# 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.

Please help me to provide a solution by calculation. Thanks a lot.

## 1 Answer

In the economy described above, set of efficient allocations is given by the red curve. Just do the slope of ICs comparisons at the boundaries and you will get that.

• Many Thanks dear Amit☺️
– 1190
Jan 25 at 15:15