Marvin's utility function is U_m(x₁,x₂)= x₁_m+ 2x₂_m, where x₁_mand x₂_mare quantities of goods x₁ and x₂he chooses. Similarly, Shelly's utility function is U_s(x₁,x₂)= 2x₁_s+ x₂_s. In total they have 10 units of x₁and 10 units of x₂. Suppose the initial allocation is such that Marvin has all 10 units of good x₁and Shelly has all 10 units of good x₂. Relative to the initial allocation, the allocation in which each of them has 5 units of each good: A)is a Pareto- improvement, and also Pareto optimal. B)is a Pareto improvement, and is not Pareto optimal. C)is not a Pareto- improvement. D)makes Marvin better- off and Shelly worse- off.

Question

Quizplus · Accepted Answer

The allocation where each has 5 units of each good is a Pareto improvement because both individuals' utility increases due to the diversification of goods, which aligns with their utility functions. However, without further information, we cannot conclude it's Pareto optimal, as there might be other allocations that could make at least one person better off without making the other worse off.

Marvin's Utility Function Is Um(x1,x2)= X1m + 2x2m, Where X1m

Marvin's Utility Function Is U_m(x₁,x₂)= X₁_m+ 2x₂_m, Where X₁_m