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BECE-015
BACHELOR'S DEGREE PROGRAMME Term-End Examination
L'D C3)
December, 2012
C\.! BECE-015 : ELEMENTARY MATHEMATICAL METHODS IN ECONOMICS Time : 3 hours Note :
Maximum Marks : 100
Answer any two from section 'A', any four from section 'B', any four from section 'C'.
1.
SECTION-A Answer any two questions from this section. Construct ordinary and compensated demand 20 functions for the two commodities q1 and q2, for the utility function U = 2q1q2 + q2.
2.
Consider the following macroeconomic model : C= C(Y),
0
I = I(r),
41 <0
Md =L(Y,r),
Ly >0 and Lir <0
20
Where C is consumption, Y is the national income, I is investment, Md is demand for money, r is rate of interest, and Cy , 41 , oy, or are the usual first order derivatives. BECE-015
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P.T.O.
Equilibrium conditions are described as follows : Y=C+ I+ Z, where Z is exogenously given and > 0 Mil = M , where AJ is money supply. Determine the comparative static properties of dr dY dY dr and dM dZ dM dZ 3.
A person must get certain minimum requirements 20 of carbohydrate proteins and minerals for good health. His diet consists of the major items : I and II, prices and nutritional contents of the same are shown below : Item I
Item II
Daily Minimum Requirements
0.60
1.00
10
4
20
Proteins
5
5
20
Minerals
2
6
10
Price Rs. Carbohydrates
Write the above as a linear programming problem to minimize cost and solve the same. 4.
(a) Find the mixed strategy Nash Equilibrium 15 of the following : Player 2 Player 1 Top Bottom
Left
Right
0, 0
0, -1 -1, 1
1, 0
(b) What will be the solution of the above mentioned game if players adopt max-min principle ? BECE-015
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5
5.
6.
SECTION-B Answer any four questions from this section. Suppose that a revenue maximizing monopolist 12 requires profit of at least Rs. 1500. His demand and cost functions are P = 304 — 2q and C = 500 + 4q + 8q2. Demonstrate the KuhnTucker conditions for this problem. (Note that the final solution is required here.) (a) Find the limit when x 0 of the following 8+4 (1+x)6 -1 function : (1+x) 2 -1 (b) Also check the continuity property of the above function.
7.
The existence of the unique solution of the 12 following system depends on what condition (say, for Cramer's Rule method) : x+y+z= 19 2x + 3y — z = 6 5x — y + az = 10 where x, y, z are the unknowns and a, h are some constants.
8.
Differentiate between strongly dominated strategy 12 and weakly dominated strategy.
9.
Consider the following consumer problem : Max U= x.y s.t. P xx + PY-if = M Find out the indirect utility function for this problem.
BECE-015
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12
P.T.O.
SECTION-C 10.
Short questions. Attempt any four out of six. (a) Write the expression of Envelope Theorem. (b) Write the expression of Roy's Identity. (c)
(d) (e) (f)
BECE-015
Transform the following primal problem into a dual problem : Max U= U(x, y) Subject to Pxx+Pyy=M Define the compensated demand function. Define the Hotelling Lemma. Define a feasible solution in linear programming.
4
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BECE-015
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BECE-015
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