Hello @antonio and @fdovali what happens when prices are equal p1=p2?
Then, demands are:
For agent 1: x1=y1…(1) and for agent 2: x2=2*(y2)…(2)
Using the market clearing conditions: x1+x2=1…(3) and y1+y2=1…(4), we can rearrange (3) using (1) and (2), so it is: y1+2*(y2)=1…(5)
Now (4) and (5) are a system of 2 eqs. and 2 unknowns, and the answer is: y1=1 and y2=0, and that implies x1=1 and x2=0 which is an equilibrium.
It is an equilibrium that can be reached as the Second Welfare Theorem states, by reallocating endowments, for Agent 1=(1,1) and Agent 2=(0,0)