aps3x313_f05 - B = tP G . If that is the case, then by...

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1) Anni has the following utility function: u = x 1/2 y 1/2 . Suppose initially that Px = Py = $20 and that I = $4000. Suppose the price of x now increases to Px = $80. a) Note that this is a Cobb-Douglas utility function with α = ½, so we know that x*=I/(2*Px) and y*=I/ (2*Py). So: x 0 *=100, y 0 *=100 and u 0 *=100 while x 1 *=25, y 1 *=100 and u 1 *=50. b) You need to solve two equations simultaneously to get the Hicks bundle. First: (x*y) 1/2 = 100 so that you are on the same indifference curve. You also need MRS = the new ERS. The new ERS = 4, and the MRS = (y/x). So, y/x = 4 or y = 4x. By substitution, (4x 2 ) 1/2 = 100. Solving you get: x H *=50 and y H *=200 and u H *=100. c) See graphs below. 0 100 200 300 400 0 50 100 150 200 x y BLo ICo = 100 BL1 IC1 BL hicks E 0 E H E 1 Econ 313.1 - Wissink - Fall 2005 PS#3 – XtraQ - ANSWERS
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2) So: X B = K – sP B and X G = F - tP G and we are given that K = F. This means that η B = s*P B /[ K – sP B ] and η G = t*P G /[ F - tP G ]. Note that if we are at prices so that X G = X B then K – sP B = F - tP G . And since we know that K=F, it must be true that sP
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Unformatted text preview: B = tP G . If that is the case, then by simple substitutions, B = G. 3) Ralph was better off in period 0. In period 0 his income was $2*10 + $1*80 = $100. Note in period 0 he could have afforded the bundle he consumes in period 1, it would cost $2*15 + $1*65 = $95, but he didnt, so by direct revelation of preference, we know that the bundle (10, 80) is preferred to the bundle (15, 65) so in period 0 he consumed a bundle he likes better than one the he ends up consuming in period 1. 4) Note: with a wage increase for all hours, the laborer can be at either point A or point B, depending on his indifference curve map. If overtime wages are offered for hours only after the normal working day, the laborer must choose a bundle between points Eo and F. This guarantees less leisure consumed so more labor supplied. Its only the substitution effect now....
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aps3x313_f05 - B = tP G . If that is the case, then by...

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