Suppose there is a two-person and two goods pure exchange economy in which both persons have the same, strictly convex utility function and their utilities are increasing in their consumption of both goods

Suppose there are two persons A and B and two goods X and Y. Both the persons have strictly convex utility function and their utility is increasing in their consumption of both the goods. Thus, assuming Cobb-Douglas utility function for both the consumers A and B. The contract curve as shown in the figure below is a collection of all Pareto optimal points. The contract curve begins from the origin of consumer A, where A consumes nothing and ends at the origin of consumer B, where B consumes nothing.

Thus, the points where one has everything and other person has nothing is Pareto optimal as to improve the welfare of one individual (one who is consuming nothing) we need to reduce the welfare of another individual (the one who is consuming everything) by taking away some goods from him.

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