Stacy likes to eat pancakes for breakfast. Her utility (happiness) function is u (x) = x 1/3, where x is the number of pancakes consumed per week. Suppose Stacy currently consumes 8 pancakes each week. Stacy's doctor orders her to cut down her pancake consumption by 2 per week. Approximately how much has her happiness changed since she started cutting back on her pancake consumption for a week?

Question

Mathematics

Carolina Gilmore

22 March, 12:49

Stacy likes to eat pancakes for breakfast. Her utility (happiness) function is u (x) = x 1/3, where x is the number of pancakes consumed per week. Suppose Stacy currently consumes 8 pancakes each week. Stacy's doctor orders her to cut down her pancake consumption by 2 per week. Approximately how much has her happiness changed since she started cutting back on her pancake consumption for a week?

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Answers (1)

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Sergio Hull · Answer 1

1.26

u (8) - u (2) = 0.74

Step-by-step explanation:

Given

u (x) = ∛x

where x is the number of pancakes consumed per week

and

u (x) is her utility (happiness)

If x = 8

u (8) = ∛8 = 2

Now, if x = 2

u (2) = ∛2 = 1.26

then

u (8) - u (2) = 2 - 1.26 = 0.74