DSE 2004 Question 3: General equilibrium and exchange economies

Consider a competitive exchange economy with two agents ($1$ and $2$) and two goods ($X$ and $Y$). Agent $1$'s endowment of $(X,Y)$ is $(1000,0)$ and Agent $2$'s endowment is $(0,1000)$. Each Agent $i$ maximizes utility $\min\{x_i,y_i\}$. The set of all Pareto efficient allocations for this economy consists of allocations of the form $(x_1,y_1)$ and $(x_2,y_2)=(1000-x_1,\,1000-y_1)$ where