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Intermediate Microeconomics Homework Set 4: Demand and Revealed Preferences Due 10/11 (Beginning of class) Exercise 1 Marie's utility function is...

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Intermediate Microeconomics Homework Set 4: Demand and Revealed Preferences Due 10/11 (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 p , and income is m . (1) Show that a ) both goods are normal, b ) good 1 is an ordinary good, c ) good 2 is a gross substitute for good 1. (2) Start with m = 10 and p = 1 . 5, and suppose that the price of good 1 increases by 25%. Compute the substitution and the income eﬀect. Exercise 4 You are given the following partial information about a consumer’s purchases. He consumes only two goods. Year 1 Year 2 Quantity Price Quantity Price Good 1 100 100 120 100 Good 2 100 100 ? 80 1
Note that you do not know how his income has changed from year 1 to year 2. Over what range of quantities of good 2 consumed in year 2 would you conclude: (1) That his behavior is inconsistent (i.e., in contradiction with the WARP)? (2) That good 1 is an inferior good (at some price) for this consumer? (Assume that the WARP is satisﬁed) 2

2.
The Weak Axiom of Revealed Preference requires that given {B, C(.)}, where B is the budget
set and C(.) is the choice set, with x,y ԑ B, i.e. x and y belong to the budget set, if C(B) =x (i.e....

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