ajaz_204_2013_2014_HW_4

E as along the y axis where we have along the x axis

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Unformatted text preview: e: | | ). The consumer perceives goods 1 and 2 as “imperfect substitutes” with diminishing (i.e. as Along the y-axis (where ) we have along the x-axis (where ) we have ; and at any interior bundle . Thus, the consumer may choose bundle on the boundary and/or in the interior of the consumption set. 7 University of Toronto, Department of Economics, ECO 204, 2013 - 2014 Question 3 (a) Show that the indifference curves of the utility function derived from a “log positive monotonic transformation” of √ will have the exact same slope as the original utility function (albeit with different utility values). Answer: The slope of an indifference curve of √ is: √ (√ The slope of an indifference curve of ) is: √ √ √ For all bundles other than ( ) we have: √ (b) Show that the indifference curves of the utility function derived from a “raise to the power 3 positive monotonic transformation” of utility values). √ will have the exact same slope as the original utility function (albeit with different Answer: The slope of an indifference curve of √ is: √ The slope of an indifference curve of (√ ) is: (√ ) (√ For all bundles other than ( √ ) ) we have: 8 University of Toronto, Department of Economics, ECO 204, 2013 - 2014 √ Question 4 Consider the following UMP for “good/neutral” good: goods where at least one of the goods is a “good” good and the other good is a ( ( ) ) [ After you solve this UMP you will get due to, all else equal, a small change in [ [ . Use the envelope theorem to derive expressions for the change in . Answer The UMP is: ( ( ) ) [ [ [ If we knew the utility function then we’d solve this UMP as follows: ⏟ ⏟ [ [ [ From the FOCs and KT conditions we see that at the optimal solution (make sure you know why): ( ) [⏟ ⏟[ ⏟[ 9 University of Toronto, Department of Economics, ECO 204, 2013 - 2014 ( Thus, a change in theorem: is equivalent to a change in ( Ceteris paribus, the change in Ceteris paribus, the change in Since ( ) ) due to due to [ ) . The change in [ can be found by applying the envelope [ is: is: we see that: In words: 10...
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