EC1102_2015Answers(1).pdf - UNIVERSITY OF LONDON BSc EXAMINATION 2015 For Internal Students of Royal Holloway MODEL ANSWERS EC1102 QUANTITATIVE METHODS

# EC1102_2015Answers(1).pdf - UNIVERSITY OF LONDON BSc...

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UNIVERSITY OF LONDON BSc EXAMINATION 2015 For Internal Students of Royal Holloway MODEL ANSWERS EC1102: QUANTITATIVE METHODS IN ECONOMICS 1 Time Allowed: TWO hours Answer ALL questions EC calculators are permitted Distribution Tables and Formula sheet attached c Royal Holloway, University of London 2015
EC1102 SECTION A Answer ALL questions from this section. QUESTION 1 Answer YES or NO to the following questions: (a) Is it true that 1 7 5 i =2 i = 2 ? (3 Marks) Model Answer YES (b) You sell a project for \$ 865 , 000 . Exactly one year ago you bought the project for \$ 200 , 000 . Is it true that the annual rate of return on the project was 243% ? (3 Marks) Model Answer NO (c) Suppose f ( x ) = 4 x 2 + 89 . Is it true that f 0 ( x ) = 8 x ? (3 Marks) Model Answer YES (d) Let f ( K, L ) = 10 K 1 / 3 L 2 / 3 . Is f ( K, L ) homogeneous of degree 1? (3 Marks) Model Answer YES Marks so far: 15 Page 1 of 14 NEXT PAGE
EC1102 (e) Does lim x 0 e x - 1 x exist? (3 Marks) Model Answer YES (f) Is it true that R x 5 dx = 1 4 x 4 + C , where C is an arbitrary constant? (3 Marks) Model Answer NO (g) Suppose f ( x, y ) = αx 3 + βx 2 + γy 2 + ηy + θx 2 y where α , β , γ , η and θ are constants. Is it true that ∂x f ( x, y ) = αx 2 + β + θy ? (3 Marks) Model Answer NO (h) Suppose f ( K ) = 12 K 0 . 5 . Is it true that El K f ( K ) = 0 . 5 ? (4 Marks) Model Answer YES (Total 25 marks) QUESTION 2 Answer YES or NO to the following questions: (a) The sum of the estimated residuals in any given regression analysis is zero. (4 Marks) Marks so far: 29 Page 2 of 14 NEXT PAGE
EC1102 Model Answer YES (b) “If a population is uniformly distributed, the means of the samples of size 52 drawn randomly from this population are also uniformly distributed.” Is this statement true? (4 Marks) Model Answer NO. It is (approximately) normally distributed as the CLT applies. (c) “For an exponential distribution, the mean and the variance are always equal.” Is this statement true? (4 Marks) Model Answer NO (d) An exponential distribution, which is continuous, is closely related to the Poisson distribution, which is discrete. Is this statement true? (4 Marks) Model Answer YES (e) Suppose the alternative hypothesis in a hypothesis test is: the population mean is smaller than 70. If the sample size is 80 and alpha = .01. Is it true that the critical value of z is -2.33? (4 Marks) Model Answer YES (f) Output across firms is normally distributed with a mean of 78 and a variance of 25. Is it true that the z-value for an output of 90 is 0.48? (5 Marks) Marks so far: 50 Page 3 of 14 NEXT PAGE
EC1102 Model Answer NO, it is 90 - 78 5 = 2 . 4 (Total 25 marks) SECTION B Answer ALL questions from this section.

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