Alpha Chiang's book - Fundamental Methods of Mathematical Economics presents a question:
Is this homogeneous? If so, of what degree?
- f(x,y) = ($x^2 - y^2)$$^0.^5$
My main issue is how to simplify it in order to multiply it by constant and find the answer.
Yes it is; to see this, substitute $tx, ty$ in for $x, y$ to get $$f(tx,ty) = \sqrt{(tx)^2 - (ty)^2} = \sqrt{t^2x^2 - t^2y^2} = \sqrt{t^2(x^2 - y^2)} = t\sqrt{x^2-y^2} = t\cdot f(x,y). $$ Thus by definition $f$ is homogenous of degree $1$ since $t^1$ could be pulled out of the equation.