 marks)
(iv) Find the value of equilibrium income if a=10, b=0.5, to=100, ro=4 ml=4, rl=2,
Go=2000,Xo=500, tr=O.", R=0.20 (4 marks)
(v) Find the value of the multiplier using the above values and interpret your answer
(4marks)
(vi) If government expenditure increases from 2000 to 3000. Using the values in (iv) find the
change in equilibrium income. (4marks)
(b) State four importance of mathematics for the economists (4 marks)
QUESTION TWO
(a) Proof that the following function is continuous at x=o ( 6marks)
(x2+14x+ 15)/(x+5) OSxS20
(b) Given the following total cost function:
TC=a+b1 Q+b2Q2-b3Q3
Find;
(i) ATC, AFC, AVC, MC (8 marks)
(ii) Find the value of Q at which Me are equal to zero ifbl=4, b2=5, b3=6 (6 marks)
QUESTION THREE
Given the following demand and total cost functions:
P=1O-7Q
TC=20+3Q+4Q2+5Q3
Find :-
(i) The level ofQ, P that will maximize profits (8 marks)
(ii) The level ofQ that will maximize total revenue ( 6 marks)
(iii) The level ofQ that will maximize MC and AVC (6 marks)
QUESTION FOUR
Given the following production function
Q=AKaLb A>O,a,b<l
(i) Express the following in terms of Q:
MPK, MPL, slope ofMPK, and MPL (10 marks)
(ii) Explain the coefficients A, a, and b (3 marks)
(Hi) Ify= (2X12X2-3x2)/(X12+4x2Xl) .
Find the partial derivatives of the above function (7 marks)
QUESTION FIVE
Given the following demand functions for two different firms:
Firm A: P=20..;lQ
Firm B: 3p2+4PY..7Q=20
(i) Find the price elasticity of demand for each firm ( 4marks)
(ii) Find the price elasticity of demand for each firm at P=6 and Q= 10 ( 2 marks)
(iii) Comment on the values obtained in part (ii) above (4 marks)
(b)A two commodity market model is given by the following:
Commodity ONE: Qd=50-3P\+4P2
QS=10+5P\
Commodity Two: Qd=20-7P2+ 3P}
QS=-15+4P2
Determine the equilibrium prices and quantities for the two commodities ( 10 marks)
2
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