Alice enjoys consuming goods x and y. Where (x; y)

Alice enjoys consuming goods x and y. Where (x; y) is the consumption bundle and

0 < < 1, Alice's utility is:

u?x,y?=x^ay^a-1

(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) Find Alice's equivalent variation.