# In a competitive equilibrium, can price of a commodity ever be zero?

I don't think they can be, but I'm not very sure. Are their special cases where the equilibrium is competitive even when prices are zero?

Consider an economy with two consumers ($A,B$) and two goods ($x,y$). Both consumers have preferences represented by their utility function $$U_i(x_i,y_i) = \min(x_i,1) + y_i.$$ If the initial endowments are such that the total supply of $x$ is larger than 2 then the equilibrium price of $x$ is 0. (The numeraire is the good $y$.)