Demand function doubt

[Spiti]

This may be a little bit silly.., What is (marshallian) demand function for x, given U(x,y)=x^2+y^2, Income is m and prices p1 and p2..

[The Villain]

Use lagrange
Z= x^2+y^2.+lamda(m-p1x-p2y)
just find x and y fr here...thats ur marshallian dd

[Dreyfus]

This utility func represents concave preference....when p1>p2 then consumer will exhaust all his income on x2 so demand func will be x1=0 x2=m/p2
similarly when p2>p1 then x1=m/p1 nd x2=0
Nd when prices are equal! Either x1=0 x2=m/p2 or x1=m/p1 x2=0

[Spiti]

So, the demand curve would be exactly like in case of perfect substitutes. Correct?

[Dreyfus]

No! In case of perfect substitutes when prices are same consumer chooses to consume both goods but in this case he only consumes exactly one goods even when prices are same!

[phelps.phan]

its more like a max function..infact the demanded bundles are exactly like max function(i'm not very sure though)