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ALLAMA IQBAL OPEN UNIVERSITY, ISLAMABAD (Department of Economics) WARNING 1. PLAGIARISM OR HIRING OF GHOST WRITER(S) FOR SOLVING THE ASSIGNMENT(S) WILL DEBAR THE STUDENT FROM AWARD OF DEGREE/CERTIFICATE, IF FOUND AT ANY STAGE. 2. SUBMITTING ASSIGNMENT(S) BORROWED OR STOLEN FROM OTHER(S) AS ONE’S OWN WILL BE PENALIZED AS DEFINED IN “AIOU PLAGIARISM POLICY”. Course: Mathematics for Economists (803) Semester: Autumn 2016 Level: M.SC Economics Total Marks: 100 Pass Marks: 40 ASSIGNMENT No. 1 (Units: 1–4) Q.1 Elucidate the ingredients of mathematical model with examples. Also discuss various kinds of variables. Q.2 Give the following model: Y= C+1o + G C = a + b (Y – To), G = gY (a) Identify the endogenous variables (b) Give the economic meaning of the parameter ‘g’ (c) Find the equilibrium national income Q.3 Use Crammer’s rule to solve the following equation systems: a) 8x1-x2=16 (b) -x1+ 3x2 +2x3= 24 2x2+ 5x3 = 5 x1 + x3 = 6 2x2+ 3x3 = 7 5x2 – x3 = 8 Q.4 Discuss with the help of examples the applications of derivatives in economic theory. Q. 5 Use the Jacobian determinants to test the existence of functional dependence between the paired functions. (a) y1 = 3x 21 + x2 y2 = 9x41+ 6x21 (x2 + 4) + x2 (x2 + 8) + 12 (b) y1 = 3x12 + 2x22 y2 = 5x1 + 1 1 ASSIGNMENT No. 2 (Units: 5–9) Total Marks: 100 Pass Marks: 40 Q.1 Find the derivatives using the implicit function derivative technique for the following functions (a) F (x, y) + 3x2y – 5xy2 + 3xy – 4x + 9y – 10 (b) F (x, y) = x2 + y2 – 9 Q.2 Describe in detail the formulas for calculating simple growth rate, compound rate and average compound rate of growth. Q.3 A monopolist sell two goods have its demand functions as: X = 25 – 0.5PX and y = 30 - PY The joint cost function is: C = x + 2xy + y2 + 20 Find the quantity of each good where the cost of monopolist is minimum (a) The price charge for “x” and “y” (b) The profit of monopolist Q.4 Explain the difference between concave function and strictly concave function, convex and strictly convex function. Q.5 If C = 45x2 + 90 x y + 90y2 while the production quota is 2x + 3y = 60 (a) Find quantities where costs are minimized. (b) Check second order conditions with Boarder Hessian Determinant. 2