1UNIVERSITY OF THE FREE STATE: BLOEMFONTEIN CAMPUSEECM3714: INTRODUCTORY MATHEMATICAL ECONOMICSDEPARTMENT OF ECONOMICSMAIN MID-YEAR EXAM 2017 (PAPER 1)ASSESSORS:MODERATOR:MARKS: 100;TIME: 240 MINUTESDie 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. Thisexam counts 40% of your final mark.INSTRUCTIONS1.Answer all the questions.2.Label and number questions and subsections of questions clearly.3.Write legibly inONLYblack or blue ink, andDO NOTwrite in the margins of the answer sheet.4.Show all steps and calculations used to obtain final answers.5.Round all answers to the nearestFOURdecimal places. For greater accuracy, use radicals (e.g.√2)and fractions (e.g.23) in your calculations.QUESTION 1 1.1)ACME Corporation’s cost function is𝐶 = 2?3+ 4? + 5001.1a) Find the level(s) of?that minimise ACME’s average cost (AC). Verify thatthis (these) value(s) ofsatisfies (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)21.2a)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. find𝑑?. (2)1.2d)Find an expression for the capital elasticity of production,?.?.𝑑?