LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034  M.A. DEGREE EXAMINATION – ECONOMICS

AN 20

FIRST SEMESTER – NOV 2006

         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.                  (5 x 4 = 20 marks)

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 if
6. Find the maxima / minima of
7. Find if

Part – B

 

Answer any FOUR questions in about 300 words each.           (4 x 10 = 40 marks)

8. Solve by using Crmer’s rule
9. Show that
10. Find the relative maximum, minimum and point of inflexion from the following function .
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

13. Show that elasticity of substitution form a CES production function is where
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

 

 

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

RF 29

M.A. DEGREE EXAMINATION – ECONOMICS

FIRST SEMESTER – APRIL 2007

EC 1809 – MATHS & STATISTICS FOR ECONOMISTS

 

 

 

Date & Time: 30/04/2007 / 1:00 – 4:00      Dept. No.                                       Max. : 100 Marks

 

 

Part  – A

 

Answer any FIVE questions in about 75 words each.                   (5 x 4 = 20 marks)

 

1. Distinguish between partial and multiple correlation.
2. Define ‘Multiple Regression’.
3. Distinguish between secular trend and seasonal variation.
4. Define ‘derivative’.
5. State the conditions for maxima and minima in y = f(x)
6. Define the distribution which explains improbable events.
7. Find , if (i) (ii)

 

Part – B

 

Answer any FOUR questions in about 300 words each.               (4 x 10 = 40 marks)

8. State the properties of determinants.
9. Find the output vector from the following input coefficient matrix and final demand vector
10. Calculate Karl Pearson’s coefficient of correlation

X:     6       8          12        15        18        20        24        28        31

Y:    10      12        15        15        18        25        22        26        28

11. Fit a straight line regression from the following data:

X:     0       1          2          3          4          5          6

Y:     2       1          3          2          4          3          5

12. Define limit and continuity. Determine the right side limit and left side limit of the following functions and discuss the types of discontinuity.

(i) ,   (ii)

13. Evaluate the following derivatives:

(i)                (ii)             (iii) ,

(iv)         (v)

14. Discuss the conditions of maxima and minima and saddle point form the function Z = f(x,y).

 

 

 

 

 

 

Part – C

 

Answer any TWO questions in about 900 words each.                 (2 x 20 = 40 marks)

15. Derive the properties (Characteristics) of Cobb Douglas production function.
16. Discuss the rules of differentiation with examples.
17. Fit a Poison distribution to the following data:

No of mistakes per page:              0          1          2          3          4          5

No of pages:                                  40        30        20        15        10        5

18. A normal distribution was fitted to the distribution of new business brought by 100 insurance agents with following results:

New business (in ‘000 Rs)	10-20	20-30	30-40	40-50	50-60
Observed frequency	10	20	33	22	15
Expected frequency	9	22	32	25	12

Test the goodness of fit.

 

 

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BC 32

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

M.A. DEGREE EXAMINATION – ECONOMICS

FIRST SEMESTER – APRIL 2008

EC 1809 – MATHS & STATISTICS FOR ECONOMISTS

 

 

 

Date : 05-05-08                  Dept. No.                                        Max. : 100 Marks

Time : 1:00 – 4:00

                Part A                                                (5×4=20 Marks)

 

Answer any five of the following, each answer not exceeding 75 words:

 

1. What are the conditions for matrix addition and multiplication?
2. Define Symmetric Matrix. Give example.
3. What is meant by maximum value of a function?
4. For the production function X=K³-8K²+10KL+5KL²-3L³, find the direct and the cross partial derivatives.
5. What is an inter-industry economy?
6. The probability is 2/5 that a batsman scores 100 runs in a cricket match. What is the probability that in 5 matches the batsman will score 100 runs in at least three matches.
7. What are the properties of Normal Distribution?

 

                                   Part B                                                         (4×10=40 Marks)

 

Answer any four of the following, each answer not exceeding 300 words:

 

8. Verify that the matrix multiplication satisfies the laws of commutative, associative, and distributive.

 

9. Solve the linear equations, which directly involve finding inverse:

3X₁+X₂+X₃=4                  X₁-X₂-X₃=0                 2X₁+X₃=5

 

10. The input-output matrix for two industry economy is expressed by the following table:

                                                    Input

                                  Industry I           Industry II    Level of output

Output

 Industry I                    300                       800                       2400

 Industry II                   600                       200                       4000

 

a)    Determine the level of final demand, which can be met by the two industries.

 

b)    Determine the matrix of technology coefficient for the two-industry economy.

11. A firm has a demand curve given by the function 2Q-160+3P=0. The average cost curve of the firm is given by the relationship AC-3Q³=63+5/Q-18Q. Find the level of output, which minimizes total revenue.

12. Find the first-order and second –order derivatives for the following function:

                                              X²-Y²

                               Z= log   ———-

                                             X²+Y² 

13. Bring out the differences between correlation analysis and regression analysis.

14. Explain the method of least – squares.

                                         Part C                                                      (2×20=40 Marks)

 

Answer any two the following, each answer not exceeding 900 words:

15. Given the following demand and supply functions for products X,Y, Z, find the equilibrium prices for the three products, using Cramer’s rule.

Qdx=8-2Px+3Py-Pz

Qdy=4-4Py+Px+3Pz

Qdz=6-Pz+3Px+3Py

Qsx=10

Qsy=2Py+2

Qsz=8+Pz

0.1   0.3   0.1

16. Show that the inverse of the Leontief Matrix A= 0      0.2   0.2

0      0      0.3   is

1.11   0.42   0.28

(I-A)^-1 =      0        1.25   0.36

0        0        1.43

17. From the following, obtain the two regression lines:

X:  18   19   20  21   22   23   24   25   26   27

Y:  17   17   18   18   19   19   19   20   21   22

18. A manufacturer of swimming pools has the following production function:

 

40Q=1800-4(x-12)²-3(y-20)²

where Q is the number of pools built over the year, and

x and y are the amount of labour and materials used.

The price of the pool is Rs. 500, and the cost per unit of the inputs are(under perfect competition) are Rs. 200 for labour, and Rs. 150, for materials. Using the method of Lagrange determine the optimum quantities of the two inputs.
 

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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   r_23.1.
• 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:

1. Profit maximizing Output.
2. 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:-

1. The coefficients of regression.
2. 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:

1600. Percentage of workers getting wages above Rs.1600.
1601. 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

 

 

 

 

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