ajaz_204_2013_2014_HW_4

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

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online