# B.A. DEGREE EXAMINATION  –     ECONOMICS

FIFth SEMESTER  – NOVEMBER 2003

EC 5404  MATHEMATICS  FOR  ECONOMICS

12.11.2003                                                                                        Max: 100 Marks

1.00 – 4.00

PART A                                                    (5 ´ 4 = 20 Marks)

Answer any FIVE each carries FOUR marks.

1. What is differential calculus?
2. Find out the derivative of a function y = x2 .
3. What is meant by partial differentiation? Give an illustration.
4. For the utility function of two commodities U = (x1 – 2)2 (x2 +1)3 .  Find the

marginal  utility of x1 and x2 at x1= 3, x2 = 4.

1. Define integral calculus.
2. Solve .
3. The marginal cost function of a firm in 100-10x + 0.1x2 where x is the output.

Obtain the total cost function of the firm when the fixed cost in Rs.500.

PART B                                                  (4 ´ 10 = 40 Marks)

Answer any FOUR; each questions carries TEN marks.

1. Differentiate the function:  x3 y + y -2x = 0.
2. Prove that the first order differentiation of the function ex is ex.
3. If f(n) = x3 -5x2 + 7, find the second order derivative of f(x) and for that value of x does f 1(x) vanish?
4. Examine the curve y = x3 for convexity.
5. If the demand law is    , find ed with respect to price at the point

where p =3.

1. Integrate :   .
2. Find the area bounded by the parabola x2 = 4by, the x – axis and the ordinate at x =3.

PART C                                                  (2 ´ 20 = 40 Marks)

Answer any TWO each carries TWENTY marks.

1. Find the maximum and minimum values of the following function y = x3 -3x +1.
2. Evaluate I = log x.dx.
3. Max U = 48 -(x -5)2 -3 (y -4)2

s.t x+3y = 9   ”  x, y b³ 0.

1. Give the demand and supply functions and

Find the price of the quantity demanded and the consumer surplus.

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## Loyola College B.A. Economics April 2004 Select Constitution Of The World Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI 600 034

B.A DEGREE EXAMINATION –  ECONOMICS

THIRD SEMESTER-APRIL 2004

# HT 3100/ HIS 100 SELECT CONSTITUTION OF THE WORLD

19.04.2004

1.00 –4.00                                                                                         Max. 100 Marks

PART A                 (10 ´ 2 = 20 Marks)

Answer any TEN of the following questions in not exceeding Ten lines each.

1. Judicial Review
2. Rule of Law
3. Secret ballto system
4. Chancellor of Exchequer
5. Mid – term Poll
6. Double citizenship
7. Aristocrasy
8. Privy COUNCIL
9. Spoil system
10. Recall
11. Unitary State
12. Federalism

PART B                                (4 ´ 10 = 40 marks)

Answer any FOUR of the following questions in not exceeding a page each.

1. Explain the impeachment procedure for the president of USA.
2. Write a short note on the powers and functions of the Prime Minister of UK.
3. Explain the salient features of the Swiss constitution.
4. Point out the significant features of the French Judiciary.
5. Explain the meaning, merits & demerits of Democracy.
6. Examine the functions of the speaker of House of Representative of USA.

PART C                             (2 ´ 20 = 40 Marks)

Answer any TWO of the following questions in not exceeding 4 pages each.

1. The president of US combines the powers of prime Minister of Indian and the

Queen of England -substantiate.

1. Examine the legislative, executive and Judicial functions of the British Crown.
2. Evaluate the Direct Democratic devices in Switzerland.
3. Assess the powers and functions of the Senate in France.

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## Loyola College B.A. Economics April 2004 Econometrics Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI –600 034

B.A., DEGREE EXAMINATION – ECONOMICS

# ST 4204/STA 204 – ECONOMETRICS

07.04.2004                                                                                                           Max:100 marks

9.00 – 12.00

SECTION -A

Answer ALL questions.                                                                               (10 ´ 2 = 20 marks)

1. Define the term ‘econometrics’.
2. Give any two properties of expectation.
3. List down the axioms of probability.
4. Mention the difference between statistic and parameter.
5. Give any two properties of least square estimates.
6. Consider the regression of y on x given by y = . How will you interpret the regression coefficients?
7. What is analysis of variance?
8. Give an example for structural change.
9. Mention the consequences of multicollinearity.
10. What is meant by heteroscedasticity?

SECTION – B

Answer any FIVE questions.                                                                                     (5 ´ 8 = 40 marks)

1. a) A, B and C are mutually exclusive and exhaustive events associated with a random experiment. find P(A) given that P (B) =  P(A);  P(C) =  P(B).
2. b) If 2 dice are thrown, what is the probability of getting a sum greater than 8?
3. c) If find P(A) and P(B). Hence show that A and B are independent.                                                                                                  (2+2+4)

1. a) Explain the term ‘linear’ with reference to a regression model.
2. b) Write down the assumptions in a simple linear regression model. (4+4)

1. Suppose that a researcher is studying the relationship between gallons of milk consumed by a family per month (y) and the price of milk each month (x in dollars / gallon). The sample consists of observations in 12 consecutive months.  Analysis of the data assuming a linear model of y on x reveals the following:

.  For this sample, find (i)  (ii)  (iii) Least squares slope (iv) Least squares intercept (v) Standard error of regression  (vi) standard error of slope (vii) Test the hypothesis that the slope coefficient is zero at 5% level.

1. Consider the following data set:

Sample No:       1          2          3        4          5

y :      15        10        14        8          3

x:         1          2          3        4          5

1. i) Calculate the least square estimates for and assuming the model

y =  for the above data.

1. ii) Calculate for each sample.

1. iv) Calculate the coefficient of determination.

1. Justify / interpret the following statements:
2. P { – 0.725 < b1 < 2.35} = 0.90
3. R2 = 0.6735
• the estimates obtained by the least squares method are the best when compared with the estimates obtained by some other method.
1. .

1. Explain the concept of interval estimation.

1. What are dummy variables? Explain how the data matrix is specified in the presence of dummy variables.

1. Explain the method of Generalized least squares.

SECTION – C

Answer any TWO questions.                                                                       (2 ´ 20 = 40 marks)

1. a) The joint probability distribution of two random variables X and Y in given by

X

-1      0      1

-1    0      0      1/3

Y     0     0      0      0

1     0     1/3   1/3

find i) the marginal distribution of X and Y.

1. ii) Var(X),  Var(Y)

iii) Cov(X,Y)

1.        iv)  Conditional probability of X given Y = 1.
2. v) Var(X + Y)

1. b) Define: Independent events, mutually exclusive events and sample space. (15+5)

1. a) Explain the test of overall significance of a multiple regression.

1. b) Consider the following ANOVA table:

 SOURCE df Sum of Squares All Variables (X1, X2, X3, X4) ? 800 First two Variables (X1, X2) ? 300 Difference ? ? Residual ? ? Total 25 1500
1. Complete the table by filling the missing values.
2. Test H0: b1 = b2 = b3 = b4 = 0

Vs

H1 :  atleast one bk 0,  k = 1,2,3,4  at 5% level

iii)       Test H:    b1 = b2 = 0

Vs

H1:  b1 0 (or) b2 0 at 5% level.

1. iv) Test H0 : b3 = b4 = 0 Vs H1: b 0 (or) b4 0 at 1% level                             (8+12)

1. a) Consider the following data

y          X1        X2

1          1          2

3          2          1

8          3          -3

Based on this data, estimate the following regressions:

y = a0+ a1 X1 i + u1i

yi = b0 + b1X1i+ b2X2i +u2i

Is a1 = b1?  Why or why not?

1. b) i) Explain the concept of structural change.
2. ii) Give the steps involved in ‘Chow test’ to test for structural change. (10+10)

1. a) Explain the remedial measures for multicollinearity.

1. b) Write short notes on:
2. Coefficient of determination
3. Statistical inference

Random variables.                                                                                   (10+10)

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## Loyola College B.A. Economics Nov 2004 Mathematical Economics Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI –600 034

B.A., DEGREE EXAMINATION – ECONOMICS

# EC 5404 – MATHEMATICAL ECONOMICS

03.11.2004                                                                                                           Max:100 marks

9.00 – 12.00 Noon

### SECTION – A

Answer any FIVE questions                                                                         (5 ´ 4 = 20 marks)

1. What do you mean by variable?

1. Define Function.
2. Find the value of x for which the following function is not defined .
3. What is meant by derivative of a function?

1. Find if y = x2 + y2 + c.

1. If P = 200 – 10q is the demand function. Obtain the MR when the sale q = 5.

1. If z = 2x3 + 10xy + 5y2 then find out higher – order derivatives with respect to x & y.

### SECTION – B

Answer any FOUR questions                                                                       (4 ´ 10 = 40 marks)

1. Explain the different types of variables.

1. Discuss the rules of differentiation.

1. If  .

1. Find , when .

1. Minimize q = 12 L3/4 . K1/4

S.t. 3L + K = 80.

1. Discuss the properties of definite integral.

1. If , Prove that  .

### SECTION – C

Answer any TWO questions                                                                          (2 ´ 20 = 40 marks)

1. Briefly explain the role of differential calculus in economic theory.

1. Find the maximum value of for positive value of x.

1. Find the area included between the two parabolas: y2 = 4x and x2 = 4y.

1. Find the producer’s surplus when

Pd = 3x2 – 20x + 5

Ps = 15 + qx when x is quantity.

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