# Is the Cobb-Douglas Utility Function Locally Non-Satiated at (0,0)?

My understanding of local non-satiation is that increasing your allocation of one good by a marginal amount increases utility. Suppose your utility takes the following form: $$U(x,y)=x^\alpha y^\beta$$ and your initial endowment is $(0,0)$. Now, if you increase either good without increasing the other, your utility does not increase. Does this mean that your utility is not locally non-satiated?

• Actually no, wait. Local non-statiation does NOT mean that. Locally non satiated in common words mean that for every possible allocation there exists an allocation arbiitrarily close to it that gives strictly more utility. It could be increasing both goods. What you mean is strictly monotone, not locally non satiated. – MathUser Jun 21 '16 at 11:32