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Ollscoil na hÉireann, Gaillimh GX_____
National University of Ireland, Galway
AUTUMN Examinations 2007 / 2008
Exam Code(s) 2BA1, 2BA6, 1EM1, 1OA1, 1EK1, 1EK Exam(s) 2 nd B.A., 2 nd B.A. (PSP), Erasmus, Occasional, H.Dip.Econ.Sc. Module Code(s) EC22 9 Module(s) Quantitative Methods in Economics Paper No. Repeat Paper Repeat External Examiner(s) Professor Robert E. Wright Internal Examiner(s) Mr. Brendan Kennelly Dr. Srinivas Raghavendra Instructions: PLEASE FOLLOW INSTRUCTIONS CAREFULLY. Answer any four questions from each section and each question carries 2 5 marks. Duration 3 hours No. of Pages 5 Department(s) ECONOMICS Course Co-ordinator(s) Dr. Srinivas Raghavendra Requirements : MCQ Handout Statistical Tables Graph Paper Log Graph Paper Other Material
EC229 Quantitative Methods in Economics Answer any four questions from each section and each question carries 2 5 marks. Section A
- Maximize profits! for a firm, say Supermacs, given total revenue R = 4000 Q! 33 Q 2 and total cost C = 2 Q 3 ! 3 Q 2 + 400 Q + 5000 , assuming Q > 0. [Hint:! =R-C]
- The demand and supply functions for two interdependent commodities are given by: QD1 = 100 – 2P 1 + P 2 QD2 = 5 + 2P 1 - 3P 2 QS1 = - 10 + P 1 QS2 = - 5 + 6P 2 Where QDi, QSi and P denote the quantity demanded, quantity supplied and price of good i respectively. Determine the equilibrium price and quantity for this two – commodity model.
- Define the following concepts using suitable examples: (i) Union of two sets (ii) Intersection of two sets (iii) Complement of a set (iv) If S I V = S and S U V=V , then using Venn diagram show that S! V. (v) Power set.
- Show that the following production functions are homogenous and comment on their returns to scale: a) Q = 7KL 2 b) Q = 50K 1/ L 3/
- Evaluate f ’ (x) for each of the following functions at the given point. a f x x at 9 . ( )= 3 x = 1. b. f(x) = x 2 - 2x at x= c. f(x) = x 3 - 4x 2 +2x-8 at x= d. f(x) = 5x^4 - (4/x^4 ) at x = - 1 e. f(x) = x! 2 / x at x = 4.
Section B
- The mean income of a group of sample observations in €500; the standard deviation is €40. According to Chebyshev’s theorem, at least what percent of the incomes will lie between €400 and €600?
- Roberta’s is a very popular restaurant located in Salthill. They serve a variety of pizzas and other Italian delicacies. During the summer season, they do not take reservations or accept “call ahead” seating. Management of the restaurant is concerned with the time a patron must wait before being seated for dinner. Listed below is the wait time, in minutes, for the 25 tables seated last Saturday night: 28 39 23 67 37 28 56 40 28 50 51 45 44 65 61 27 24 61 34 44 64 25 24 27 29 a. Explain why the times are a population b. Find the mean and median of the times. c. Find the range and the standard deviation of the times.
- Determine the median and the values corresponding to the first and third quartiles in the following data. Also calculate the inter-quartile range for this distribution. 46 47 49 49 51 53 54 54 55 55 59
- A large group of Air Force inductees was given two experimental tests – a mechanical aptitude test and a finger dexterity test. The arithmetic mean score on the mechanical aptitude test was 200, with a standard deviation of 10. The mean and standard deviation for the finger dexterity test were: x = 30 and s = 6. Compare the relative dispersion in the two groups.
- Listed below are the salaries, in €000, for a sample of 15 chief financial officers in the electronics industry: 516 548 566 534 586 529 546 523 538 523 551 552 486 558 574 i) Determine the coefficient of skewness using Pearson’s method. [16] ii) What is your conclusion regarding the skewness of the data? [4]
- An automatic Shaw machine fills plastic bags with a mixture of beans, broccoli, and other vegetables. Most of the bags contain the correct weight, but because of the variation in the size of the beans and other vegetables, a package might be underweight or overweight. A check of 4000 packages filled in the past month revealed: Weight Event Number of packages Probability of occurrence Underweight A 100 0. Satisfactory B 3600 0. Overweight C 300 0. Total 4000 1. What is the probability that a particular package will be either underweight or overweight?
- The board of directors of Tarbell Industries consists of eight men and four women. A four-member search committee is to be chosen at random to conduct a nationwide search for a new company president. a. What is probability all four members of a search committee will be women? b. What is the probability all four members will be men? c. Does the sum of the probabilities for the events described in parts (a) and (b) equal 1? Explain.
- From the data given below, calculate the following: First Event Second Event A 1 A 2 A 3 Total B 1 3 2 3 8 B 2 2 3 3 8 Total 5 5 6 16 (i) Determine P (A 1 ). (i) Determine P (B 1 |A 2 ). (ii) Determine P (B 2 and A 3 ).
