hmk4.pdf - Intermediate Microeconomics Homework Set 4...

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Intermediate Microeconomics Homework Set 4: Demand and Revealed Preferences Due 02/23 (Beginning of class) Exercise 1 Marie’s utility function is u ( x 1 , x 2 ) = min { 3 x 1 + 2 x 2 , 2 x 1 + 5 x 2 } , where x 1 is the number of units of sugar she consumes and x 2 is the number of units of spice she consumes. She is currently consuming 12 units of sugar and 40 units of spice and she is spending all of her income. (1) Draw a graph showing her indifference curve through this point. (2) The price of spice is \$1. In order for this to be her consumption bundle, what must the price of sugar be and what must be her income? Exercise 2 Denote French restaurant by F , Italian restaurant by I , and Chinese restaurant by C . Let X = { F, I, C } . Consider the choice structure ( B , C ( . )) with B = {{ F, I } , { I, C } , { F, C } , { F, I, C }} , and C ( { F, I } ) = { F } , C ( { I, C } ) = { I } , and C ( { F, C } ) = { C } . Show that ( B , C ( . )) violates the WARP. Exercise 3 Consider a consumer who consumes two goods and has utility function u ( x 1 , x 2 ) = x 2 + x 1 . The price of good 2 is 1, the price of good 1 is