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# Homogeneous function question watch

1. Hi, I've been stuck on this question:

Determine for which values of the parameters a and b the following function is homogeneous:

z(x,y) = [(x^a)(y^2b)+x(y^a)] / [x^b-2(y^a)]

Sorry for lack of maths font.

I've used the definition z(tx,ty)=t^k z(x,y) then I tried substituting y=x and then t=x but I still can't solve for a and b. Any suggestions please?
2. Writing out your definition of a homogeneous function using this function, we get:

Clearly if this is to be the case, then we need the powers of both multiples of t on the top to be equal, and the powers of t on the bottom to be equal (simplifying it first makes this easier). This gives you simultaneous equations in a,b to solve.
3. Thanks, so a+2b=a+1 for the top and a=b for the bottom?
4. (Original post by takeonme79)
Thanks, so a+2b=a+1 for the top and a=b for the bottom?
Yup Depending on what level you're working at, your solution might need to show that this is a necessary and sufficient condition for the function to be homogeneous.
5. Thanks very much!

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