consumer theory doubt

[Noel]

a consumer of three goods has utility function
u(x,y,z)=((min{x,y})^a).z^a, with 0<a<1.
determine the demand functions for x,y and z.

[Dreyfus]

Noel are u sure both terms hv power a...?

[Noel]

yes

[Dreyfus]

I m getting following dd functions,
x=y=(m/2(P1+P2))
z=m/2P3
Where P1, P2 & P3 are prices of x, y & z respectively and m is income

[Noel]

thank you dreyfus..can you please show the workings

[Dreyfus]

I proceeded this way, there are three goods x, y and z so that the budget constraint is P1x+P2y+P3z=m
With x and y being perfect complements the agent will always choose equal amounts of both no matter what the prices are.
So the utility function and budget constraint can be written as either U(x,z) = (x^a)*z^a, (P1+P2)x+P3z=m or U(y,z) = (y^a)*z^a, (P1+P2)y+P3z=m. Now you can solve either of these set of equations.

[Harshita...]

May be the ans.  Is M/3Px for X*  , M/3Py for Y* , M /3Pz for Z*