Find Pareto optimal allocations and the core for the following economies
Consider an exchange economy with two agents and two goods. Let consumption sets are the nonnegative orthant. Agent 1’s utility is represented by $x+y$ and agent 2’s utility is $xy$. Endowments are (e,0) for agent 1, and (0,e) for agent 2 with 𝑒 > 0.
When I find MRS and equalize them, I am going to find $x_2=y_2$ This is interior point (contract curve. ). By feasibility constraint, $x_1=y_1$.
Its core is given as follows. Why?
How can we find (determine) core? What it’s appropriate calculation to find core? For example, why we assume $e/2$?