Consider an exchange economy with two consumers and two goods. The consumption sets of the consumers are R_+^2. Each consumer has the same utility function u(x_1,x_2) = min{x_1, x_2}. Provide a complete characterization of all the allocations which are in the core of this economy for all possible values of the initial endowments. (Recall that an allocation is in the core if it is i) Pareto optimal and ii) Individually rational (weakly preferred to the endowment))