[BA 4th Sem Question Papers, Dibrugarh University, 2013, Economics, Major, Mathematics for Economics]
1. Choose the correct answer: 1x8=8
- Given
and
.
is
- None of the above.
is a form of
- Constant function.
- Polynomial function.
- Exponential function.
- Logarithmic function.
- 13
- – 13
- 16
- – 16
- Which of the following is a symmetric matrix?
- Given
is
- 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
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
, 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 consume
and marginal propensity to save
.
and 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
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
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
. Obtain the producer’s surplus when market price is Rs. 6Also Read: Dibrugarh University Question Papers
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
with
(ii) In a cobweb model
Obtain the time path of
and analyze the condition for its convergence.
and analyze the condition for its convergence.
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