# Find Pareto optimal allocations and the core for the following economies

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.