2014

(May)

EEONOMICS

(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

- is

- Given

- In the determinant, the minor of element 8 is

- 0
- 8
- – 3
- – 6

- Given thefunctionthefunction is

- Rank of the matrixis

- 1
- 2
- 3
- 4

- The functionis not continuous at

- 1
- 2
- 3
- None of the above

2. Answer any four of the following: 4x4=16

- Find the numbers a and b that make A the inverse of B, when

- Illustrate Hawkins-Simon conditions.
- Draw the graph of
- Derive the elasticity of substitution for Cobb-Douglas production function.
- Evaluate:
- Given the input coefficient matrix

Explain the economic meaning of the third column sum and the third row sum.

3. (a) (i) Define the following with examples: 1x4=4

Null set; Disjoint set; Convex set; Union of sets.

(ii) Define limit of a function.

(iii) A function is given by

find whether the function is continous ator not. 4

Or

(b) (i) If,; find 3

(ii) Solve the following pair of equations graphically: 5

(iii) Define continuity of a function. 3

4. (a) (i) Consider the following macro-economic model of two countries, that trade with each other:

Here is income, is consumption, is (exogenous) autonomous expenditure, denotes exports anddenotes imports of country . Find the equilibrium values of and by matrix algebra. 7

(ii) Distinguish between the following: 2+10=12

(a) Static and Dynamic input-output models.

(b) Open and Closed input-output models.

Or

(b) (i) Verify that the following Matrix A is idempotent: 10+2=12

(ii) Given the technical coefficient matrix (A) and the final demand vector (F), find the consistent level of sectoral output in a static input-output framework:

5. (a) Distinguish between Cobb-Douglas production function and CES production function. State and prove the properties of CES production function. 2+10=12

Or

(b) (i) A consumer has a utility function. Does the utility function display diminishing marginal utility? 5

(ii) Find out, when 3

(iii) The AR function is given byfunction is given by. Find the elasticity of demand at. 4

6. (a) (i) Find 5

(ii) Given the MC function, find the level of outputat which thewill be minimum. 6

Or

(b) (i) Given the marginal propensity to importand the information thatwhen, find the import function. 4

(iii) Define consumer’s surplus. Given the demand functionand the supply function, find the consumer’s surplus at equilibrium. 2+10=12

7. (a) (i) Let the demand and supply functions be, 10+2=12

Assuming that the rate of change of price over time is directly proportional to the excess demand, find the time path.

(ii) Briefly explain the use of differential equations in economics.

(b) (i) In a market model

and . Find the time pathand test whether the time path is convergent.

(ii) Write a note on the cobweb model.