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Ollscoil na hÉireann, Gaillimh GX_____
National University of Ireland, Galway
REPEAT Examinations 2008/
Exam Code(s) 2BA1, 2BA6, 1EK2, 1EM1, 1EK Exam(s) 2 nd B.A., 2 nd B.A. (PSP), H.Dip.Econ.Sc., Erasmus, Occasional Module Code(s) EC Module(s) Quantitative Methods in Economics Paper No. Repeat Paper 1 External Examiner(s) Professor Robert Wright Internal Examiner(s) Professor Eamon O’Shea Dr. Srinivas Raghavendra Instructions: SECTION A. Answer any FOUR questions. Each carries 25 marks. SECTION B. Answer any FOUR questions. Each carries 25 marks. Duration 3 hours No. of Pages 5 Department(s) Economics Course Co-ordinator(s) Dr. Srinivas Raghavendra Requirements : MCQ Handout Statistical Tables Yes Graph Paper Yes Log Graph Paper Yes Other Material
EC229 Quantitative Methods in Economics Section A 1. If the average cost function of a good is
Q
AC Q
Find an expression for MC. If the current output is 15, estimate the effect on TC of a three unit decrease in Q. 2. 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 goods respectively. Determine the equilibrium price and quantity for this two – commodity model. 3. 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. 4. Show that the following production functions are homogenous and comment on their returns to scale: a) Q = 7KL 2 b) Q = 50K1/4L3/ 5. Evaluate (^) f '^ (x)for each of the following functions at the given point a. f(x) = 3x^9 at 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.
3. 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 4. 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. 5. The following are the earnings per share for a sample of 15 software companies for the year 2005. The earnings per share are arranged from smallest to largest. Find the coefficient of skewness using Pearson’s estimate. What is your conclusion regarding the shape of the distribution? 6. 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? 7. A study of 200 grocery chains revealed these incomes after taxes: What is the probability a particular chain has under $1 million in income after taxes? What is the probability of grocery chain selected at random has an income of greater than $20 million? What rule of probability was applied?
Income after Taxes Number of Firms Under $10 million 102 $20 million to $50 million 61 $50 million or more 37
8. A survey of undergraduates in the School of Social Sciences at Western University revealed the following distribution regarding the gender and majors (assume they take one specialized subject) of students: (i) What is the probability of selecting a female student? (ii) What is the probability of selecting a political science or economics major? (iii) What is the probability of selecting a female or an economics major? (iv) What is the probability of selecting an economics major given that the person selected is male?
