(Pages : 4)
Reg. No. : .................................... Name : .........................................
Final Year B.A. Degree Examination, March 2009 Part III – Group III : ECONOMICS Paper VI – Optional (vi) : Mathematical Economics (New Scheme – 2005 admn. onwards) Time : 3 Hours
Max. Marks : 100
Instruction: Answers may be written either in English or in Malayalam. I. Choose the correct answer. Write only the alphabet. 1) Which theory made use of General Equilibrium framework ? a) Linear programming b) Input-output table c) Game theory 2) TV second order condition of profit maximisation is ∂2 π <0 a) ∂ x2
∂2 π >0 b) ∂ x2
∂ π2 <0 c) ∂ x2
examquestionpapers.com 3) The nature of apparent real income in slutsky equation is a) decreasing b) increasing c) constant 4) The elasticity of supply for the function s = 100 – 5p2 at p =3. a) Less than one b) One c) More than one 5) At q = 2, the function x2 – 2x – 7, is ___________ a) decreasing b) increasing c) stationary (5×1=5 Marks) II. State True or False : 6) Saddle point is another name for dominant equilibrium. 7) Product differentiation is a feature of monopoly. 8) Expansion path is the locus of the optimal input combinations as the output level changes input prices remaining constant. 9) Lagrangian multiplier is unconstrained optimisation technique. 10) The Engel curve for an inferior good is negatively sloped.
(5×1=5 Marks) P.T.O.
III. Fill in the blanks : 11) ___________ of a given matrix is the new matrix obtained by interchanging its rows and columns. [Transpose, Determinants] 12) _________ is that the price derivative of a demand function can be decomposed into an income effect and substitution effect. [Euler’s Theorem/Slutsky Equation] 13) _______ measures the rate at which substitution between factors takes place. [Elasticity of substitution/Marginal rate of substitution] 14) Perfect price discrimination is also termed as _________ [First degree discrimination/Third degree discrimination] 15) ___________ developed input-output model. [Robinson/Leontieff]
IV. Define any four of the following : 16) Saddle point. 17) Market equilibrium. 18) Budget line. 19) Returns to scale. 20) Quadratic equation.
V. Answer any seven of the following not more than half a page. 21) What are the assumptions of input-output model ? 22) Explain Prisoner’s dilemma. 23) Explain consumer’s surplus. 24) From the demand function X = 80 – 4P – P2, determine price elasticity of demand when P = 5. 25) Differentiate y = (x2 + 3) (2x3 + 4x). 26) If the total cost is TC = 50 + 10q + 25q2. Find the Average Cost and Marginal Cost when q = 2.
27) Find the equilibrium price and quantity P = 50 −
7 Q (demand function ) 8
P = 15 +
3 Q (sup ply function ) . 4
28) Determine which type of returns to scale is the following production function Q = 2K + 3L + KL. 29) Distinguish between primal and dual. 30) Explain price effect.
VI. Answer any six of the following, each not more than one page. 31) Examine the following function for its maxima or minima and determine its value C = 2x2 – 12x + 40.
32) Explain CES production function.
33) Explain economic interpretation of time margin function. 34) Solve the LPP by graphic method : Maximise Z = 3x1 + 4x2 Subject to x1 + x2 < 6 2x1 + 4x2 < 21 x1, x2 > 0 35) The cost function of a monopolist is TC = 500 + 20q2 The demand function is P = 400 – 20q. What is the profit maximising output ? k3 36) Production function is given by Q = − + 2k 2 + 12k . Beyond what points 3 do diminishing returns do exist ?
37) Explain Ridge Lines. 38) Explain dynamic input-output model. 39) State and prove Adding-up Theorem. 40) The supply function for a commodity P = 2 + Q2. Find the producer’s surplus when price is Rs. 18. (6×5=30 Marks) VII. Answer any three of the following not exceeding three pages each. 41) Explain Cobweb Model. 42) Find firm’s equilibrium and cost function if the production function is CobbDouglas function. 43) Explain constrained optimisation. Optimise the function z = 2x3 + 3x 2 – 2x2y2 subject to x + y = 10. 44) The demand function of a monopolistic firm is
examquestionpapers.com P = 8000 – 4q
LAC = 8000 – 7q + 0.002q2. Find profit maximising price and output. 1
45) Production function is given by Q = 2K 2 L 2 . Assume that K = 9, P = 6 and wage rate (w) = 2. Determine optimal quantity of labour. If wage rate is increased to Rs. 3/-, find the optimal quantity of labour. 46) Explain Simplex method of Linear Programming. ——————