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hw2_Solution

# hw2_Solution - Intermediate Microeconomics Homework Set 2...

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Intermediate Microeconomics Homework Set 2: Solutions Exercise 2 1. Jerry, Pat and Oral have the same preferences as Jim since their utility function are monotonic transformations of Jim’s. 2. Jerry, Pat, Oral, Tammy, Marjoe, and Francis have indifference curves which look like Jim’s, but Tammy and Francis have different preferences. 3. Francis’s utility is a decreasing transformation of Jim’s, so he orders his indiffer- ence curves in the opposite way. Tammy’s utility function is a transformation of Jim’s but is sometimes increasing and sometimes decreasing. Exercise 4 1. ∂u ( x 1 , x 2 ) ∂x 1 = 1 2 x 1 , so ∂u (2 , 3) ∂x 1 = 1 2 2 . 2. ∂u ( x 1 , x 2 ) ∂x 2 = 1 3 x 2 3 2 , so ∂u (3 , 2) ∂x 1 = 1 3 × 2 2 3 . 21. 3. MRS ( x 1 , x 2 ) = - ∂u ( x 1 , x 2 ) ∂x 1 ∂u ( x 1 , x 2 ) ∂x 2 = - 3 x 2 / 3 2 2 x 1 so MRS (2 , 2) ≈ - 1 . 7. 4. You simply have to remember that ∂ln ( u ( x 1 , x 2 )) ∂x i = ∂u ( x 1 ,x 2 ) ∂x i u ( x 1 , x 2 ) . Moreover the MRS is not affected by monotonic transformations, so it is un- changed.

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