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

AN 11

FIFTH SEMESTER – NOV 2006

         EC 5404 – MATHEMATICS FOR ECONOMISTS

 

 

Date & Time : 03-11-2006/9.00-12.00         Dept. No.                                                       Max. : 100 Marks

 

 

 

Part  – A

 

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

1. What is the use of differential calculus in economics?
2. Specify any two application of integral calculus in economics.
3. Find the rate of change of Y w.r.t. a small change in X, when Y = (5/2 X – 7) ^1/3
4. Define partial derivative.
5. Define limit of a function.
6. What do you mean by continuity of a function?
7. Find

 

Part – B

 

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

8. Discuss the theorems on limit.
9. Prove that the function y = x² is continuous at the point x = 2.
10. If , prove that
11. If , find
12. Find out the derivative of the following implicit function

 

13. If D = 2P stands for the demand function find the point elasticity ‘’ when P = 5.
14. A student has Rs. 100 per month to spend on two goods, the money can be spent either on clothing which costs Rs. 50 per item or on cinema, which costs Rs.10 per visit. If is the number of items on clothing bought and  is the number of visits to cinema, then the student’s utility function is defined as . Show that the student will spend equal amounts of his income on each item under equilibrium.

 

 

 

 

 

Part – C

 

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

15. Explain the advantages and disadvantages of using mathematics in economics.
16. Derive the rules to obtain the derivatives.
17. Determine the extreme values of the function
18. (i) Evaluate

(ii) The demand law of a certain product is P = 25-2q. Calculate the consumer’s surplus when the equilibrium price for the product is Rs. 5

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.A. DEGREE EXAMINATION – ECONOMICS

FIFTH SEMESTER – APRIL 2012

EC 5404 – MATHEMATICS FOR ECONOMISTS

 

 

 

Date : 30-04-2012              Dept. No.                                       Max. : 100 Marks

Time : 1:00 – 4:00

PART – A

 

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

 

1. Define continuity of a function.
2. If marginal revenue is R’ = 15 – 9x – 3x², find the total revenue and demand functions.
3. Find elasticity of demand (y) with respect to price (x), y = 100 – 5x
4. Evaluate    ò 2x (x² + 1) dx
5. State the conditions for saddle point.
6. The Total revenue (R) and Total cost (C) functions of a firm are given by:           R = 30Q – Q² and C = 20 + 4Q, where Q is the output. Find the equilibrium output of the firm.
7. Write the two cross elasticities of demand for commodities x₁ & x₂ and prices p₁ & p₂.

 

 

PART – B

 

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

 

1. Briefly explain the various properties of limits.
2. Examine the following function for maximum and minimum values:

Z = 4 x³ + y² – 4x + 8y

3

1. Show that AC and MC curves intersect at the lowest point of the Ac function.
2. Determine maxima and minima, sketch the curve representing each function for   y = x⁴ – 4x³ + 12
3. Explain the various types of discontinuities with examples.
4. State and prove the Euler’s theorem.
5. Find the total differential of

1. Z = 2x² + 5x²y + xy² + y²
2. Z = (2x² + y) (x + 2y²)

 

 

PART – C

 

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

 

1. Derive the relation between Average and Marginal Revenue curves.
2. Explain the various rules for differentiation. Enumerate the correction procedures for 0/0 case, ¥ case and rational polynomial functions.
3. Find the maximum of the function f(x, y) = 5x² + 6y² – xy under the condition that x+2y =24.
4. If Demand: y = 50 – 6x and Cost: y_c = x² + 9x, determine maximum profit for the monopolist and the maximum revenue for the government if a tax of ‘t’ per unit is imposed.

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.A. DEGREE EXAMINATION – ECONOMICS

FIFTH SEMESTER – NOVEMBER 2012

EC 5404 – MATHEMATICS FOR ECONOMISTS

 

 

 

Date : 16/11/2012             Dept. No.                                       Max. : 100 Marks

Time : 9:00 – 12:00

 

PART – A

 

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

1. State the condition for minima in case of a function with only one independent variable.
2. Define a ‘Limit’.
3. Find dy  for y  = ( 2x² + 4x – 5 )⁶

dx

1. The Total Cost is given as y = 200 + 1000x – 24x² + 4x³ + x⁴. Find the Average Cost and Marginal Cost.
2. What is point of inflection? Support your explanation with relevant diagram.
3. Evaluate    ò (x³ – 4x² + x) dx
4.  Find the Total Differential of

 

PART – B

 

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

 

1. Find the relative maxima and minima (if any) for y = x³ + 3x² + 2
2. Explain the various types of discontinuities with relevant examples.
3. If Z = 2x²  5x²y+ xy² + y², find

 

 

1. Explain the various properties of limits.
2. The demand function faced by a firm is p = 500 – 0.2x and its cost function is     C = 25x + 10000, where p is the price, x is output and C is the total cost. Find the profit maximizing output and price.
3. The average cost function is given as

. Find the minimum average cost and show that at the minimum average cost, marginal cost and average cost are equal.

1. State and prove the Euler’s theorem.

 

 

PART – C

 

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

 

1. Minimise f (x,y) = x² + 2y² – xy subject to x + y = 8.
2.  The demand and supply functions under pure competition are, respectively,          P_d = 16 – x² and P_s = 4 + x. Find the producer’s surplus and consumer’s surplus.
3.  Derive the relationship between AC and MC.
4. Explain the significance of differentiation in Economics.

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