Asked by Abigail Rodefer on Jul 02, 2024
Verified
An economy has two people, Charlie and Doris.There are two goods, apples and bananas.Charlie has an initial endowment of 3 apples and 8 bananas.Doris has an initial endowment of 6 apples and 4 bananas.Charlie's utility function is U(AC, BC) ACBC, where AC is his apple consumption and BC is his banana consumption.Doris's utility function is U(AD, BD) ADBD, where AD and BD are her apple and banana consumptions.At every Pareto optimal allocation,
A) Charlie consumes 9 apples for every 12 bananas that he consumes.
B) Charlie consumes more bananas per apple than Doris does.
C) Doris consumes equal numbers of apples and bananas.
D) Charlie consumes the same number of apples as Doris.
E) Doris consumes 6 apples for every 4 bananas that she consumes.
Pareto Optimal
A state of allocation of resources in which it is impossible to make any one individual better off without making at least one individual worse off.
Initial Endowment
The initial quantity of goods, services, assets, or resources that an individual, institution, or economy possesses.
- Explain thoroughly the concept of Pareto optimality and its obligatory conditions in a dyadic economic model.
- Utilize Pareto optimality principles to review allocations within a two-good economic framework.
Verified Answer
ZK
Zybrea KnightJul 03, 2024
Final Answer :
A
Explanation :
According to the utility functions, Charlie's marginal rate of substitution between apples and bananas is equal to the ratio of their prices (1:1), which is given by the MRSAB= MUACMUBC=1 In other words, at every Pareto optimal allocation, Charlie consumes apples and bananas in a ratio of 1:1.
Therefore, if Charlie consumes 9 apples, he must consume 9 bananas as well to reach his highest level of satisfaction. But his initial endowment does not allow him to do that. In fact, if he consumes 9 apples, he only has 2 bananas left for consumption. Similarly, if he consumes 12 bananas, he only has 1 apple left.
Therefore, the only Pareto optimal allocation that satisfies Charlie's utility function is where he consumes 3 apples and 4 bananas. Consequently, he consumes 9 apples for every 12 bananas that he consumes, which is (A) the correct answer.
Therefore, if Charlie consumes 9 apples, he must consume 9 bananas as well to reach his highest level of satisfaction. But his initial endowment does not allow him to do that. In fact, if he consumes 9 apples, he only has 2 bananas left for consumption. Similarly, if he consumes 12 bananas, he only has 1 apple left.
Therefore, the only Pareto optimal allocation that satisfies Charlie's utility function is where he consumes 3 apples and 4 bananas. Consequently, he consumes 9 apples for every 12 bananas that he consumes, which is (A) the correct answer.
Learning Objectives
- Explain thoroughly the concept of Pareto optimality and its obligatory conditions in a dyadic economic model.
- Utilize Pareto optimality principles to review allocations within a two-good economic framework.
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