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1 UNIVERSITY OF THE FREE STATE: BLOEMFONTEIN CAMPUS EECM3714: INTRODUCTORY MATHEMATICAL ECONOMICS DEPARTMENT OF ECONOMICS MAIN MID-YEAR EXAM 2017 (PAPER 1) ASSESSORS: MODERATOR: MARKS : 100; TIME : 240 MINUTES Die Afrikaanse vraestel is op die keersy. || The Afrikaans paper is on the reverse. This exam paper consists of 3 questions on 3 pages. A formulae sheet is affixed to the back of this paper. This exam counts 40% of your final mark. INSTRUCTIONS 1. Answer all the questions. 2. Label and number questions and subsections of questions clearly. 3. Write legibly in ONLY black or blue ink, and DO NOT write in the margins of the answer sheet. 4. Show all steps and calculations used to obtain final answers. 5. Round all answers to the nearest FOUR decimal places. For greater accuracy, use radicals (e.g. √2 ) and fractions (e.g. 2 3 ) in your calculations. QUESTION 1 [42] 1.1) ACME Corporation’s cost function is 𝐶 = 2? 3 + 4? + 500 1.1a) Find the level(s) of ? that minimise ACME’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 minimise AC. (2) 1.2) Consider the production function ? = 2(0.4? 0.5 + 0.6? 0.5 ) 2 1.2a) Show that this production function is homogenous of degree one. (2) 1.2b) Find an expression for the isoquant if ? = 800 . (2) 1.2c) Use implicit differentiation to find the marginal rate of technical substitution (MRTS), i.e. find 𝑑? . (2) 1.2d) Find an expression for the capital elasticity of production, ? . ? . 𝑑?

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