200 Test 1 October 2016.pdf

# 3 marks clara has utility function preferences ux y x

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[3 marks] Clara has utility function preferences u(x, y) = x 1/2 + y 1/2 . She has income m = 48 and pays p X = 4, p Y = 2. Now p X falls to 2. Provide a labelled diagram that decomposes this price change using the Slutsky decomposition SE (A to B) and TE (B to C) and the Hicksian decomposition SE (A to H) and TE (H to C). Bundle A: MRS = (y/x) 1/2 = o-cost = 4/2 implies y = 4x and b-line 4x + 2y = 48 imply A(4, 16), u = 6 Slutsky cost 2 x 4 + 2 x 16 = 40 so CBL is 2x + 2y = 40, Slutsky compensation is 48 – 40 = 8 Bundle B: tan: y = x and b-line 2x + 2y = 40 imply B(10, 10) Bundle C: tan: y = x and b-line 2x + 2y = 48 imply C(12, 12) Bundle H: x 1/2 + y 1/2 = 6 and tan: x = y imply H(9, 9) costing 36 so CBL is 2x + 2y = 36 Hicksian compensation is 48 – 36 = 12 24 0 2 4 6 8 10 12 14 16 18 20 22 24 0 2 4 6 8 10 12 14 16 18 20 22 X Axis Y Axis C A B 2x + 2y = 48 2x + xy = 40 2x + 2y = 36 Hicks CV = \$12 Slutsky CV = \$8 SE (H) SE (S)
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• Summer '15
• RobertBarber
• Utility, Professor Stern, Professor Goodheart

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