nehu-economics.info MA/MSc Mathematics for Economists Question Paper : North-Eastern Hill University
Name of the Organisation : Department Of Economics,North-Eastern Hill University, Shillong
Exam : MA/MSc Question Papers
Subject : Mathematics for Economists
Year : 2015
Document Type : Previous Years’ Question Papers
Website : https://www.nehu.ac.in/
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MA/MSc Mathematics for Economists Question Paper :
Full Marks: 75;
Time: 3 hours
Note :
** The figures in the margin indicate full marks for the questions
** Answer five questions, selecting at least one from each Credit.
Related : North-Eastern Hill University Pre-PhD Question Papers : www.pdfquestion.in/13306.html
CREDIT – I :
1. (a) Discuss the properties of determinants. 6
(b) Solve the system of equations by Cramer’s Rule. 9
2. (a) Find the Eigen values and associated Eigen vectors of the following square matrix 10
(b) Prove that for subsets A, B, and C of a universal set ? 5
3. (a) Following are the demand functions of three commodities produced by a discriminating monopolist firm and its cost (C) function 10
(b) Write a note on properties of linearly homogeneous production function. 5
5. (a) Solve the following Linear Programming Problem using Simplex Method 10
b. functions always homogeneous? Explain your answer with appropriate examples. 2+3=5
7. (a) Write an explanatory note on Cobweb model. 8
(b) Given the following demand and supply functions, find inter temporal equilibrium price and determine whether the equilibrium is stable
8. (a) Write an explanatory note on market model with inventory. 8
Mathematics for Economists 2014 :
Full Marks: 75;
Time: 3 hours
Note :
** The figures in the margin indicate full marks for the questions
** Answer five questions, selecting at least one from each Credit
Credit – I :
1. (a) Find the length of the difference between two vectors,V1=(x1,y1)(x2,y2) using appropriate diagram
(b) Given the function,z=x1+3x1x2+2×1-x2-x2x3 find the Hessian matrix and determine the sign of the Hessian matrix evaluating its principal minors.
Credit – II :
L and K represent labor and capital respectively. Prove that 5+10
(a) The given production function is homogeneous of degree one; and
(b) Its elasticity of substitution is constant.
4. (a) Derive the necessary and sufficiency conditions of utility maximization given the following utility function (U) and budgetary constraint (B) as follows
MaximizeU = U(x,y)
(b) Solve the following Linear Programming Problem using Simplex Method Xpx+Xpy=B
Credit – III :
(a) Solve and determine the time path whether it is damped/ uniform/explosive fluctuation. 7
(b) Write an explanatory note on Phase diagram. 8
(a) Write a note on market model with price expectations. 6
(b) Explain growth model of Solow, How does it vary from Domar growth model? 7+2
CREDIT – IV :
(a) Derive the time path of y, given the second order difference equation having constant coefficient and constant termy1+a1ya+a2y2=c 10
(b) Solve: Yx+1+3yt=4; y(0) =4 5
(a) Given the following demand and supply functions, find the inter temporal equilibrium price and determine whether the equilibrium is stable Q=18-3p and Q1=49t-1-3 5
(b) Explain Samuelson’s multiplier-accelerator interaction model. 10
Mathematics for Economists 2013 :
Full Marks: 75;
Time: 3 hours
Note :
** The figures in the margin indicate full marks for the questions
** Answer five questions, selecting at least one from each Credit
CREDIT – I :
(a) Prove that for subsets of a given universal set U 3+3
i.(XUY)-Z = (X-Z)U(Y-Z)
ii. X-(YUZ) = (X-Y)^(X-Z)
2. (a) Provide geometric interpretation of a determinant having two rows and two columns. 7
(b) Given the function, find the Hessian matrix and determine the sign of the Hessian matrix evaluating its principal minors. 3+5
CREDIT – II :
3. (a) Write an explanatory note on Cobb-Douglas production function and its properties.
(b) Given the cost (C) function of a multi-product firm and the sales prices (P1, P2) of commodities produced, find the maximum level of profit earned by the firm if quantity of commodities produced are Q1, and Q2
4. (a) Derive the necessary and sufficiency conditions of utility maximization given the following utility function (U) and budgetary constraint (B) as follows:
(b) Given the function, test whether the function ‘H’ is homogeneous and homothetic. 5+2
CREDIT – III :
5. (b) Make a critical assessment of Domar growth model 5
(b) Explain the procedure of solving a Bernoulli equation. 5
CREDIT – IV
6. (a) Derive the time path of Y, given the first order difference equation having constant coefficient and constant term:
(b) What is a Cobweb model? What does it explain?
7. (a) Given the following demand and supply functions, find the inter temporal equilibrium price and determine whether the equilibrium is stable 8
(b) Examine the stability conditions of equilibrium price of a market in which inventory exists. 7