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Unformatted text preview: 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 , 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 consumers preference relation is convex. 2. Find a connection between the consumers 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 toconsumption decision....
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- Fall '10