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Make sure you write your name and number IN THE BLUE BOOK. THE ONLY ANSWERS WE WILL CONSIDER ARE THE ONES IN THE BLUE BOOK NOT IN THE TEST! I.- True or False. Make sure you explain your answer or you get no points. No points for the right answer with the wrong explanation. (8 points each, total 48 points) 1.- A consumer prefers more to less of every good. Her income rises, and the price of one of the goods falls while other prices stay constant. These changes must have made her better off. TRUE 2.- If someone has the utility function U = 1,000 + 2 min { x , y }, then x and y are perfect complements for that person. TRUE since it is still true that given some X,Y such that min(X,Y)=X=Y increasing Y (or X) without increasing X (or Y) will not increase his utility. Consumption has to take place in fixed proportions. 3.- Henrietta’s utility function is U ( x 1 , x 2 ) = x 1 x 2 . She has diminishing marginal rate of substitution between goods 1 and 2. TRUE, since these are Cobb-Douglas preferences which are STRICTLY convex (perfect substitutes are convex but no decreasing MRS for example). That is since 2 1 X MU = and 1 2 X MU = then 1 2 X X MRS = and as 1 X increases the MRS decreases which is what we mean by decreasing MRS. 4.- Charlie’s utility function is U ( x , y ) = xy 2 . His marginal rate of substitution between x and y does not change if the amount of both goods doubles. TRUE since preferences are homothetic. That is it is true since x y xy y MRS 2 2 2 = = and, if we double x’=2x and y’=2y we get x y x y x y MRS 2 ) 2 ( 2 ) 2 ( ' 2 ' = = = . M’/P’1

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