Question

2) Consider a pure exchange economy where there are H consumers and N commodities. Denote xh as the consumption bundle for consumer h; {xh} the consumption allocation for the economy; e? commodity ; and uh(xh) a) Define feasibility of a consumption allocation b) Define a Pareto improvement. c) Define a Pareto efficient allocation d) Is it possible that a efficient allocation to a Pareto efficient allocation might be a bad idea from е сс as as consumer h's endowment of as the utility function for consumer h. policy change which moves you from a Pareto in- society's perspective. Explain fully

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Answer 1

a) A consumption allocation is said to be feasible if the amount of consumption equals the total endowment in the economy. In this example, an allocation x^h of the hth consumer is feasible if the sum of consumption allocations of the N consumers in this manner is equal to the sum of the endowment in the economy which is e_i^h for the hth individual.

b) Pareto improvement occurs when a change in consumption allocation makes at least one individual better off without making any other individual in the economy worse off in comparison to the initial allocation. This means that if a new allocation makes the hth individual better off without making any other individual in the economy worse off, then this new allocation is a Pareto improvement.

c) A Pareto efficient allocation is such an allocation that after this allocation has been reached, no individual can be made better off without making at least one individual worse off than she was before. If x^h is a Pareto efficient allocation then we cannot make a new allocation that will increases the utility of all individuals in the economy. If the new allocation improves the utility of one individual, then the utility of some other individual in the economy has necessarily decreased. We cannot make one person better off without making another person worse off.

d) An allocation where the 10th individual has the entire endowment and all other individuals have 0 amount of the good is a Pareto efficient allocation by definition. This is because to improve the condition of the N-1 individuals with 0 amount of the good, the 10th individual will necessarily have to give up some amount if her consumption allocation which is equal to the total endowment. Thus a society with extreme inequality where one individual owns everything is Pareto efficient. If a policy change moves us to such a Pareto efficient allocation where one individual owns everything and the others own nothing then it will undoubtedly be a bad idea from the society's perspective. Extreme inequality is Pareto efficient by definition as explained above but it is never socially desirable.