[BA 4th Sem Question Papers, Dibrugarh University, 2015, Economics, Major, Mathematics for Economics]
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.
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 
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
, 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
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
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
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
is output produced is reduced from 10 to 5 units? 5Also Read: Dibrugarh University Question Papers
7. (a) (i) Solve the differential equation 
3
3
(ii) Analyze the following market model for stability: 8
Or
(b) (i) Solve the first-order difference equation 
and 
4
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
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