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# midI10fas - Your name Econ 420K Midterm Exam I Fall 2010...

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Your name: Econ 420K Midterm Exam I Fall 2010 Svetlana Boyarchenko Please read all the questions carefully. You have 75 minutes for this test. You can earn a total of 75 points on the test. The number of points assigned to each question roughly indicates the number of minutes which is reasonable to spend on each question. Don’t be stuck on a question!! It’s better to move on and then return if time permits. There are also a bonus question that gives to the intrepid extra 10 points. You must show all your work to get full credit. Partial credit will be given at my discretion, and it is non-negotiable. Solutions Alice enjoys goods x and y according to the utility function u ( x, y ) = xy. (1) (5 points) Find Alice’s marginal rate of substitution at the point (3 , 6). To find Alice’s MRS, we need, first, to calculate the marginal util- ities of goods x and y : MU 1 ( x, y ) = ∂u ( x, y ) ∂x = y ; MU 2 ( x, y ) = ∂u ( x, y ) ∂y = x. Now we can find the MRS as MRS( x, y ) = MU 1 ( x, y ) MU 2 ( x, y ) = y x ; MRS(3 , 6) = 6 3 = 2 .

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midI10fas - Your name Econ 420K Midterm Exam I Fall 2010...

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