Asked by Shannon Gibbons on Jul 25, 2024
Verified
Suppose that Mutt's utility function is U(m, j) max3m, j and Jeff's utility function is U(m, j) 2m j.Mutt is initially endowed with 2 units of milk and 2 units of juice, and Jeff is initially endowed with 6 units of milk and 6 units of juice.If we draw an Edgeworth box with milk on the horizontal axis and juice on the vertical axis and if we measure goods for Mutt by the distance from the lower left corner of the box, then the set of Pareto optimal allocations includes the
A) left edge and bottom edge of the Edgeworth box.
B) right edge of the Edgeworth box but no other edges.
C) left edge of the Edgeworth box but no other edges.
D) bottom edge of the Edgeworth box but no other edges.
E) right edge and top edge of the Edgeworth box.
Pareto Optimal
A situation in the allocation of resources where it's not feasible to benefit one person without harming another.
Utility Function
A mathematical representation that assigns a numerical value to different bundles of goods, indicating the level of satisfaction or happiness the consumer derives from their consumption.
- Comprehend the purpose and analysis of an Edgeworth box when studying how resources are allocated.
- Elaborate on the idea of Pareto optimality and the necessary conditions within an economy involving two individuals.
Verified Answer
JC
Jaylen CoferhiBmlAug 01, 2024
Final Answer :
D
Explanation :
To find the set of Pareto optimal allocations, we need to find the points where the indifference curves of Mutt and Jeff are tangent to each other.
At Mutt's initial endowment point, his indifference curve is a straight line with slope of -1. Jeff's indifference curve is given by the equation m=0.5j, which implies a slope of -2 when drawn on the Edgeworth box.
The only points where these two indifference curves are tangent to each other are along the bottom edge of the box, since any allocation above the bottom edge would have a higher level of utility for one of the individuals.
Therefore, the set of Pareto optimal allocations includes only the bottom edge of the Edgeworth box, which is answer choice D.
At Mutt's initial endowment point, his indifference curve is a straight line with slope of -1. Jeff's indifference curve is given by the equation m=0.5j, which implies a slope of -2 when drawn on the Edgeworth box.
The only points where these two indifference curves are tangent to each other are along the bottom edge of the box, since any allocation above the bottom edge would have a higher level of utility for one of the individuals.
Therefore, the set of Pareto optimal allocations includes only the bottom edge of the Edgeworth box, which is answer choice D.
Learning Objectives
- Comprehend the purpose and analysis of an Edgeworth box when studying how resources are allocated.
- Elaborate on the idea of Pareto optimality and the necessary conditions within an economy involving two individuals.