2015

(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 option/Answer the following: 1x8=8

- Let matrix is of dimension and matrix is of dimension . Then and are conformable for multiplication in the form if

- Define diagonal matrix.
- Mention one property of CES production function.
- If is an average cost function, where of the following is its marginal cost for?

- 20
- 30
- 25
- None of the above.

- Given, , where is consumption expenditure and is National Income. Which of the following is marginal propensity to save?

- 1
- 0.7
- 0.3
- None of the above

- Given is

- Write the necessary and sufficient conditions for the maximization of a function

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

- Write the assumptions of input-output analysis. 4
- Write four properties of determinants. 4
- Write the meanings of the following: 1+2+1=4

- Idempotent matrix.
- Rank of matrix.
- Norms of matrix.

- The total cost of a firm is given by

Find the value of at which marginal cost equals average cost.

- The marginal revenue function is given by Find the point elasticity of demand

3. (a) (i) Define the following with examples: 2x4=8

Unit set; Power set; Proper subset; Intersection of sets.

(ii) If find

(b) (i) Distinguish between relation and function with example.

(ii) Draw the graph of

4. (a) In a three-sector economy, the input coefficient matrix and find demand vector are given below: 11

Find the sectoral output

Or

(b) Solve the following National Income model using Cramer’s rule:

5. (a) (i) In a perfectly competitive market, the price of a product (q) is Rs. 4 and the total cost (C) of a firm is given by , Find profit maximizing output and maximum profit. 6

(ii) Show the relationship among Marginal Revenue, Average Revenue and Price Elasticity of Demand. 6

Or

(b) The production function of a firm is given by where and are labour and capital inputs respectively. The cost function is given by Find the least cost capital labour ratio, where 12

6. (a) (i) Briefly discuss the uses of integral calculus in economics. 5

(ii) Define producer’s surplus. Given the producer’s supply function and market price is 10. Find the producer’s surplus. 2+4=6

Or

(b) (i) Define marginal propensity to save Given function and saving is zero when income is 81. Find the aggregate saving function. 2+4=6

(ii) Given the marginal cost function

What is the decrease in total cost is output produced is reduced from 10 to 5 units? 5

7. (a) (i) Solve the differential equation 3

(ii) Analyze the following market model for stability: 8

Or

(b) (i) Solve the first-order difference equation and 4

(ii) Given the demand and supply functions for cobweb model

Find the intertemporal equilibrium price and also examine whether you will get stable equilibrium. 7