# hw1 - ECO 207h Honors Intermediate Micro Homework 1 Due...

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ECO 207h Honors Intermediate Micro Homework 1 Due: Friday 2 February 2007 2.1 Suppose U ( x, y )=4 x 2 +3 y 2 . 1. Calculate ∂U/∂x , ∂U/∂y . 2. Evaluate these partial derivatives at x =1 , y =2 . 3. Write the total di f erential for U . 4. Calculate dy/dx for dU =0 — that is, what is the implied trade-o f between x and y holding U constant? 5. 6. Show U =16 when x =1 , y =2 . 7. In what ratio must x and y change to hold U constant at 16 for move- ments away from x =1 , y =2 ? 8 .Moregenera l ly ,whatistheshapeo fthe U =16 contour line for this function? What is the slope of that line? 2.3 Suppose that f ( x, y )= xy .F indthemax imumva luefo r f if x and y are constrained to sum to 1 . Solve this problem in two ways: by substitution and by using the Lagrangian multiplier method. 2.5 The height of a ball that is thrown straight up with a certain force is a function of the time ( t ) from which it is released given by f ( t )= o.

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1. Howdoesthevalueof t at which the height of the ball is at a maximum, depend on the parameter g ? 2. Use your answer to part 1 to describe how maximum height changes as the parameter g changes. 3. Use the envelope theorem to answer part 2 directly. 4. On the Earth g =32 , but this value varies somewhat around the globe. If two locations had gravitational constants that di f ered by 0 . 1 ,what would be the di f erence in the maximum height of a ball tossed in the two places? 2.9
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## This note was uploaded on 06/09/2008 for the course ECO 207h taught by Professor Pavan during the Spring '07 term at Rochester.

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hw1 - ECO 207h Honors Intermediate Micro Homework 1 Due...

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