In: Economics
Consider an exchange economy. Is it possible to have a Pareto optimal allocation where one consumer is worse off than she is at a different allocation that is not Pareto optimal? Explain.
Pareto Optimality & Allocation
Pareto optimality refers to the situation where a re-allocation of
resources or goods cannot make a consumer better-off without making
anyone worse-off. Any other re-allocation cannot be considered as
Pareto Optimal if it makes anyone worse-off while making other
better-off. In a situation where one consumer is worse-off than
other where the previous was even not Pareto optimal, the chance
for Pareto optimality exists. If a situation is not Pareto optimal,
it is said that an efficient re-allocation of exchange of goods can
attain Pareto optimality. Also, an inefficient re-allocation can
make the situation worse than that of before.
Pareto optimal conditions demand for efficient re-allocation.
Inefficiency can always make the situation worse than before. Two
consumers who have been opted their preferences on goods by the
utility they derive, may be inefficiently allocate to their
preferences. That can leads to a situation where it is not Pareto
optimal. To attain the situation, the marginal rate of substitution
of two goods must be the same for every individual who consumes
both. The ratio of substitution should be equal to their prices.
Consumer equates the price ratios of both with MRS of the goods. If
the re-allocations fails in satisfying the MRS, that is
inefficient. This can only leads to worsen the situation as
suggests. But if the condition is satisfied, it leads to an
efficient re-allocation attaining Pareto optimality.