Nora is a runner looking for a new pair of running shoes. She found a pair that looks nice and fits well. However, Nora cannot determine the shoes' quality until they are too well worn to return. There is a 3/4 chance the pair is high-quality and worth $256 to her (256 = .75), and a 1/4 chance it is low-quality and worth only $36 to her (736 = .25). Nora's preferences over money (W)-or over the equivalent value represented by how much the shoes are worth to her-can be represented by the following utility function:

ENGR.ECONOMIC ANALYSIS
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Chapter1: Making Economics Decisions
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Nora is a runner looking for a new pair of running shoes. She found a pair that looks nice and fits
well. However, Nora cannot determine the shoes' quality until they are too well worn to return.
There is a 3/4 chance the pair is high-quality and worth $256 to her (256 = .75), and a 1/4
chance it is low-quality and worth only $36 to her (736 = .25).
Nora's preferences over money (W)-or over the equivalent value represented by how much the
shoes are worth to her-can be represented by the following utility function:
U(W) = √W
a. Calculate Nora's expected value of the pair of shoes and expected utility. Which is larger, her
expected utility or her utility of receiving the expected value with certainty?
b. What level of wealth (that means, money not spent on shoes) would make Nora indifferent
between purchasing or not these shoes? Why?
c. Using the graph below, label the following amounts:
i.
The expected value of the pair of shoes to Nora (on the horizontal axis).
ii.
Nora's utility with a gift card worth this expected value in dollars (on the vertical axis).
Nora's expected utility of buying these shoes (on the vertical axis).
iii.
iv.
The level of wealth that makes Nora indifferent between purchasing the shoes or not
(on the horizontal axis).
V.
The risk premium (a distance, or interval, on the horizontal axis).
Transcribed Image Text:Page Nora is a runner looking for a new pair of running shoes. She found a pair that looks nice and fits well. However, Nora cannot determine the shoes' quality until they are too well worn to return. There is a 3/4 chance the pair is high-quality and worth $256 to her (256 = .75), and a 1/4 chance it is low-quality and worth only $36 to her (736 = .25). Nora's preferences over money (W)-or over the equivalent value represented by how much the shoes are worth to her-can be represented by the following utility function: U(W) = √W a. Calculate Nora's expected value of the pair of shoes and expected utility. Which is larger, her expected utility or her utility of receiving the expected value with certainty? b. What level of wealth (that means, money not spent on shoes) would make Nora indifferent between purchasing or not these shoes? Why? c. Using the graph below, label the following amounts: i. The expected value of the pair of shoes to Nora (on the horizontal axis). ii. Nora's utility with a gift card worth this expected value in dollars (on the vertical axis). Nora's expected utility of buying these shoes (on the vertical axis). iii. iv. The level of wealth that makes Nora indifferent between purchasing the shoes or not (on the horizontal axis). V. The risk premium (a distance, or interval, on the horizontal axis).
Utility
36
256
U(W) = √W
EU36U (36) + 7256U (256)
W (Wealth)
Transcribed Image Text:Utility 36 256 U(W) = √W EU36U (36) + 7256U (256) W (Wealth)
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