LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
M.A. DEGREE EXAMINATION – ECONOMICS
FIRST SEMESTER – NOVEMBER 2012
EC 1809 – MATHS & STATISTICS FOR ECONOMISTS
Date : 09/11/2012 Dept. No. Max. : 100 Marks
Time : 1:00 – 4:00
PART – A
Answer any FIVE Questions (5×4=20marks)
- State any four properties of determinant of a Matrix.
- Define Partitioned Matrix. Write the formula for finding A-1 using Partitioned Matrix.
- Prove that .
- The simple correlation coefficients between two variables out of three is given as r12 = 0.86 r13 = 0.65 r23 = 0.72. Find r3 and r23.1.
- State the condition for unconstrained optimization with two independent variables.
- Define Eigen values. Calculate the Eigen values for the following matrix A = .
- State the pdf of Binomial Distribution by highlighting its properties.
PART – B
Answer any FOUR Questions (4×10=40marks)
- Solve the following National income models using Cramers’ rule:
Y = C + I0 + G0
C = α + β(Y-T) (α > 0; 0 < β < 1)
T = γ + δY (γ > 0; 0 < δ < 1)
- Prove that CES production function being linearly homogenous satisfies Euler’s Theorem.
- Briefly explain the various applications of derivatives in economics.
- A firm under perfectly competitive situation produces the products Q1 and Q2 jointly and the Total Cost function is given by:
C =Q12 + Q22 + 2Q1Q2 + 20
If the price of Q1 and Q2 are 20 and 24 respectively, find:
- Profit maximizing Output.
- Maximum Profit.
- The following table gives the yield of 15 sample fields under three varieties of seeds A, B and C:-
| A | B | C |
| 20 | 18 | 25 |
| 21 | 20 | 28 |
| 23 | 17 | 22 |
| 16 | 25 | 28 |
| 20 | 15 | 32 |
Test the 5% level of significance whether the average yields of land under different varieties
of seeds show significant differences. (Table value of ‘ F’ at 5% level for V1=2 and V2=12 is
3.88)
- Given below are the figures of production (in Lakh Kg) of a sugar factory:
| Year | 2005 | 2006 | 2007 | 2008 | 2009 | 2010 | 2011 |
| Production | 40 | 45 | 46 | 42 | 47 | 50 | 46 |
Fit a Linear Trend line by the Least Square method and tabulate the trend values.
- In an Industry, 200 workers, employed for a specific job, were classified according to their performance and training received / not received to test independence of a specific training and performance. The data is summarized as follows:
| PERFORMANCE | Total | ||
| GOOD | NOT GOOD | ||
| TRAINED | 100 | 50 | 150 |
| UNTRAINED | 20 | 30 | 50 |
| 120 | 80 | 200 | |
Use χ2 test of independence at 5% level of significance and write your conclusion.
(Table value of χ2 at 1 d:f ; 5% = 3.84)
PART – C
Answer any TWO questions (2×20=40 marks)
- Find the consistent level of sectoral output in dynamic Input-Output frame work given:
A= B= G= F=
- Given the Utility function U = 2 + X + 2Y + XY and the budget constraint 4X + 6Y = 94, Find out the equilibrium purchase of X and Y in order to maximize the Total Utility.
- Following is the distribution of students according to their heights and weights:
| Height
in inches |
Weight in pounds | |||
| 90-100 | 100-110 | 110-120 | 120-130 | |
| 50-55 | 4 | 7 | 5 | 2 |
| 55-60 | 6 | 10 | 7 | 4 |
| 60-65 | 6 | 12 | 10 | 7 |
| 65-70 | 3 | 8 | 6 | 3 |
Calculate:-
- The coefficients of regression.
- The two regression equations.
- The correlation coefficient.
- (a) State the various properties of Normal distribution.
(b) The mean and standard deviations of the wages of 6000 workers engaged in a factory are Rs 1200 and Rs 400 respectively. Assuming the distribution to be normally distributed, estimate:
- Percentage of workers getting wages above Rs.1600.
- Number of workers getting wages between Rs.600 and Rs.900.
- Number of workers getting wages between Rs.1100 and Rs.1500.
The relevant values of the area table (under the normal curve) are given below:
| Z : | 0.25 | 0.5 | 0.6 | 0.75 | 1.00 | 1.25 | 1.5 |
| Area: | 0.0987 | 0.1915 | 0.2257 | 0.2734 | 0.3413 | 0.3944 | 0.4332 |
Latest Govt Job & Exam Updates: