Essay about Econ1202 Semester 2 2008 Final Exam - 1301 Words

THE UNIVERSITY OF NEW SOUTH WALES SCHOOL OF ECONOMICS ECON1202/2291 QUANTITATIVE MEHODS A FINAL EXAMINATION SESSION 2 2008 TIME ALLOWED - 3 HOURS THIS PAPER IS WORTH 60% OF THE TOTAL SUBJECT MARK Questions: 7 Students must attempt no more than 6 questions Marks per question: 10 Exam weighting: 60%. Instructions to Students: - Complete all of the details required on the front page of the examination booklet. - Make sure that you note the SIX(6) questions attempted on the front of your examination booklet - If Seven questions are attempted, the first SIX(6) will be marked. - You may use a non-programmable calculator - Graph paper will be provided. - Answers are to be written in ink. Pencils are permitted for graphing purposes. - The†¦show more content†¦(3 marks) c) Determine the optimal number of bus and train travelers. (2 marks) d) Say a train strike signiï ¬ cantly reduced the number of trains available. By how much would the train capacity constraint have to fall for the optimal solution to be altered? (2 marks) 4 Question 5: a) Consider the implicit function 2x4 (y − 1) + exy = 7 Find the rate of change of y with respect to x when x = 2, y = 1. (2 marks) b) Find: 12y + 6 dy +y+3 y2 (3 marks) c) In the small town of Lametopia, which has a population of 80,000 people, the town council (of 100 people) hears in advance that the town might have won â€Å"Tidiest city 2008.† News circulates about the town quickly, such that by the end of the ï ¬ rst week (one week after the council heard the news!) 1000 people know the rumour. Assuming growth is logistic, ï ¬ nd how many individuals should have heard the rumour after two weeks. (5 marks) 5 Question 6: a) An importer of antiquities knows that he can sell bowls and carved ï ¬ gurines to the domestic market. If q1 is this number of ï ¬ gurines sold, their price will be $(60 − 2q1 ). If q2 bowls are sold, $(10 − q2 ) will be the price of bowls. Figurines cost $16 and bowls $4 to the importer and ï ¬ xed costs are $200. i) How many each of ï ¬ gures and bowls should be sold to maximise proï ¬ t. ii) Is this indeed a maximum? Justify using second order conditions. iii) What price is