# Expected utility level

1. Joe is currently unemployed and without health insurance coverage. He derives utility (U) from his interest income on his savings (Y) according to the following function:

U = 5(Y1/2)

Joe presently makes about $40,000 of interest income per year. He realizes that there is about a 5 percent probability that he may suffer a heart attack. The cost of treatment will be about $20,000 if a heart attack occurs.

a. Calculate Joeâ??s expected utility level without any health insurance coverage.

b. Calculate Joeâ??s expected income without any insurance coverage.

c. Suppose Joe must pay a premium of $1,500 for health insurance coverage with ACME insurance. Would he buy the health insurance? Why or why not?

d. Suppose now that the government passes a law that allows all peopleâ?"not just the self-employed or employedâ?"to have their entire insurance premium exempted from taxes. Joe is in the 33 percent tax bracket. Would he buy the health insurance at a premium cost of $1,500? Why or why not? What implications can be drawn from the analysis?

https://brainmass.com/economics/utility/expected-utility-level-350225

#### Solution Preview

Joe is making $40000 per year. It is given that there is a 5% chance of heart-attack that will cost him $20000. It is also given that his utility function is U = 5Y^(1/2).

The first thing to do is find the expected income. There is 5% chance that he will have a heart-attack that will cost $20000, thus bringing down his income to $20000 ($40000 income - $20000 cost of treatment = $20000 in remaining income). That means, there is a 95% chance that he will earn $40000. This mean his expected income is

(40000*95%) + (20000*5%) = (40000*0.95) + (20000*0.05) = 38000 + 1000 = 39000.

(a) Now Joe's expected utility is E(U) = 5E(Y)^(1/2) = 5*(39000)^(0.5) = 987.420.

(b) His expected income without any insurance coverage is ...

#### Solution Summary

This posting offers help with calculating expected utility levels.

SPSS/compute expected utility/compute correlation matrix

Please see the attached file for full problem description.

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1. A respondent was presented 18 hypothetical alternatives or profiles described on five attributes of carpet cleaner. The attributes are:

o package design (described on three levels)

o brand name (described on three levels)

o price (described on three levels)

o Good Housekeeping seal of approval (described on two levels)

o money-back guarantee (described on two levels)

Based on the attributes, 108 possible profiles could be created. This is given by 3 × 3 × 3 × 2 × 2 = 108. The respondent was given a particular set of 18 and was asked to rank the profiles from the most preferred (rank of 1) to the least preferred (rank of 18). The data is given in the table below. The first five columns represent the five attributes and the last column is a respondent's ranking.

Package

Design Brand

Name Price Good

Housekeeping

Seal Money

Back

Guarantee Respond

(Rank)

A K2R 1.19 No No 13

A Glory 1.39 No Yes 11

A Bissell 1.59 Yes No 17

B K2R 1.39 Yes Yes 2

B Glory 1.59 No No 14

B Bissell 1.19 No No 3

C K2R 1.59 No Yes 12

C Glory 1.19 Yes No 7

C Bissell 1.39 No No 9

A K2R 1.59 Yes No 18

A Glory 1.19 No Yes 8

A Bissell 1.39 No No 15

B K2R 1.19 No No 4

B Glory 1.39 Yes No 6

B Bissell 1.59 No Yes 5

C K2R 1.39 No No 10

C Glory 1.59 No No 16

C Bissell 1.19 Yes Yes 1

6. Code all five attributes (including price) using dummy variables. Enter the ranks and the dummy variables for each of the 18 profiles into an SPSS data set. Convert the rank orders so that the higher the number the more preferred the object. In the table above, the most preferred object is ranked 1. Simply subtract each rank given in the last column from 19 to get the converted ranks. Hint: model your matrix after page 5 in the conjoint handout.

7. Compute the correlation matrix of the dummy variables. What do you notice in the correlation matrix? What does this say about the particular set of 18 profiles that was presented to the respondent? If any of the off-diagonal elements are not zero, explain why.

8. Run a regression using the rank as the dependent variable and the dummy variables as the predictors (Disregard your suspicion that the dependent variable is ordinal -- as I said in class, the dependent variable for regressions must be interval scaled.). The regression coefficients of the dummy variables can be treated as utilities.

9. Compute the relative importance of each attribute. Hint: see page 6 in the conjoint lecture.

10. Calculate the predicted utilities for the following options:

1. Package A, K2R, $1.19, no Good Housekeeping seal, no money-back guarantee

2. Package C, Bissell, $1.19, no Good Housekeeping seal, money-back guarantee

3. Package B, Bissell, $1.59, Good Housekeeping seal, money-back guarantee

11. What is the highest predicted utility that can be obtained? What are the characteristics of that option?