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econ212quiz2 - Econ 212 Quiz 2 30 minutes 1 Math Questions...

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Econ 212 Quiz # 2 30 minutes 1. Math Questions: Find the value of x at which y is at its maximum value. 4 2 4 2 + - - = x x y x y - = 3 x y = Find the partial derivatives of y with respect to x and z. 2 4 ln 10 xz z x y - =
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2. True/False Indicate whether the statement is true or false. ____ 1. If there are two goods, if a consumer prefers more of each good to less, and if she has a diminishing marginal rate of substitution, then her preferences are convex. ____ 2. If preferences are convex, then for any commodity bundle x , the set of commodity bundles that are worse than x is a convex set. ____ 3. Alice’s utility function is U ( x , y ) = x 2 y . Steve’s utility function is U ( x , y ) = x 2 y + 2 x . Alice and Steve have the same preferences since Steve’s utility function is a monotonic transformation of Alice’s. ____ 4. A person with the utility function U ( x , y ) = 10 + y 2 + x has convex preferences. ____ 5. If preferences are transitive, more is always preferred to less. ____ 6. If someone has the utility function U = 1,000 + 2 min { x , y } , then x and y are perfect complements for that person.
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