LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
M.A. DEGREE EXAMINATION – ECONOMICS
FIRST SEMESTER – NOV 2006
AN 20
EC 1809 - MATHS & STATISTICS FOR ECONOMISTS
Date & Time : 02-11-2006/1.00-4.00
Dept. No.
Max. : 100 Marks
Part - A
Answer any FIVE questions in about 75 words each.
1. Define ‘Hypothesis’.
2. Mention the types of discontinuities.
3. What is meant by partial correlation?
4. What are the components of time series?
5. Compute  12.3 if  12  0.2,  13  0.3,  14  0.4
(5 x 4 = 20 marks)
6. Find the maxima / minima of y  x 2  2 x  3
dy
7. Find
if y  ( x 2  5x  3)e
dx
Part – B
Answer any FOUR questions in about 300 words each.
8. Solve by using Crmer’s rule
x yx 6
2x  y  z  7
x  y  2z  9
(4 x 10 = 40 marks)

1
9. Show that MR  AR 1  
 ed 
10. Find the relative maximum, minimum and point of inflexion from the following
x3 5
function y   x 2  6 x  10 .
3 2
11. A sample of 900 members has a mean of 3.4 cms and standard deviation of 2.61
cms. can the sample be regarded as one drawn from a population with mean 3.25
cms? (level of significance 5%)
12. Measure seasonal variation by the method of simple averages.
Year
Q1
Q2
Q3
Q4
1990
65
58
56
61
1991
68
63
60
69
1992
70
67
68
66
1993
67
62
60
64
1994
70
60
60
70
1
13. Show that elasticity of substitution form a CES production function is
1 
where Q  A  L   (1   )k   

1

14. Estimate the regression of Y on X for the following data:
X:
1
2
3
4
5
6
Y:
9
8
10
12
11
13
Part – C
Answer any TWO questions in about 900 words each.
(2 x 20 = 40 marks)
15. Discuss the role of mathematics and statistics in applied economics.
16. (a) Show that average cost and marginal cost intersect at the lowest point of the
average cost function.
(b) For a linear average revenue function, the slope of the corresponding marginal
revenue function is twice that of the average revenue function.
17. Find the partial regression coefficient of X3 on X1 and X2
X1: 3
5
6
8
12
14
X2: 16
10
7
4
3
2
X3: 90
72
54
42
30
12
18. A farmer applied three types of fertilizers on 4 separate plots. Determine whether
there is any significant difference in yield.
Plots \ Fertilizer Nitrogen Potash Phosphate
1
6
7
8
2
4
6
5
3
8
6
10
4
6
9
9