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# HW02 - Economics 11 Winter 2006 Homework Assignment#2 Due...

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Economics 11, Winter 2006; Homework Assignment #2 Due Thursday January 26, 3PM. 1. Which of the following utility functions represent the same preferences as u ( x, y ) = x 1 / 2 y 1 / 2 ? Explain briefly. v 1 ( x, y ) = xy v 2 ( x, y ) = x 4 y 4 v 3 ( x, y ) = sin( xy ) v 4 ( x, y ) = log x + log y v 5 ( x, y ) = - 1 xy 2. On one sketch, draw indifference curves through the points (1 , 1) and (2 , 2) corresponding to the following Cobb-Douglas utility functions. Show all the points where these indifference curves intersect (if any). Be careful about what happens near the coordinate axes. (a) u ( x, y ) = x 1 / 2 y 1 / 2 (b) u ( x, y ) = x 2 / 3 y 1 / 3 (c) u ( x, y ) = x 3 / 4 y 1 / 4 3. On one sketch, show indifference curves through the points (1 , 1) and (2 , 2) corresponding to the following quasi-linear utility functions. Show all points where these indifference curves intersect (if any). Be careful about what happens near the coordinate axes. (a) u ( x, y ) = x - 1 y (b) v ( x, y ) = x + 4 y (c) w ( x, y ) = x + log y 1

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4. Many people care about others: siblings, parents, humanity in general; this is not hard to model. To make life simple, let’s think about ONE
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HW02 - Economics 11 Winter 2006 Homework Assignment#2 Due...

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