Is it possible to have a pareto efficient where someone is worse off than he is at an allocation that is not pareto efficient? Explain and provide a diagram for illustration ?

No, it is not possible to have a Pareto efficient allocation where someone is worse off than they are at an allocation that is not Pareto efficient. Pareto efficiency is a concept in economics that refers to a state where it is impossible to make any individual better off without making someone else worse off.

To illustrate this concept, let's consider a simple example with two individuals, A and B, and two goods, X and Y. We can represent their utility or well-being with a utility function, where higher values indicate higher levels of satisfaction.

In the diagram below, the axes represent the quantities of goods X and Y. The initial allocation is represented by point A, where individual A has 4 units of X and 2 units of Y, and individual B has 2 units of X and 4 units of Y.

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