Download Marginal Cost Function - Quantitative Methods in Economics - Exam and more Exams Quantitative Techniques in PDF only on Docsity!
Ollscoil na hÉireann, Gaillimh GX_____
National University of Ireland, Galway
Semester 1 Examinations 2009/
Exam Code(s) 2BA1, 2BA6, 3BA12, 2BCW1, 2BFS1, 2BHR1, 2BIS1, 2BTP1, 2BWM1, 1EM1, 1OA1, 1EK Exam(s) 2 nd B.A., 2 nd B.A. (PSP), 2 nd B.A. (Humanities & Society), 2 nd B.A. (Creative Writing), 2 nd B.A. (Film Studies), 2 nd B.A. (Human Rights), 2nd^ B.A. (Irish Studies), 2nd^ B.A. (Theatre & Performance), 2nd^ B.A. (Global Women’s Studies), Erasmus, Occasional, H.Dip.Econ.Sc. Module Code(s) EC Module(s) Quantitative Methods in Economics Paper No. 1 Repeat Paper External Examiner(s) Professor Robert Wright Internal Examiner(s) Professor John McHale Dr. Srinivas Raghavendra Instructions: Section A: Answer any five questions. Each question carries 20 marks Section B: Answer any five questions. Each question carries 20 marks Duration 3 hrs. No. of Pages 4 Department(s) Economics Course Co-ordinator(s) S. Raghavendra Requirements : MCQ Handout Statistical Tables Yes Graph Paper Yes Log Graph Paper Other Material
EC229 Quantitative Methods in Economics Section A
- Calculate the x - intercepts: a) (x - 1)(x + 2) = 0 b) (2x – 1)(x + 10) = 0 c) (3x + 5)(4x – 9) = 0 d) (x – 2)(x + 1)(4 – x) = 0
- The demand and supply functions of a good are given as follows: P = - 5Qd + 80 P = 2Qs + 10 Where P, Qd, Qs denote price, quantity supplied and quantity demanded respectively. (i) Find the equilibrium price and quantity [12] (ii) If the government deducts, as tax, 15% of the market price of each good, determine new equilibrium price and quantity. [8]
- Maximize profits for a firm, given total revenue and the total cost , assuming.
- Show that the following production functions are homogenous and comment on their returns to scale: a) Q = 10KL 2 [10] b) Q = 70K 1/ L 3/ [10]
- Evaluate for each of the following functions at the given point. 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) = at x = 4.
- If the average cost function of a good is AC = 15/Q + 2Q + 9 Find an expression for TC. What are the fixed costs in this case? Calculate the marginal cost function.
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 [4] b. Find the mean and median of the times. [8] c. Find the range and the standard deviation of the times. [8] 3 The Midland National Bank selected a sample of 40 student checking accounts. Below are their end-of-the-month balances $404 74 234 149 279 215 123 55 43 321 87 234 68 489 57 185 141 758 72 863 703 125 350 440 37 252 27 521 302 127 968 712 503 489 327 608 358 425 303 203 (i) Tally the data into a frequency distribution using $100 as a class interval and $0 as the starting point. [ 4 ] (ii) Draw a cumulative frequency polygon. [8] (iii) The bank considers any student with an ending balance of $400 or more a “preferred customer”. Estimate the percentage of preferred customers. [ 4 ] (iv) The bank is also considering a service charge to the lowest 10 percent of the ending balances. What would you recommend as the cutoff point between those who have to pay a service charge and those who do not? [ 4 ]
- A group of fresh arts graduates were 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: and s = 6. Compare the relative dispersion in the two groups.
- Bank of Ireland customers select their own three-digit personal identification (PIN) number for use at ATMs. (i) Think of this as an experiment and list four possible outcomes. [ 8 ] (ii) What is the probability Mr. Smith and Mrs. Smith select the same PIN? [ 8 ] (iii) Which concept of probability did you use to answer (ii)? [ 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 sample check of 4000 packages in the past month revealed the following information:
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? [4] b. What is the probability all four members will be men? [4] c. Does the sum of the probabilities for the events described in parts (a) and (b) equal 1? Explain. [12]
- 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?
