Homework Answers
(a) Utility is maximized when MUX/MUY = Px/Py
MUX/MUY = Y/X = 4/10 = 2/5
Y = 2X/5
Substituting in budget line:
100 = 4X + 10Y
50 = 2X + 5Y
50 = 2X + 5(2X/5)
50 = 2X + 2X = 4X
X = 12.5
Y = (2 x 12.5)/5 = 5
(b) Utility is maximized when MUX/MUY = Px/Py
MUX/MUY = Y/X = 4/10 = 2/5
Y = 2X/5
Substituting in budget line:
100 = 4X + 10Y
50 = 2X + 5Y
50 = 2X + 5(2X/5)
50 = 2X + 2X = 4X
X = 12.5
Y = (2 x 12.5)/5 = 5
(c) The utility-maximizing bundle is identical in (a) and (b). This is because both utility functions represent same preferences, since (MUx/MUY) ratio is identical in both cases.
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