Question

Suppose that a lifetime utility function is given by the equation

Answer 1

based on the lifetime utility function and the combinations given, the correct match for the combinations with the same level of utility is:

• (100, 50) = (79.37, 100)
• (80, 80) = (90, 56.19)
• (50,300) = (120, 21.7)
• (110, 45) = (53.1, 400)

which functions give the same utility?

first, find the utilities on the left side:

U(100, 50) = (100 ⁰.⁷⁵ x 50⁰.²⁵) = 84.09

U(80, 80) = (80 ⁰.⁷⁵ x 80⁰.²⁵) = 80

U(50, 300) = (50 ⁰.⁷⁵ x 300⁰.²⁵) = 78.25

U(110, 45) = (110 ⁰.⁷⁵ x 45⁰.²⁵) = 87.97

the utilities on the right:

U(79.37, 100) = (79.37 ⁰.⁷⁵ x 100⁰.²⁵) = 84.09

U(90, 56.19) = (90⁰.⁷⁵ x 56.19⁰.²⁵) = 80

U(120, 21.7) = (120 ⁰.⁷⁵ x 21.7⁰.²⁵) = 78.25

U(53.1, 400) = (53.1 ⁰.⁷⁵ x 400⁰.²⁵) = 87.97

the correct matching would be:

• (100, 50) = (79.37, 100)
• (80, 80) = (90, 56.19)
• (50,300) = (120, 21.7)
• (110, 45) = (53.1, 400)

find out more on utility functions at brainly.com/question/21326461.

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