EC1102 (3)(1).pdf - EC1102 UNIVERSITY OF LONDON BSc EXAMINATION 2018 For Internal Students of Royal Holloway DO NOT TURN OVER UNTIL TOLD TO BEGIN EC1102

# EC1102 (3)(1).pdf - EC1102 UNIVERSITY OF LONDON BSc...

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UNIVERSITY OF LONDON BSc EXAMINATION 2018 For Internal Students of Royal Holloway DO NOT TURN OVER UNTIL TOLD TO BEGIN EC1102: QUANTITATIVE METHODS IN ECONOMICS Time Allowed: TWO hours Answer ALL questions EC Calculators are permitted c Royal Holloway, University of London 2018 Page 1 of 4 2017-18 EC1102 1 of 13 2017-18 BLANK PAGE Page 2 of 4 2017-18 EC1102 2 of 13 2017-18 EC1102 QUESTION 1 Answer YES or NO to the following questions: (a) Suppose (ln( x ) + 1) y = 4 . Is y 0 = - 2 at ( x, y ) = (1 , 4) ? (4 Marks) (b) Suppose f ( x ) = 4 x 2 - 12 x + 9 . Is f 0 (2) = 4 ? (4 Marks) (c) Suppose g 0 ( x * ) = 0 and g 00 ( x * ) > 0 . Is x * a local minimum? (4 Marks) (d) Is f ( K, L ) = 14 K 3 10 L 2 10 homogenous of degree 1 / 2 ? (4 Marks) (e) Does lim x 3 x 2 - 9 x - 3 exist? (4 Marks) (f) Is the function f ( x, y ) = xy + 4 homothetic? (4 Marks) (g) Is it true that R e 1 3 x dx = 3 ? (4 Marks) (h) Suppose f ( x, y ) = 3 x 2 + 4 xy - 6 y 2 . Is 2 ∂y∂x f ( x, y ) = - 8 ? (4 Marks) (i) Consider f ( x ) = 2 ln( x ) . Is it true that El x f (2) = 1 2 ? (4 Marks) (j) Let f ( x, y ) = x 4 - y 2 . Is ( x, y ) = (0 , 0) a saddlepoint? (4 Marks) (k) The linear equation through (1 , 1) and (3 , 4) is y = 3 2 x - 1 2 . True or false? (4 Marks) (l) The inverse function of y = e x - 2 is y = ln( x + 2) . True or false? (6 Marks) (Total 50 marks) QUESTION 2 Consider an individual who derives utility U ( x, y ) = 2 ln x + ln y from consuming two goods in quantities x and y . The individual has an income of m . The unit price of good x is p and the unit price of good y is q . Page 3 of 4 2017-18 NEXT PAGE EC1102 3 of 13 2017-18 