## Tuesday, January 01, 2019 2014
(May)
EONOMICS
(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
1. is
1. 2. 3. 4. 1. Given 1. 2. 3. 4. 1. 1. 2. 3. 4. 1. In the determinant , the minor of element 8 is
1. 0
2. 8
3. – 3
4. – 6
1. Given the function the function is
1. 2. 3. 4. 1. Rank of the matrix is
1. 1
2. 2
3. 3
4. 4
1. The function is not continuous at
1. 1
2. 2
3. 3
4. None of the above
1. 1. 2. 3. 4. 2. Answer any four of the following: 4x4=16
1. Find the numbers a and b that make A the inverse of B, when  1. Illustrate Hawkins-Simon conditions.
2. Draw the graph of 3. Derive the elasticity of substitution for Cobb-Douglas production function.
4. Evaluate: 5. 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 at or 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 and denotes 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 by function is given by . Find the elasticity of demand at .    4
6. (a) (i) Find 5
(ii) Given the MC function , find the level of output at which the will be minimum.          6
Or
(b) (i) Given the marginal propensity to import and the information that when , find the import function . 4
(iii) Define consumer’s surplus. Given the demand function and 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 path and test whether the time path is convergent.
(ii) Write a note on the cobweb model.

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