Find Pareto optimal allocations and the core for the following economies.
There are two consumers and two goods. Utility functions are $u_1(x_1,y_1)= 10x_1-(y_1-2)^2$ and $u_2(x_2,y_2) = 10y_2 − (x_2 − 2)^2$. The endowments are (0,4) for agent 1 and (4,0) for agent 2.
I have its intuitive solution but I don’t understand this.
Please help me to provide a solution by calculation. Thanks a lot.