Suppose that choice sets are convex.State assumptions about tastes that are necessary and sufficient to guarantee that the solution to the consumer optimization problem is a unique interior solution.(Explain)

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The Answer is To rule out corner solutions, it is necessary and sufficient to assume that all goods are essential. To rule out multiple interior solutions, it is necessary and sufficient to assume that tastes are (strictly) convex. While these assumptions are not necessary for the solution to be a unique interior solution, they are necessary to guarantee that the solution to be unique and in the interior.

Suppose That Choice Sets Are Convex