hmk4_sols_hs1.pdf - Intermediate Microeconomics Homework...

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Intermediate Microeconomics Homework Set 4: Demand and Revealed Preferences Solutions 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 In the examples considered in class, the consumer chooses among a continuum of op- tions and is constrained by prices and income. However, the Weak Axiom of Revealed Preference can be defined for more general choice structures, as follows. Let X be the set of alternatives. Choice behavior is represented by a choice structure ( B , C ( . )): 1
1. B is a family of nonempty subsets of X , that is, B ∈ B , B X ( B represents all the situations in which the individual can be asked to make a choice). 2. C ( · ) is a choice rule. For each B ∈ B

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