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Rubinstein2005-page143

Rubinstein2005-page143 - 12:18 master Sheet number 141 Page...

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October 21, 2005 12:18 master Sheet number 141 Page number 125 Review Problems 125 Problem 2 (Princeton 2001) A consumer has to make his decision before he is informed whether a certain event, which is expected with probability α , happened or not. He assigns a vNM utility v ( x ) to the consumption of the bundle x in case the event occurs, and a vNM utility w ( x ) to the consump- tion of x should the event not occur. The consumer maximizes his expected utility. Both v and w satisfy the standard assumptions about the consumer. Assume also that v and w are concave. 1. Show that the consumer’s preference relation is convex. 2. Find a connection between the consumer’s indirect utility func- tion and the indirect utility functions derived from v and w . 3. A new commodity appears on the market: “A discrete piece of information that tells the consumer whether the event oc- curred or not.” The commodity can be purchased prior to the consumption decision. Use the indirect utility functions to characterize the demand function for the new commodity. Problem 3 (Princeton 2001) 1. Define a formal concept for “
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