Asked by andisha nesbitt on May 09, 2024
Verified
Ken's utility function is U(QK, WK) QKWK and Barbie's utility function is U(QB, WB) QBWB.If Ken's initial endowment were 4 units of quiche and 10 units of wine and Barbie's endowment were 8 units of quiche and 10 units of wine, then at any Pareto optimal allocation where both persons consume some of each good,
A) Ken would consume 4 units of quiche for every 10 units of wine.
B) Ken would consume 12 units of quiche for every 20 units of wine that he consumes.
C) Barbie would consume 8 units of quiche for every 10 units of wine that she consumes.
D) Barbie would consume twice as much quiche as Ken.
E) None of the above.
Pareto Optimal
An allocation of resources from which it is impossible to reallocate without making at least one individual worse off.
Utility Function
A mathematical representation that captures the level of satisfaction or happiness that consumers derive from consuming goods and services.
Initial Endowment
The original distribution of resources, wealth, or abilities that individuals or groups possess in an economic model.
- Unpack the idea of Pareto optimality and its critical conditions within a dual-agent economic environment.
- Harness the principle of Pareto optimality to evaluate economic allocations in a setting involving two kinds of goods.
Verified Answer
For Ken, MRS = MUqs/MUws = QK/WK
For Barbie, MRS = MUqs/MUws = QB/WB
At the optimal allocation, both MRS values will be equal and hence we have:
QK/WK = QB/WB
Simplifying it gives:
QK/QB = WK/WB
This implies that Ken and Barbie will consume the goods in the ratio of their marginal utilities.
Using Ken's utility function:
MUqs/MUws = QK/WK
We know that Ken's endowment is 4 units of quiche and 10 units of wine. Hence,
MUqs/MUws = QK/WK = MUqs(4)/MUws(10)
Similarly, using Barbie's utility function, her ratio of consumption will be:
MUqs/MUws = QB/WB = MUqs(8)/MUws(10)
Equating both ratios gives us:
MUqs(4)/MUws(10) = MUqs(8)/MUws(10)
Simplifying this equation gives us MUqs(4) = MUqs(8), which implies that Ken and Barbie would consume quiche in the same ratio as their endowments, which is 4:8 or 1:2.
Therefore, for every 20 units of wine, Ken would consume 12 units of quiche, which gives us choice (B) as the correct answer.
Learning Objectives
- Unpack the idea of Pareto optimality and its critical conditions within a dual-agent economic environment.
- Harness the principle of Pareto optimality to evaluate economic allocations in a setting involving two kinds of goods.
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