2013

(May)

ECONOMICS

(Major)

Course: 401

(Mathematics for Economics)

Full Marks: 80

Pass Marks: 32

Time: 3 hours

The figures in the margin indicate full marks for the questions

1. Choose the correct answer: 1x8=8

- Givenand.is

- is a form of

- Constant function.
- Polynomial function.
- Exponential function.
- Logarithmic function.

- 13
- – 13
- 16
- – 16

- Which of the following is a symmetric matrix?

- Givenis

- The elasticity of substitution Cobb-Douglas production function is

- 0
- 1
- More than 1
- Less than 1

- None of the above

2. Write short notes on (any four): 4x4=16

- Rank of matrix.
- Properties of determinant.
- Mathematical derivation of the relationship between AC and MC.
- Mathematical derivation of the relationship between AR and MR.
- Consumer’s surplus.
- First-order difference equation.

3. (a) (i) Given the universal set

Find the complement of 2

(ii) Show the operations of sets with the help of Venn diagram. 6

(iii) Find the limit of the function as 3

Or

(b) (i) What is ordered pair? How is it related to function? 5

(ii) Prepare a brief note on different forms of functions and their graphs. 6

4. (a) (i) Show how the sectoral equilibrium output can be estimated in a framework of static open input-output model. 7

(ii) From the following market model, find the equilibrium output and price using Cramer’s rule: 4

Or

(b) (i) Given 3

and

Find

(ii) Find the determinant of, where 4

(iii) Given 4

Find

5. (a) (i) Find the derivative of the following function: 4

(ii) Given the consumption function 4

Find out the marginal propensity to consumeand marginal propensity to save.

(iii) Prove mathematically that for substitutes indifference curves are negatively sloped. 4

Or

(b) (i) Explain the geometrical interpretation of derivatives in case of a single-independent variable. 6

(ii) Prove that Cobb-Douglas production function satisfies the Euler’s theorem. 6

6. (a) (i) Find 5

(ii) Obtain the consumer’s surplus of the following demand function when the market price is Rs. 16 per unit.

6

(b) (i) Find 3

(ii) Derive total cost function from the following marginal cost function when fixed cost is Rs. 500: 3

(iii) Given the supply function. Obtain the producer’s surplus when market price is Rs. 6

7. (a) (i) Solve the differential equation

With initial condition

(ii) Analyze the following market model for stability:

Or

(b) (i) Solve the following difference equation: with

(ii) In a cobweb model

Obtain the time path ofand analyze the condition for its convergence.