In: Economics
Alice enjoys consuming goods x and y. Where (x; y) is the
consumption bundle and
0 <a< 1, Alice’s utility is: u(x; y) =
xay1-a
(a) Originally, Alice has income m = 16, and faces prices
px = py = 1, and consumes
a bundle at which her utility (subject to her budget) is maximised.
Then, py
rises to 4. Alice is sadder with the new bundle she chooses, and
tells you that her
compensating variation is 16: that is, she would need an extra 16
dollars to be
as happy at the new prices as she was at the old ones. Assuming
Alice is telling
you the truth, find a.
(b) Using the information in part (a), find Alice’s equivalent
variation.