Economics
posted by Brett on .
Ive been stuck on this forever now if someone could please walk me through it i was appreciate it:
1: Suppose John had a utility function of U=X^2/3Y^1/3 . Derive Johns demand function from his utility function showing all the necessary steps.
i know that the MUx=MUy and first i derive the equation to
2/3X^1/3 1/3Y^2/3
then im stuck i don't know what hes asking or how to simplify it do i just solve for X and Y? help please!

I remember how to do this as "onetoone" mapping problem, which can be solved graphically.
Let me try to solve with calculas and algebra.
CAVEAT EMPTOR  let the buyer beware.
First its MUx/Px=MUy/Py or MUx/MUy = Px/Py.
MUx,MUy are the first derivitive of U.
MUx = (2/3)X^1/3 Y^1/3
MUy = (1/3)Y^2/3 X^2/3
Put MUx over MUy (i.e. MUx/MUy) then collapse like terms. That is:
MUx/MUy = 2Y/X = Px/PY
Thus: Px = 2PyY/X
Let Z = total (fixed income). The guy spends all his income on X and Y. So,
Z=PxX + PyY so PyY = ZPxX substitute this into the equation above. Thus:
Px = 2(ZPxX)/X = 2Z/X  2Px soooooo
Px = (2/3)Z/X a nice little demand function
QED 
Thank you soo much im a little confused with the simplification so MUx/MUy simplifies to 2y over x ? and for some reason i thought that it would have to end in a demand function of X = something