Posted by Brett on Tuesday, September 18, 2007 at 7:58pm.
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!

Economics  economyst, Wednesday, September 19, 2007 at 2:18pm
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

Economics  Brett, Wednesday, September 19, 2007 at 8:43pm
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
Answer This Question
Related Questions
 Micro econ  1: Suppose John had a utility function of U=X^2/3Y^1/3 . Derive ...
 economics  1.. Suppose that U(x; y) = min(x; y) with px = 1 and py = 1. ...
 economics  Suppose a person has a utility function U=YX. What is the minimum ...
 Micro Economics  Briefly explain the following: (a)Economic cost and accounting...
 economics  Let U(x; y) = 5x:8y:2 showing all derivation work, find: (a) the ...
 economics  Suppose 15 peaches and 20 oranges need to be divided between fred ...
 economics  Suppose a monopolist faces production function Q = 3KL and demand ...
 microeconomics  Suppose a person has a utility function U=YX. What is the ...
 Economics  Luisâ€™s utility function is u=x^.4y^.6 Suppose that Luis wants to get...
 economics  Consider a consumer who has an experienced utility function given ...
More Related Questions