special Exam.pdf - UNIVERSITY OF THE FREE STATE...

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1 UNIVERSITY OF THE FREE STATE: BLOEMFONTEIN CAMPUS EECM3714 INTRODUCTORY MATHEMATICAL ECONOMICS DEPARTMENT OF ECONOMICS ASSESSORS: MODERATOR: MARKS : 100; TIME : 240 MINUTES This exam paper consists of 3 questions on 3 pages. A formulae sheet is attached to the back of this paper. This exam counts 40% of your final mark. The Afrikaans paper is on the reverse. INSTRUCTIONS 1) Answer all the questions. Number your answers clearly! 2) Write legibly, using only black or blue ink. Do not write in the margins of your answer book. 3) Show your work. 4) Where necessary, round final answers to the nearest four decimals (except when this yields unsatisfactory results). a. Use fractions (e.g. 2 3 ) and radicals (e.g. √2 ) for greater accuracy when performing calculations. b. Use scientific notation (e.g . 0.000067 = 6.7 × 10 −5 ) if your answers are very small. 5) PLEASE SUBMIT THIS QUESTION PAPER AFTER COMPLETION OF THIS EXAM. QUESTION 1 [42] 1.1 ) Oscorp’s short-run cost function is ? = 3? 2 + 7? + 12 1.1a ) Find the level(s) of ? that minimise Oscorp’s average cost (AC). Verify that this (these) value(s) of satisfies (satisfy) the first- and second-order conditions for the minimisation of AC. [ 4 ] 1.1b ) Show that AC is equal to marginal cost (MC) at the level(s) of ? that minimises (minimise) AC. [ 2 1.2 ) Consider the production function ? = 8 ( 3 ? 0.5 + 1 3 ? 0.5 ) 4 . 1.2a ) Does this production function exhibit increasing, decreasing or constant returns to scale? Show/explain. . ? ] 2 [ 3 ] 1.2b ) Write down the expression for the isoquant if ? = 128 . [ 2 1.2c ) Use implicit differentiation to find the marginal rate of technical substitution (MRTS), i.e. find 𝑑? 𝑑? . [ 2 ] 1.2d ) Find an expression for the capital elasticity of production, ? ]

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