I have this function
$$ w(q) = (1 - \alpha)q^nBk^\alpha + c $$
The paper I'm reading says that w is homogenous of degree
$$ n/(1-\alpha) $$
and so small differences in q cause large differences in w. Why is it 'homogenous' to this degree and why does that cause large differences in q to occur with small change in w?
If we assume $\alpha,n,B,k,c$ are all constant, then for small $\epsilon$ we have $$w(q+\epsilon)\approx w(q)+\epsilon w'(q)=w(q)+\epsilon n(1-\alpha)q^{n-1}Bk^{\alpha}$$ So if $n$ is large then that small change in $q$ has made a big change in $w$.